\‘l'u-‘Jv ' :‘Q:§£.’"3’ ,.‘ a La v‘fi‘hfi‘kfiw . '_ , a..._-J.'_-—dfi 1._,2__.-_..?1, Lam 4: is: an] This is to certify that the dissertation entitled l. Lineshapes of IR Zero Frequency Double Resonance Spectra in CH F. ll. lR-MW Sideband Laser Spectroscopy of the v and 2v v Bands of l3CH F and lZCH F. ll]. lR-IR Dauble Résonagce of I3CH F b; means of 2 Waveguide C02 Laser and an lR-MW sideb nd Laser. presented by SANG KUK LEE has been accepted towards fulfillment of the requirements for Ph.D. Chemistry degree in @/W% I . Ri cha rdMFl‘.)t pgoéfiivoendeman DateL [ZIZ/‘t/é? MS U is an Affirmative Action/Eq ual Opportunity Institution 0-12771 MSU LIBRARIES m v RETURNING MATERIALS: Place in bookgdrop to remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. I. LINESEAPES OF INFRARED ZERO FREQUENCY DOUBLE RESONANCE SPECTRA IN 0E3? II. INFRARED-MICROWAVE SIDEEAND LASER SPECTROSCOPY OF 13 12 TEE v3 AND 2V3 e vs BANDS OF CEaF AND 033? III. INFRARED-INFRARED DOUBLE RESONANCE OF 13083? DY MEANS OF A WAVEGUIDE CO2 LASER AND AN INFRARED-MICROWAVE SIDEEAND LASER By Sang Kuk Lee A DISSERTATION Subaitted to Michigan State University in partial fulfill-eat of the requirement for the degree of DOCTOR OF PHILOSOPHY Department of Che-iatry 1986 be 11 thl q ABSTRACT I. LINESRAPES OF INFRARED ZERO FREQUENCY DOUBLE RESONANCE SPECTRA IN CB3F II. INFRARED-MICROWAVE SIDEBAND LASER SPECTROSCOPY OF 13 12 THE v3 AND 2V3 e 93 BANDS 0F CE3F AND CEaF III. INFRARED-INFRARED DOUBLE RESONANCE OF 13CB BY MEANS OF A WAVEGUIDE CO2 LASER AND AN INFRARED-MICROWAVE SIDEBAND LASER 3F By Sang Kuk Lee Experimental measurements and theoretical calculations of infrared zero frequency double resonance (IR-2F) spectra in a symmetric top molecule without inversion are described. The IR-ZF spectra are infrared radiofrequency double resonance spectra at RF frequencies tending toward zero. Spectra are shown for a near-resonant transition in the v3 13 band of CR3F that is resonant with the 9P(32)CO2 laser line in the absence of a 0.0. field and for a transition in the v3 band of 12on3: that 1. resonant with the 99(22)co2 laser line in the presence of a D.C. field. All of the experimental lineshapes are in good qualitative agreement Sang Euk Lee and the spectra in a Stark field are in excellent quantitative agreement with lineshapes predicted by the theory that is presented. The theory treats the effect of the RF radiation as a high-frequency Stark field and is shown to predict the known lineshape of infrared microwave two-photon transitions in symmetric top molecules without inversion. A large number of transitions in the v3 and 2V3 o v3 bands of 12083F and 13083? have been recorded at Doppler- limited resolution by means of an infrared laser microwave sideband spectrometer which was assembled at Michigan State University. For the 12 CH3F spectra, the spectrometer was modified to include power leveling by incorporating a feed-back control to the microwave source. The sidebands were generated in a CdTe single crystal that was simultaneously irradiated by a 002 infrared laser and a high power microwave source operating in the 8.2 - 18.0 GB: region. The J and K structures of the bands were well resolved except for the lowest K values. Frequencies of transitions involving J values up to 39 and K values up to 16 for 12 13 Olaf and J values up to 47 and K values up to 16 for 083! are reported. Vibration-rotation parameters for the v3 = 0, l, and 2 states were obtained by fitting to the experimental frequencies. These parameters reproduce the experimental values with standard deviations for an object of unit weight (SD) of 1.33 MHz for the fundamental and 1.37 1208 F and 2.45 M82 for the MB: for the hot band for 3 Sang Kuk Lee fundamental and 1.37 MHz for the hot band for lacflal. A waveguide 002 laser for pumping and an infrared- microwave sideband laser for probing were used to study infrared-infrared double resonance in 130831. With the tunable range of a sideband system, several kinds of three— level double resonance and many four-level double resonance experiments could be carried out. The evidence for direct pumping of a particular velocity component could be observed by three-level double resonance. Evidence for indirect pumping of all rotational energy levels in the first excited vibrational state (v3 = l) was obtained by four-level double resonance experiments. Finally, evidence for vibration- vibration energy transfer was confirmed. The indirect pumping effect appeared to be useful not only for identification and observation of hot bands but also for characterizing the mechanism of the optical pumping. To my family II ACKNOWLEDGMENTS I would like to thank my advisor. Professor Richard H. Schwendeman for his kindly guidance and encouragement during the course of this study and preparation of this thesis. I wish to thank all of my family for their support and endurance. The financial support of the National Science Foundation is gratefully acknowledged. Finally, I acknowledge all the members of this group and Mr. Martin Rabb for their friendship and stimulating discussions. III CH CH TABLE OF CONTENTS Chapter Page LIST OF TABLES . . . . . . . . . . . . . . . . . VII LIST OF FIGURES . . . . . . . . . . . . . . . . . IE PART I. LINESHAPES OF INFRARED ZERO FREQUENCY DOUBLE RESONANCE SPECTRA IN CH3F . . . . . 1 CHAPTER I. INTRODUCTION . . . . . . . . . . . . . 2 CHAPTER II. THEORY . . . . . . . . . . . . . . . 6 CHAPTER III. EXPERIMENT . . . . . . . . . . . . . 17 CHAPTER IV. CALCULATIONS . . . . . . . . . . . . 25 Doppler Width . . . . . . . . . . . . . . . . 26 RF Rabi Frequency . . . . . . . . . . . . . 26 IR Rabi Frequency . . . . . . . . . . . . . . 27 CHAPTER V. RESULTS AND DISCUSSION . . . .. . . . 30 APPENDIX A . . . . . . . . . . . . . . . . . . . 42 ssrsasucss . . . . . . . . . . . . . . . . . . . 45 PART II. INFRARED MICRONAVE SIDEBAND LASER SPECTROSCOPY OF THE v3 AND 2V3 a v3 BANDS or l3on3: AND 12c113! . . . . . . . 47 CHAPTER I. INTRODUCTION. . . . . . . . . . . . . . 48 CHAPTER II. THEORY . . . . . . . . . . . . . . . . 54 IV RE PA. C34 C34; Introduction . . . . . . . . . . . . . . . Rotational Energy - General Theory Rigid Symmetric Top Molecules . . . . . . . Symmetric Top Wave Functions . . . . . . Nonrigid Symmetric Top Molecules . . . . . Intensities of Symaetric Top Transitions CHAPTER III. INSTRUMENTATION . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . Generation of IR - MW Sideband Radiation Structure of the Modulator . . . . . . . . . Adjustment of the Crystal Position in the Modulator . . . . . . . . . . . . . . CHAPTER IV. EXPERIMENT . . . . . . . . . . . . . . CHAPTER V. RESULTS AND DISCUSSION. . . . . . v3 Fundamental and 2V3 ~ v3 Hot Bands 13 or CH3? O O O O O O O O O O O O O O O O 0 p3 Fundamental and 2V3 v v3 Hot Bands 12 of CH3F . . . . . . . . . . . . . nsrnanncss . . . . . . . . . . . . . . . . . . PART III. INFRARED-INFRARED DOUBLE RESONANCE OF 13CH3F BY MEANS OF A WAVEGUIDE CO2 LASER AND AN INFRARED-MICROWAVE SIDEBAND LASER . CHAPTER I. INTRODUCTION. . . . . . . . . . . . . CHAPTER II. THEORY . . . . . . . . . . . . . . . . 54 55 59 63 66 81 86 86 88 89 94 96 108 108 134 159 164 165 177 Saturation Process . . . . . . . . . . . . . 177 Double Resonance in a Three-Level System . . 184 CHAPTER III. EXPERIMENT . . . . . . . . . . . . . 187 Naveguide CO2 Laser . . . . . . . . . . . . . .189 CHAPTER IV. RESULTS AND DISCUSSION. . . . . . . . 192 Three-Level Double Resonance . . . . . . . . 196 Four-Level Double Resonance . . . . . . . . . 204 REFERENCES . . . . . . . . . . . . . . . . . . . 218 VI It Table 10. VII LIST OF TABLES Page Sources of Data for Fits of the v3 Hand of 13CHaF. . . . . . . . . . . 112 Comparison of Observed and Calculated Frequencies in the v3 Hand of 13CH3F. . . . 113 Comparison of Observed and Calculated Frequencies in the 2v3 . v3 Hand of 13CH3F. . 123 Vibration-Rotation Parameters for 13CH3F. . . 126 The Fitting Parameters of Watson’s Form of Pade Approximant for 93 Band of 130H3F. . . 132 Vibrational Dependence of Vibration-Rotation Parameters for 1308 F. . . . . . . . . . . 133 3 Sources of Data for Fits of the v3 12on r. . . . . . . . . . . . . . 137 land of 3 Comparison of Observed and Calculated Frequencies in the v3 Hand of 12083F. . . . 139 Comparison of Observed and Calculated Frequencies in the 2v3 * v3 Hand of 12CH3F. . 146 Vibration-Rotation Parameters for 12CH3F. . . 149 ll. 12. 13. 14. 15. 16. 17. VIII Comparison of Ground-State Rotational Constants of 12CH3F. . . . . . . . . . . . The Fitting Parameters of Watson’s Form of Pade Approximant for v3 Hand of 1208 F. . . 3 Vibrational Dependence of Vibration-Rotation Parameters for 12CHaF. . . . . . . . . . . Coincidences Between Calculated Frequencies 13cast and 002 1...: Frequencies. . . . . . . . . . . . . . . . for 93 Hand of Coincidences between Calculated Frequencies 13083F and 002 Laser Frequencies. . . . . . . . . . . . . . . . for 2v3 . us Hand of Coincidences Between Calculated Frequencies for v3 Hand of 12CHaF and CO2 Laser Frequencies. . . . . . . . . . . . . . . . Coincidences Between Calculated Frequencies for 293 . v3 Hand of 12CH3F and 002 Laser Frequencies. . . . . . . . . . . . . . . . 151 152 153 155 156 157 158 Figure IX LIST OF FIGURES Page --- PART I --- Block diagram of the infrared radiofrequency double resonance spectrometer used for the study of infrared sero frequency double resonance in a D.C. Stark field. . . . . . . . . . . . . . 18 IR-ZF spectra in zero D.C. Stark field for the 13 °R(4.3) transition in the v3 band of CH F. 3 The infrared source was the 9P(32)CO2 laser operating at a power of ~100 ml. The amplitude of the RF field was ~1.3 V/cm. The sample Pressures were: eee 22.9 mTorr; xxx 35.8 mTorr; +++ 44.0 mTorr. . . . . . . . . . . . . . . 21 IR-ZF spectra in sero D.C. Stark field for the QR(4,3) transition in the v3 band of 13CH3F. The infrared source was the 9P(32)COz laser operating at a power of ~100 ml. The sample pressure was 13.2 mTorr. The RF amplitudes were: eee ~l.l V/cm; xxx ~0.84 V/cm; +++ ~0.67 V/c-O O O O O O O O O O 0 O O O O O O O O O O 22 IR-ZF spectra in a D.C. Stark field of 9738.2 V/cm for the m = 1 ~ 0 component of the °P(2.l) transition in the v3 band of 12 CH3F. The infrared source was the 9P(22)CO2 laser at a power of ~100 ml. The RF amplitude was ~0.67 V/cm. The sample pressures were: eee 6.6 mTorr; xxx 4.9 mTorr; +++ 2.9 mTorr. . . . . . . . . 23 IR-EF spectra in 12CH3F. The transition. laser. and laser power were the same as in Fig. 4. The sample pressure was 6.6 mTorr. The RF amplitudes were: eee ~1.l V/cm; xxx ~0.84 V/cm; ++* .00 67 V/“. O O O O O O C O O O O O O O O 2‘ Results of least squares fit of experimental IR- ZF spectrum in 12CH3F. The transition, laser, and laser power were the same as in Fig. 4. The sample pressure was 6.6 mTorr and the RF amplitude was ~0.67 V/cm. Observed spectrum xxx; observed - calculated spectrum eee. . . . 31 Results of least squares fit of experimental IR- 2F spectrum in 12CH3F. The transition, laser, 10. 11. XI and laser power were the same as in Fig. 4. The sample pressure was 6.6 mTorr and the RF amplitude was ~l.l V/cm. Observed spectrum xxx; observed - calculated spectrum eee. . . . . . 32 Pressure dependence of calculated IR-ZF spectrum: laser power 32 ml: RF amplitude 0.73 V/cm: laser frequency offset 0.0 M88: no. of harmonics 4. Sample pressures: eee 6.5 mTorr: xxx 4.5 mTorr: +++ 3.0 mTorr. . . . . . . . . 35 RF amplitude dependence of calculated IR-ZF spectrum: laser power 32 ml: sample pressure 6.5 mTorr: laser frequency offset 0.0 MHz: no. of harmonics 4. RF amplitude: eee 1.1 V/cm: xxx 0.92 V/cm; +++ 0.73 V/cm. . . . . . . . . . . 36 Dependence of calculated IR-ZF spectra on laser frequency offset. Laser power 32 ml; sample pressure 6.5 mTorr: RF amplitude 0.73 V/cm; no of harmonics 4. Laser frequency offsets: eee 0.0 MHs: xxx 5.0 MHs: +++ 10.0 MHz. . . . . . 37 Infrared laser power dependence of calculated ‘IR-ZF spectra. Sample pressure 6.5 mTorr; RF 12. 13. XII amplitude 0.73 V/cm: laser frequency offset 0.0 MHz; no of harmonics 4. Laser powers: eee 32 ml: xxx 16 ml: +++ 9ml. . . . . . . . . . . . 38 Dependence of calculated IR-ZF spectra on no. of harmonics included in the calculation. Laser power 32 ml: sample pressure 6.5 mTorr; laser frequency offset 0.0 MHz; RF amplitude 1.5 V/cm. No. of harmonics: eee 4: xxx 3: +++ 2. . . . 39 Dependence of calculated IR-ZF spectra on no. of harmonics included in the calculation. Laser power 32 ml: sample pressure 6.5 mTorr: laser frequency offset 0.0 MHz; RF amplitude 0.73 V/cm. No. of harmonics: eee 4: xxx 3; +++ 2. . 41 ~-- PART II --- Classical motiom of a symmetric top. This is a combined rotation around the aolecular axis associated with Pa and a precession of this axis around the total angular momentum P. The aolecule represented is CHaF. . . . . . . . . 60 XIII Energy levels of typical symmetric top molecules (A) prolate, (E) oblate symmetric top. . . . . 62 Normal vibrations of a linear 3V2 molecule and the effects of Coriolis coupling. v2 is a degenerate bending vibration and the arrows attached to the atoms represent one component of the vibration. The other component (not shown) results from identical motions perpendicular to the plane of the paper. . . . . . . . . . . . 68 Coriolis coupling of the degenerate bending vibrations in a XV23 symmetric top. (A) and (3) illustrate two components of the degenerate bending mode. (C) shows the coupling effect of the Coriolis force on the (A) mode as it tends to induce the (E) mode. In all three illustrations. the figure axis is perpendicular to the plane of the paper and only off-axis atoms are shown. . . . . . . . . . . . . . . . 70 Allowed transitions and interactions for an A1 and an E fundamental of a 03v molecule. . . 74 XIV Diagrammetric representation of interaction between an Al and an E vibration states for J 8 3. Each dot represents a basis function characterised by a particular values of k and 1.; the lines represent Coriolis interactions, connecting states of the same (k - 1.). Except for the extreme values of (k - A.) the secular equation factors into (3x3) blocks. . . . . . 75 Diagram of the sideband aodulator, in which the CdTe crystal eabedded between two A1203 slabs to achieve velocity match. The tapered double- ridged waveguide section (upper half removed) provides impedance match to incoming/outgoing standard waveguide sizes. . . . . . . . . . . 91 Experimental diagram for adJusting the position of crystal inside modulator. . . . . . . . . . 93 Variation of coupling efficiency with the crystal position. (A) represents input microwave power with frequency. (3) and (C) indicate the reflected microwave power from the modulator with improper position and optimum position, respectively. . . . . . . . 95 10. 11. 12. 13. 14. XV Block diagram of IR-Ml sideband laser 13 spectrometer used for the measurement of CH F, 3 set for linear absorption spectroscopy of gases. 97 Variation of the output laser power (D) and the differential signal (A) displayed on screen with piezoelectric translator voltage. The signal due to Lamb-dip can be easily distinguished from that due to the end of mode. . . . . . . . . . 99 Unnormalised spectrum obtained by IR-Ml sideband laser spectrometer. The signal and the reference show the large fluctuation in amplitude with frequency. The lower sideband generated from the lOR(20)COz laser line used 13 with ~200 mTorr of CH3F for the v3 P(27,E) transition. . . . . . . . . . . . . . . . . . 104 block diagram of Ml feedback controlled IR-Ml sideband laser spectrometer set for linear absorption spectroscopy of gases used for 033’. O O O O O O O O O O O O O O O O O O O 106 Typical spectrum obtained by feedback controlled IR-Ml sideband systea for lineshape experiaent. 15. 16. 17. XVI The lower sideband generated from the 9P(18)CO2 laser line used with 3.2 cm long sample cell with 0.1 sec. of time constant. . . . . . . . 107 13 Typical spectrum of the v3 band of CH F 3 obtained with the IR-Ml sideband laser spectrometer. The lower sideband generated from the 10R(20)CO2 laser line was used with ~200 mTorr of sample pressure in an 1 m long sample cell. From this spectrum, the intensity rule according to E values can be clearly seen. . . . . . . . . . . . . . . . . . . . . 109 13 Typical spectrum of the 2V3 ~ v3 band of CH F 3 obtained with the IR-Ml sideband laser spectrometer. The lower sideband generated froa the 10R(30)CO2 laser line was used with ~l.0 Torr of sample pressure in an 1 m long sample cell. . . . . . . . . . . . . . . . . 111 12 Typical spectrum of the v3 band of CH F 3 obtained with the Ml feedback controlled IR-Ml sideband laser spectrometer. Two spectra were obtained at different pressure; ~100 mTorr for the spectrua at the left XVII and ~50 mTorr for spectrum at the right. This spectrum shows much improved baseline and lineshape. The lower sideband generated from the 9R(12)CO2 laser line was used. . . . --- PART III --- Diagrammatic representations of three-level double resonance spectroscopy (A)-(C) and four-level double resonance spectroscopy (D)-(F). . . . . . . . . . . . . . . . . Energy level schemes in four-level double resonance experiments. The light and heavy arrows represent low and high power radiation, respectively. The wavy arrows represent paths of collisional energy transfer. . . . . Change in the particle velocity distribution over two-levels of transition under the action of a laser wave of frequency v. The . a-component of velocity of particles interacting with the light wave is v = I". C(v - 9°)lvo. .7. . . . . . . . . . . . . . 135 168 170 172 Time evolution of the population of the excited state of a two-level system XVIII subJected to a coherent dipole perturbation. On-resonance pumping (a = slowest oscillations having the greatest amplitude. Schematic arrangement of pumping and probing radiation in many infrared-infrared double resonance experiments. . . . . . Experimental diagram of infrared-infrared double resonance by means of a waveguide CO2 laser for pumping and an infrared-microwave sideband laser for probing. . Cross sectional view of the waveguide 002 laser used for this experiment. Energy level diagrams for the waveguide CO2 laser and infrared-microwave sideband laser system used for infrared-infrared double resonance in 13 CH F in this work. 0) results in the 180 183 188 191 193 10. 11. 12. XIX Variation of the position of the pumped molecular velocity group with pumping frequency. The transition is qR(5.3) of the 2v3 ~ v3 band of 130113:. The °n(4,3) transition of the v3 band was pumped at a different frequency for each the spectra A-F. . 195 Variation of the range of the molecular velocity group pumped with the modulation amplitude of the pumping laser. The modulation amplitude was increased in steps from (A) to (n). The °n(4.3) transition of the .3 band was pumped. . . . . . . . . . . . . . . . . . 197 Observation of a saturation-dip in the oP(6.3) transition in the v3 band from three-level double resonance with a common level in the upper state. The qR(4,3) transition in the v3 band was pumped. . . . . . . . . . . . . . . 199 Observation of a saturation-dip in the oP(8,3) transition in the v3 band from three-level double resonance with a common upper level. The puaping frequency in this figure has been shifted slightly from that in Figure 11. . . 200 13. 14. 15. Observation of a saturation-dip in the oP(4,3) transition in the v3 band from three-level double resonance with a coamon level in the lower state. The °n<4,3) transition in the v 3 band was pumped. . . . . . . . . . . . . . . 202 Observation of the increased intensity of the qR(5,3) transition in the 2v3 o v3 band that results froa three-level double resonance with a common level that is the upper state for the pumping transition and the lower state for the probing transition. Also shown is the increased intensity of the remaining oR(5,E) transitions that result from increased population of the v3 8 1 state caused by pumping the °R(4,3) transition in the fundamental band. . . . . . 203 Variation of the double resonance effect on the intensity of the QR(5,3) transition in the 2V3 o v3 band with sample pressure. The lower level of this transition is directly pumped by pumping the oR(4,3) transition in the v3 band. The solid line is a smooth curve drawn through the points. . . . . . . . . . . . . . . . . . 205 18. 17. 18. 19. XXI Observation of the indirect puaping effect to all rotational energy levels in the first excited vibrational state (v3 = l) by pumping the oR(4,3) transition in the v3 band. The intensity of all transitions in the 2V3 v v 3 band appears to increase with pumping. . . . 207 Variation of the effect of indirect pumping on the intensity of the QP(l7,3) transition of the 293 o v3 band with sample pressure. The oR(4,3) transition in the v3 band was pumped. The solid line is a smooth curve drawn through the points.. . . . . . . . . . . . . . . . . . 209 Schematic diagram of the molecular population changes caused by pumping the QR(4,3) transition in the v3 band. The numbers above each level are relative populations. . . . . 210 Comparison of the effects of indirect pumping and heating on transitions in the v3 fundamental and 2v3 ~ v3 hot bands of 13 CH3F. The spectra was recorded (A) without pumping at rooa temperature, (I) with pumping of the oR(4,3) transition in the v3 band at room temperature, 2°. XXII and (C) without pulping at ~100 °C. . . . . . 212 Observation of the effect of vibrational energy transfer between 13CH3F and 12CH F on the 3 intensity of the 0O(12,9) transition in the EV ~ v3 band of 12cn3r. The °n(4,3) in the v3 band of 13CH3F was pumped. . . . . . . . . . 216 3 - PART I - LINESHAPES OF INFRARED ZERO FREQUENCY DOUBLE RESONANCE SPECTRA IN CHsF CHAPTER I INTRODUCTION Infrared radiofrequency double resonance spectra of symmetric top molecules are often characterized by a strong asymmetric absorption lineshape at very low RF frequency. The appearance of this absorption has been used as evidence of a near resonance between the laser line and a molecular transition(l). It therefore identified the laser line as a fruitful one for double resonance at higher RF frequencies. In a double resonance process, a three level system is simultaneously irradiated by two different fields of different frequencies. One radiation, which has a fixed frequency in resonance, saturates one transition; the other. field, which is generally weaker than the first one has a swept frequency. A variation of absorption is then detected on the second field when the pumping field becomes resonant with a transition. These processes were studied by Autler and Townes(2) in 1950. In 1952 Erossel and Hitter performed a double resonance experiment in which the Zeeman splitting of an excited state of a Hg atom screened by Doppler broadening was recorded(3). This technique was ultimately extended to infrared radiofrequency double resonance by Curl and Oka(4). An absorption peak in normal spectroscopy shows a particular lineshape depending on the molecular environsent; Fe in 0r rel in very low pressure gas the absorption peak exhibits a Gaussian lineshape which is dependent on the frequency of the radiation, temperature of the sample, and the molecular velocity distribution. At higher pressures, the peak is homogeneously pressure broadened, which typically shows a Lorentzian lineshape depending on the molecular dynamics. At intermediate pressures the peak appears as a Voigt profile, which is a convolution of the Gaussian lineshape and the Lorentzian lineshape. When the infrared zero frequency double resonance was first encountered by A. Jacques at Michigan State University, the observation of an apparently Doppler-free infrared absorption suggested that it might have potential for the determination of collisional relaxation rates. Therefore, an investigation was begun of the dependence on sample pressure and RF power of the infrared zero frequency double resonance that occurs as a result of the well-known near coincidences of the Q0(12,2) transition in the v3 band of 12CH3F with the 9P(20)CO2 laser line(5) and of the QR(4,3) transition in the v3 band of 13C83F with the 9P(32)CO2 laser line(6). Although most IR-RF double resonance studies have been done with an absorption cell inside the laser cavity, an extra-cavity cell was chosen in order to remove the nonlinear effects of laser gain from the recorded lineshape. An additional interesting feature of the infrared zero frequency double resonance was the fact that the rotating wave approximation, commonly used in double resonance theories(7), is expected to fail for this effect. The rotating wave approximation is based on the assunption that the frequencies of the radiation are much larger than the relaxation rates or Rabi frequencies involved. This can hardly be true if the frequency of one of the radiation sources is near zero. 'Thus, it was necessary to extend the double resonance theory to include the IR-ZF effect. The new theory resembles theories previously derived to describe the high-frequency Stark effect(8). The theory developed to explain the IR-ZF lineshape was in qualitative but not good quantitative agreement with the observed lineshapes(9). This was attributed to the m degeneracies of the states involved in the transitions. At first, a simple sum over the m components was tried without success. It was concluded then that the disagreement between theory and experiment was the result of the many level crossings of the a components that occur at zero field. These crossings were not taken into account in the theory. In order to determine whether the derived theory could accurately represent an IR-ZF lineshape, I recorded the IR- ZF absorption of a single a component of a transition brought into resonance with the laser by application of a D.C. Stark field. The transition chosen was the QP(2,l), m 12 = 1 ~ 0 in the 93 band of CH F. This transition has been 3 shown to be in resonance with the 9P(22)CO2 laser line in an electric field of 9738.2 V/cm(6). The purpose of this study is to describe the theory derived for the IR-ZF double resonance effect and to compare observed and calculated lineshapes for a single a component of a transition in resonance with an infrared laser. As a by-product, it is shown that the new high-frequency Stark effect theory provides an alternative to the usual description of infrared microwave two-photon absorption in syametric top molecules without inversion(10-12). The next chapter outlines the theory used to calculate lineshapes and Chapter 111 describes the IR-ZF experimental apparatus. In Chapter IV, the methods and equations for theoretical calculation of the input parameters are derived and in Chapter V, the experimental and calculated lineshapes are compared and discussed. Finally, in Appendix A, the theory is extended to the case of infrared microwave two-photon absorption. CHAPTER II rnsoav’ We assume a symmetric top in which the inversion splitting is negligible. In the presence of an electric field that is sufficient to separate the m components the states are singly or doubly degenerate (ignoring nuclear spin degeneracy); we assume a transition between doubly degenerate states. The basis functions are chosen to be the linear combinations of mixed parity (i.e., the t linear combinations of single parity states), in which case the electric dipole moment matrix element that connects the degenerate partners vanishes. It is therefore sufficient, within the electric dipole approximation for both radiation and collisions, to consider only one of the two pairs of states involved in the transition. We also assume that the rotating wave approximation is valid for the infrared radiation, since the infrared frequency is much greater than either the Rabi frequency or the relaxation rates. This approximation allows the two states to be separated from the states of other rotational levels so that we are left with the simple case of a two-state systea. The theory described in this chapter was developed by R. H. Schwendeman. Let us consider a two level system of a symmetric top molecule (that is the case of for CH3F) irradiated by IR and RF fields whose planes of polarization are perpendicular to one another. The sample is also in a D.C. Stark field which is assuaed to be parallel to the RF field. Since the selection rules on the IR transition are AM = :1, one M state in the ground vibrational level is connected by the IR field to either the M+l or M-l state in the upper vibrational level. We assume that only one of these transitions has significant probability at the IR frequency of interest. In the case of a symmetric top, energy levels have a first-order Stark effect, so diagonal perturbation matrix elements are non-zero. In this case, they are also time dependent because of the RF field. Starting from these points, the absorption of IR radiation by a two level system having a first order Stark effect can be calculated by using the density matrix formalism. As the first step, the Bloch equations are written in the rotating wave approximation for the IR field. The population and coherences are then developed in Fourier series dependent on the RF frequency. Density satrix elements have to be calculated by using the equation of motion of p: :1: = ‘F(P ' 9°) “ %[H.PJ (1) where r is the relaxation matrix and po is the density matrix at theraal equilibrium. The time dependence due to the IR field can be treated by using the rotating wave approximation. A change of variables is done as follows; n = Paa - pbb (2) -i(u t r k z) E l (3) pba = (u + iv)e Here, n is the population difference between levels a and b, 0‘ is the IR frequency, and k1 is the wave vector. By substituting froa Eqs. (2) and (3) for p aa’ ’bb’ ‘nd "be (= pzb)'in the density matrix, Eq. (1), and by ignoring rapidly oscillating terms (rotating wave approximation), we obtain the Bloch equations for a two-state system(7) as dn/dt = -2xv - y1(n-n°) (4) du/dt = -v8 - qu (5) dv/dt = us + %2 - sz (6) where x = ”bacz/h (7) and 8 - 0‘ - “be . (8) Here, ”he = ”ab is the dipole moaent matrix element connecting states a and b, 6° is the amplitude of the 1 electric field of the infrared radiation written as C = 6: CO. 9 t s (9) and "be = (Eb - E.)/fi with E6 and Eb the energies of the states. Finally, in Eqs. (4)-(6) Y1 and 72 are relaxation rates for n and pba, respectively, and no is the equilibrium value of n; pba is assumed to be zero at equilibrium. The effect of the RF field is introduced as an additional first-order Stark effect. Thus, we assume that - lat -iut Here, 8 = 8a in the absence of the RF field and - _ o 6b ' (”bb ”aa) (RF/2‘ (11) where (RF is the amplitude of the RF electric field written (RF = GRF cos at . (12) As a result of the oscillation of 8 at RF frequency u. 10 which may be comparable to or even smaller than x, 71' and 72’ the density matrix components, n, u, and v will oscillate at frequency a and overtones of e. n = Z nk eu‘“t (13) k:—. u = 2 uk eikot (14) k:-. v = Z vk sik”t (15) k=-¢ These Fourier representations for n, u, and v, along with Eq. (10) for 8 are substituted into the Bloch Eqs. (4)-(6). le assume that in the steady state 5k, 5k, and 3k, the time derivatives of the Fourier coefficients, vanish. The 1k"t are then collected on one side of coefficients of each a the equation and set equal to zero. The result is a series of coupled linear equations in the nk, uk, and vk. For our experiment, the important quantity is the effect of the absorption on the intensity of the infrared beam. The absorption coefficient for infrared radiation is known to be(7) a = (4'Npab"l/°) v/€: . . (16) The output of the phase-sensitive detector used to record the spectrun is filtered with a time constant whose reciprocal is much smaller than the lowest usable RF ll frequency. Therefore, we need the tine-averaged value of a, which is given by a = (4nNuabu£/c) vo/ez. (17) To solve for v0, expressions for nk and uk in terms of the vk are obtained from Eqs. (4) and (5), respectively, and are substituted into Eq. (6) to give k+2 Z 1=k-2 _ o ak,£ v; - 8k,0 xn /2 (18) where 8k,0’ the Kronecker delta, is equal to one for k = 0 and zero otherwise. The fact that only 5 non-zero terms appear in the sum is a result of the first-order perturbation form assumed for the frequency difference 8 [Eq. (10)]. In Eq. (18), , _ 2 ‘k.k~2 ‘ ak—2,k ‘ ‘b /Fk-l (19’ s = a = s s (1"1 + r'1 ) (20) k,k-l k-1,k a b k k-l _ 2 2 2 -1 -1 ak,k ‘ 'k + “ /Gk * 5s /Fk * 8b (Pk-1+Fk+l) (21) where Fk = 12 + iko and Gk = Y1 + iku. Eq. (18) can be written in aatrix form as 1! = <2. (22) with obvious definitions for A, V, and g. The result is an 12 infinite complex linear system that aust be truncated for solution. The results of calculations for different numbers of harmonics are shown in Chapter V. It is possible to transform Eq. (22) into a linear system that contains only real numbers. This systea can be solved algebraically for any number of harmonics. In order to carry out the transformation of Eq. (22) and to give an algebraic solution for v0, the time independent element of v, we apply a transformation to Eq. (22) § 1 i" i 2 = Q 9 <23) or §§=§- (24> Here, §=§1§‘.§=§!.nd§=§e- mm For the case of truncation after two haraonics, S is chosen to be (1 o 0 ll 0 1 o 1 o g:- l o If 0 o (26) E o -i o i :1 o o o i) 13 in which case §-l is easily obtained. The transformed aatrices are ( \ , p _ n _ '9 a2 b2 Ifci b2 a2 bé ai+co IEhi -s; —b§ A = J'z'ci I'z'hi a0 fin; 42c; , (27) h; a; (it; ai-co é ~ a; b§ 12s; bé aé , r \ I \ {2&5 0 {Evi 0 Y = vo , and g = xn (28) 12v; 0 EV" o \ ZJ \ I In these matrices, = ' fl - b’ + ib" 5 ° N k ' °k-1.k+1 = ck * lck ' D r. + p D r O 8' I he 3' I k and vk = vi + ivfi . Thus, the linear system in Eq. (24) has only real coaponents. To solve Eq. (24), we make use of the fact that all of the linear equations in this systea except one are homogeneous. This allows development of a general method for reducing the dimensions of the linear system by 2 at a time. In this method the first and last equations are used 14 to obtain expressions for the first and last components of E in terms of the remaining components; these are substituted into the reaaining equations. This process is repeated until only a 3x3 linear system remains. The 3x3 linear system can then be solved exactly. To carry out the procedure Just described, we let “kl now be a general element of A and VR be an element of 2. Then, except for A = 0, one of the linear equations in Eq. (22) can be written 81k vk = 0 (29) where L is the number of harmonics. The dimension of the linear system is 2L+l. le use the equations for l = L and A = -L to solve for VI and v_ as follows: L L-l V ‘3 Z a V (30) J k=-L+1J'k k for J = 1L, where ‘J,-J‘-J,k ' aJ,J°J,k (31) 'J,k + . 'J,J -J,J To obtain these expressions, the symmetry relations a_L L = F -a and a-L,-L = .L,L were used. These relations hold L,-L only for L 2 2, so the reduction process must be stopped when L = 1. However, when L = l the linear system is 3x3 and may be solved trivially. 15 After substitution for VL and v_L the linear system is of the form L-1 Z (a +a_o:_ k=-L+1 1k 1, L L,k I ‘1.L“L,k) ”k 5k,o xn°/2 (32) which is of dimension 2L-l. Two limiting solutions of Eq. (22) are of some interest. First, if 8b = 0, the usual expression for partially-saturated absorption in a two-level system is obtained. A second limiting solution is that for which 68 5 a >> x, 71’ 72, or 8b. This case of two—photon absorption in a symmetric top without inversion is discussed in Appendix A. It is shown there that two-photon absorption in such a molecule can be thought of as a consequence of a high-frequency Stark effect. The expression obtained for the two-photon absorption coefficient is the same as that obtained by a different approach by Oka and Shimizu(10). In the derivation just given, 68 [Eq.(10)] depends on "1’ the infrared frequency seen by the molecule. To take the Doppler effect into account we assume that the overall absorption is a sum of products of the absorption coefficient for each velocity group aultiplied by the relative population of each velocity group. The total absorption has to be averaged over the different velocity groups. 16 3, = I f: ; f(vz) dvz (33) where f(vz) is the Maxwellian distribution of the velocity component along the propagation axis of the radiation. However, this Doppler averaging is unusually tedious for case in which the values of x, 71, and 72 are small. Fortunately, toward the end of this project an array processor (FPS-164) becaae available for the calculations, so that not only individual lineshapes could be calculated, but also a full least squares treatment, including numerical calculation of the required derivatives, could be implemented. 17 CHAPTER III EXPERIMENT Figure 1 is a block diagram of the spectrometer used for this investigation. The CO2 laser was a 2.2 m water cooled plasna discharge flowing gas system with a 4.0 m cavity mounted on an invar frame, which has been described previously(13). One end of the cavity is a rotatable plane grating with 150 lines/mm and the other end is a partially reflecting (95 X) 10 m radius concave spherical mirror. The combination of the liquid N2 cooled photovoltaic InSb detector, the phase sensitive detector (PSD), the operational power supply (OPS) and the piezovoltaic (PET)- driven laser airror stabilized the laser output to within 2300 kHz by monitoring the saturation dip in the fluorescence from an intracavity cell filled with CO2 gas(l4). The laser radiation was linearly polarized in a direction determined by the Brewster windows of the discharge tube. The plane of polarization was rotated by using a different mirror configuration for the 0M = :1 transitions The sample cell used for this experiment was designed for conventional laser Stark spectroscopy(l3) and consisted of a 6-inch glass pipe tee that includes two solid nickel bars, 5 cm x 2 cm x 40 cm, whose large faces are flat to $0.5 pm. The bars are separated by optically flat guartz 18 AMP P30 Figure 1. Block diagram of the infrared radiofrequency double resonance spectrometer used for the study of infrared zero frequency double resonance in a D.C. Stark field. 19 spacers ~3 mm thick. The electrode spacing was determined by measuring the resonant field of the oO(l,l) transition in the v3 band of 12 CH3F(6). The RF source was a Hewlett Packard Model 8660A synthesizer whose output frequency was controlled by a Digital Equipment Corporation PDP-SE computer through an interface designed by Mr. Martin Rabb at Michigan State University. The output of the synthesizer was chopped at 33.3 kHz by means of a Mini-Circuits Laboratory Model ZAD-3SH double balanced mixer and either amplified or applied directly to the sample cell. The RF voltage at the sample cell was nonitored by means of a simple diode detection circuit. The parallel plate Stark cell was shunted by a 50 n resistor to improve its high frequency response and seemed to operate satisfactorily over the 0-5 MHz range that was used with it. A maximun of 0.5 Vr.. of RF amplitude was used. The laser radiation was monitored by a liquid N2 cooled Hg-Cd-Te photoconductive detector. The detector output was amplified and processed at the chopping frequency by a phase sensitive detector whose output was digitized and recorded by the minicomputer that controlled the RF frequency. The observed spectrum is the difference between the IR absorption in the presence of the RF field and that without the RF field. Several spectra recorded at different saaple pressures 20 and RF powers with the 9P(32)CO2 laser line with 13CH3F in the Stark cell outside the laser cavity are shown in Figs. 2 and 3. The absorption is the result of the near coincidence (~25.8 MHs) between the laser frequency and that of the 12 QR(4,3) transition in the v3 band(6). Samples of the CH F 3 spectra obtained with the laser Stark cell are shown in Figs. 4 and 5. In these spectra the absorption is of the m = 1 o 0 component of the QP(2,l) transition, which was brought into resonance with the 9P(22)CO2 laser line by application of a D.C. Stark field of 9738.2 V/ca(6). 12 The CH3F was obtained from Peninsular Chemical Research, whereas the 13CH3F was obtained from Merck. Except for the usual freeze-pump-thaw cycling, the samples were used as received. 21 ‘ C O a- a O. ‘- u m " a. .0 a. <( ' - I I .- I 2 . .- ..”. ... -.. u 0‘. .'. . a Q .. H. - O -I. ‘00 e o ... ..'. C. . O I m 0. ---I-...... . ... ‘ .---‘...- ‘N “-‘..u.......'. cl ~ee“.. ”.T‘He “HOO“~”...... ......”””. I I f 0.0 1.0 2.0 3.0 4 0 RF Freq. (MHz) Figure 2. IR-ZF spectra in zero D.C. Stark field for the QR(4,3) transition in the v3 band of 13CH3F. The infrared source was the 9P(32)CO2 laser operating The amplitude of the RF The sample pressures were: +++ 44.0 mTorr. at a power of ~100 ml. field was ~l.3 V/cn. eee 22.9 mTorr; xxx 35.8 mTorr; 22 C .2 an O. a.- L. a O ‘ .m m s n . o. I < .Oe '. . . g . . ..‘ ..a 76. ..e ..a .5 ..O ...m‘ m 0.. E.‘ o. .0... ..."Im. ............... e... Oasaaaueluuu;‘ -:::_._.:::.:::: ....:_.: " . “I“WA; v A" “A: :MAMA :: 0.0 L0 2.0 3.0 4.0 RF Freq. ( mm) Figure 3. IR-ZF spectra in zero D.C. Stark field for the QR(4,3) transition in the v3 band of 13CH3F. The infrared source was the 9P(32)CO2 laser operating at a power of ~100 ml. The sample pressure was 13.2 mTorr. The RF amplitudes were: V/cm; xxx ~0.84 V/ca; +++ ~O.67 V/cm.. eee ~1.1 23 Relative Absorption . .a -.-. O.....-I....“..IICCI.‘C... ’e 0.. 0*. Pee ”TPMNO-eeeeeeeeeeeem. 04) Figure 4. T V 21) 31) RF Freq. (MHz) r L0 41) IR-ZF spectra in a D.C. Stark field of 9738.2 V/cm for the m = 1 o 0 coaponent of the OP(2,1) 12 The transition in the v3 band of CH3F. infrared source was the 9P(22)CO2 laser at a The RF amplitude was ~0.67 eee 6.6 mTorr; power of ~100 ml. V/cm. The sample pressures were: xxx 4.9 mTorr; +++ 2.9 mTorr. 24 c o a‘a. :1. I O. ' ‘ i. y I O s ' (n a .0 .e I» < - .° ’, ‘. 0 a O . .0 .2 .6 ‘T u ‘e . .a s g . ... ..... m e. C... ............ m .. e... I....--.. ssssssssssssssssssssssss e 9°eee~eew~ cu-;:.¢i --:::;¢ AAAAA - O1) |.O 21) 31) 4ND RF Freq. ( MHz) Figure 5. IR-ZF spectra in 12CH3F. The transition, laser, and laser power were the same as in Fig. 4. The The RF asplitudes sample pressure was 6.6 mTorr. +++ ~0.67 were: eee ~l.1 V/cm; xxx ~0.84 V/cm; V/cm. 25 CHAPTER IV CALCULATIONS For the theoretical calculations, we need 11 input parameters which are as follows: the nuaber of points in the Doppler integration (NG); the frequency interval in the Doppler integration (DC): the Doppler width (Gl); the number of RF frequencies (NV); the RF frequency interval (DV); the starting RF frequency (VA); the IR offset frequency (DA), which is zero for on-resonant pumping; the RF Rabi frequency (DB) for the transition; the IR Rabi frequency (X) for the transition: and the relaxation time for population (11) and for coherence (72). Of the 11 parameters, 3 (NV, DV, and VA) are chosen to match the experimental conditions, and 2 (NO and DC) are selected to provide an efficient but accurate numerical integration. For the latter, DG should be less than the smaller of 71 and 72 and NG x DG should be greater than 6 x Gl. Of the remaining 6 parameters, 8a is known from the spectrum and Gl can be accurately calculated, as shown below. Also, DB and X can be estimated, but were normally adjusted in the fitting process for reasons that will be described. The estimation of Cl, DB, and X is described in the next 3 subsections. 26 MW The Doppler width (Gl = av”) can be accurately calculated from the expression, 9 - o ‘ (21n2)RT where we is the resonance frequency, c is the speed of light, R is the gas constant, T is the absolute temperature, and M represents the aolecular weight. RF Rab Fre ue c DB The RF Rabi frequency for a transition, as it appears in the present theory is given by 5b... 12ch .3, (35) where 63F is the amplitude of RF and u’ and p” represent the diagonal matrix elements for the dipole moment of the upper state and the lower state, respectively. The aatrix elements can be obtained from the following equation: ”Bk. " ‘ mm (36’ where ”D is the permanent dipole moaent in the vibrational 27 state. The peak RF electric field 6;, is related to the root mean square RF voltage, as follows: 0 - £RF - I? vrms/d (37) where d is the distance between the two Stark plates. The IR Rabi frequency for the transition, as it appears in the theory is given by X 8 ”fiGA/fi (38) where ”:1 is the transition dipole moment matrix element between states f and i and e is the peak amplitude of IR 1 radiation. The dipole moment matrix eleaent can be expressed as sf, = (:33) ItiQaeon3I¢J,k,-,cose eJ.k,_,de (39) 12 For the v3 band of CH F, the derivative of the 3 molecular dipole moment with respect to the normal coordinate for ya can be obtained from reported absolute 28 intensity data(l5), as follows: 2 o (S )2 - 3c v3 F3 - (40) a03 N A where v; is the harmonic frequency, c is the speed of light, N is Avogadro’s number, and r3 is the integrated absorption A coefficient for the v3 band. The calculated value of 2lasec"1 based on rs = 9056 (an/aQa) is 117.4 cm cmz/mole(16,17) and v; = 1067 cs'l(1s). For the second contribution, the normal coordinate integral is given by 2 o 4w v3 '3 = h I N *l‘l * _ I0103¢0d03 (41) Thus, tsfoasodoa = 1.62 x 10"21 gllzcm. Now, consider the directional cosine element for our experimental arrangement. The equation can be transformed into the aatrix element(l9) I’J’k’m’co'eya'J”k”a”d° = (J’k’a’leYz|J"k”m”) F N 9 D N N F 9 N 0' (J |.Y8|J > (42) a N N N S F D (J k m IOYzlJ k m > . For the transition oP(2,l), m = l o 0 29 J’ = J" - l, k’ = k”, and m’ = m" + l (43) Thus, since J” = 2, k” = l, and m" = 0, OFF «not. 1 2 21/2 (J k m I. [J k m > - I ei-J(2(J - k ) 1 Y‘ [4J(4J§-l)]l/2 x ((J-m)(J-m-l))l/2 = 0.1581 (44) For the peak amplitude of the IR radiation, we can obtain the equation eo/(V/cm) = 27.449'-% /(watt/cm) (45) from the relationship P/A = neg/6. (46) where P is the radiation power and A is the area of the beam. Finally, we can calculate the Rabi frequency froa the relationship x = (fisl/MHz = 0.50345(p/Debye)(€/V/cm) (47) 30 CHAPTER V RESULTS AND DISCUSSION Sample experimental spectra are shown in Figs. 2-7. As indicated in the Introduction, the spectra of 13CH3F in Figs. 2 and 3, taken at zero D.C. field in the presence of nultiple m degeneracy, could not be fit quantitatively with the theory presented in this paper. By contrast, spectra similar to that in Figs. 4 and 5, taken with the sample of 12CH3F in a resonant D.C. Stark field that split the m degeneracy, could be fit to high accuracy. Examples of such fits are shown in Figs. 6 and 7. The small variation of the residual shown in these figures is within the experimental uncertainty in the lineshapes. The original purpose was to obtain relaxation parameters from these spectra. Unfortunately, that was not possible in the present work. The zero D.C. field spectra could be taken at relatively high sample pressures (~50 mTorr) where pressure-dependent effects were obvious, but they did not fit the theory. The non—zero D.C. field spectra could be fit well, but because of dielectric breakdown they could not be observed at high enough sample pressure to observe linearly independent pressure effects. The absorption line chosen for the D.C. field studies (12 CH F 93 hand QP(2,l), m = 1 ~ 0) required a field of ~9.7 3 31 c 3 .9. ' ‘. a. L- a. o “g .I m ‘u a . es ..... < .'Um..mlmemlelm........... m I. .2 ‘ U .9 m c: 01) l.0 21) 31) 41) RF Freq. (MHz) Figure 6. Results of least squares fit of experimental IR- ZF spectrum in 12CH3F. and laser power were the same as in Fig. 4. laser, The The transition, sample pressure was 6.6 mTorr and the RF amplitude was ~0.67 V/cm. Observed spectrum xxx; observed - calculated spectrum eee. 32 c O .9 ‘ a. - '. L- a O 1 s m a n .C < . a) "-. e2 4 ...‘a E . ass...... é, ea aaea‘eaaeeeamsm...“......~. O1) I.O Z1) 31) 41) Figure 7. RF Freq. (MHz) Results of least squares fit of experimental IR- ZF spectrum in 12CH3F. The transition, laser, The and laser power were the sane as in Fig. 4. sample pressure was 6.6 aTorr and the RF amplitude was ~l.l V/cm. Observed spectrum xxx; observed - calculated spectrum eee. 33 kV/cm to bring it into resonance with the 9P(22)CO2 laser line. At this high field the highest sample pressure that could be maintained reliably was ~6 mTorr. Several attempts were made to fit the highest pressure D.C. field spectra to the lineshape described in the Theory section. For this purpose, we assumed that the spectrometer signal was of the form, S = C1 J- W(6a)[vo(x,y,8b,88) - vo(x,y,0,88)] d6a (48) Here x, y =‘yl = 12, 68. and 6b have already been defined; "(8a) is the probability density for 8a; C1 and C2 are constants. The functional form assumed for l was the appropriate Doppler-broadened Gaussian centered about 68 = 0. Care was taken to insure that the nuaerical integration was sufficiently accurate. The difference in square brackets in the integral in Eq. (48) is needed to represent the combined effect of chopping the RF radiation and phase- sensitive detection. All least squares fits with independent variation of the 5 parameters x, 7, 8b, Cl, and C2 diverged. By contrast, all fits with 7 fixed at the value of 20 MHz/Torr converged rapidly. The results of two such fits for spectra taken with different RF amplitudes are shown in Figs. 6 and 34 7. Some 4-parameter fits with 8b fixed at the value predicted from the fits with 1 fixed converged slowly, but showed a very high correlation between x and y. The excessive computer time required by the Doppler averaging and the predicted low reliability of the outcome led me to discontinue the numerical experimentation. It appears that use of this method for evaluation of relaxation parameters will require that the resonance occur at much lower Stark field than was the case in this work. Such an experiment could be carried out with a stable tunable laser source such as the recently developed infrared-microwave sideband laser(20). Although it was not possible to determine the relaxation parameter, the quality of the fits in Figs. 6 and 7 is sufficiently high to provide strong support for the theory presented above. In order to give an indication of the dependence of the IR-ZF lineshape with variation in parameters, several calculated spectra are shown in Figs. 8- 12. Dependence on pressure, RF field, D.C. field, laser electric field, and number of harmonics used in the calculation is shown. The dependence on pressure, RF field, and laser field appears similar at first sight, which accounts for the near linear dependence in the least squares fits. However, closer examination reveals some differences. Of interest is an apparent competition between pressure and laser electric field (Figs. 4 and 8) that is siailar to 35 d .a.-. s c -' ' o D s‘: a O. ' N i. . ‘ ° . 0 ° ° ‘ (D " . .a ' .’ < . ' ‘ m . .. Q q . .. ..O .. .. z .. .g ........ m . . '3 .................. m 0.. ..‘.Cl. ......... m .0. ...."¢ma . 'P'Cee sssss ‘ .O... aaaeaeeaelaeeemeeeIIIII ..~‘ Pee ..0.0.e0e~ 0.0.0.000“.“....“ T T fir o.o "0 2'0 3.0 4.0 RF Freq. ( MHz 1 Pressure dependence of calculated IR-ZF spectrum: laser power 32 ml; RF amplitude 0.73 V/cm; laser frequency offset 0.0 MHz; no. of harmonics 4. eee 6.5 mTorr; xxx 4.5 aTorr; Figure 8. Sample pressures: +++ 3.0 mTorr. 36 q .a ‘ a s C o ' ' 4.0 q . O. h e c, I m s e n ’e a <( O . . a . e I 2 ’ ‘ '5 ‘ . . . a 2 - ‘ ' . I a, a a: . ° ' . I I . I I e 'a I e .. ... I .- I ‘ °.. .." e e ..."0a . .Iem .. GUI-samaaaeaa ... eeaeaeeeee 0.. 00.... O.“ 00eeeeeeeeseeeeese-eeeeeeeeoeu” j f r RF Freq. (MHz) RF amplitude dependence of calculated IR-ZF sample pressure 6.5 no. of Figure 9. spectrum: laser power 32 ml; laser frequency offset 0.0 MHz; mTorr; eee 1.1 V/cm; xxx harmonics 4. RF amplitude: 0.92 V/cm; +++ 0.73 V/cm. 37 J a. T s C s a. "o - b s . O O 'l ' . I m l .c -. ° - ‘( ° ' e . ‘- 0 ‘ ‘s > at .. I I I- I U .. .m to e .‘m — I. 0 ° " e .. -"a m .. ......-I.. . ........... .3. '0 seaseeeesaeeeeeeeesa q o... ‘e 8...... e M eegeeeeoeeeoeeeeeeeeeeeeeeeee v V v Figure 10. RF Freq. (MHz) Dependence of calculated IR-ZF spectra on laser frequency offset. Laser power 32 ml; sample pressure 6.5 mTorr; RF amplitude 0.73 V/cm; no of harmonics 4. Laser frequency offsets: eee 0.0 MHz; xxx 5.0 MHz; +++ 10.0 MHz. 38 C a. .9 .‘ - ‘c‘i . - b I O «1 - m , . -D . ‘1 .:fl. . o - ' '. > -‘ I 6 . 23 ‘ a 2 . e .. ........ 0 e. a ................ Q: 9. 5...... ...................... ....NM -_ M v '“u A AAuA‘A‘A 01) L0 21) 31) ‘LO RF Freq. ( MHz) Figure 11. Infrared laser power dependence of calculated IR—ZF spectra. Sample pressure 6.5 mTorr; RF aaplitude 0.73 V/cm; MHz; no of harmonics 4. ml; xxx 16 ml; +++ 9ml. Laser powers: eee 32 laser frequency offset 0.0 39 c .' ‘ .9 . .. ' a 5.0. .9 T h . O I o ‘. ° - m ' ' .0 a ’ I. 4 a ., ‘. 4) .0 ..m e2 1 .. ..I an e '. 2 O .0 ... G3 .0. ...m.. m e.. ‘ ..-... eeeeee” g... 0.0 l O 2 O 3.0 4 0 RF Freq. (MHz) Figure 12. Dependence of calculated IR-ZF spectra on no. of harmonics included in the calculation. Laser power 32 al; sample pressure 6.5 aTorr; laser frequency offset 0.0 MHz; RF amplitude 1.5 V/cm. No. of harmonics: eee 4; xxx 3; +++ 2. 40 ordinary saturation effects. In each of these figures, comparison of the relative peak heights to that of the offset shown at the right of the figure indicates that the intensity increases with pressure between the two lower figures, but decreases with pressure between the two upper figures. Finally, the dependence on the nuaber of harmonics included in the calculation (Fig. 12) justifies the derivation of a theory that goes beyond the rotating wave approximation. As expected, however, and shown in Fig. 13, there is little if any dependence on the number of harmonics when the RF anplitude is low enough. 41 d ... c ' ‘ O ' . e- ' 0. ed ’ ' a e b . . O 4 -e . ' m ° - .0 . e O < . . - e e a g . Q .. .e '3 " e I .°' a .' e a N" g e '0. ............... Q . .. .... ....................... a: a .e ...'-e .. aaeeaee.......- ‘ ..... easasaaasaaaaeaaaaeaea O... “e e. .M.”..~“ AAAAAAAAAAAAA I ' V 0.0 1.0 2.0 3.0 4.0 RF Freq. ( MHz) Figure 13. Dependence of calculated IR-ZF spectra on no. of harmonics included in the calculation. Laser power 32 ml; sample pressure 6.5 mTorr; laser frequency offset 0.0 MHz; RF aaplitude 0.73 V/cm. No. of harmonics: eee 4; xxx 3; +++ 2. 42 APPENDIX A The purpose of this Appendix is to give a solution of Eq. (22) for the case [Sal - a >> 6b, 71, and 12. This is the case for infrared radiofrequency or infrared nicrowave two-photon spectra for a symmetric top without inversion. The solution will be developed to third order in the product of 8b and x, the factors that depend on RF and infrared amplitudes, respectively. It is sufficient to consider only one harmonic; therefore, the linear system that must be solved is ft * ‘ Fs‘ ’ ‘ ‘11 801 0 v1 0 ’ - °/2 (11) 801 8oo 801 v0 ‘ x“ ' _‘° a01 811 j ,‘vl , g 0 y, The ak£ are given by Eqs. (19)-(21). This system is readily solved to yield xno/2 ' a* 2 a 2 _ ___Ql__ - ___Ql___ (A2) 2 800°11 800°11 43 OF 8 2 2 0 a a “n 1 + _—Ql—; + ——91—— . (13) 00 a00‘11 a00°11 v0 2a After rationalization, this is F 92_ «2 w s w xno 281(1)1 b1 ) + 4alblb1 vo ' 2a 1 + ,2 ,2 ' (‘4) 0 ao(a1 + a1 ) The nomenclature of Chapter II, i.e., 800 = so, all = ai + N - F fl is , a01 - b1 + ibl, has been used. The third-order terms in Eq. (A4) are in the ratio in parentheses. These say be written A/B, where after substitution from Eqs. (19)-(21), 2 2 2 8 Y 48 5b _ 2 2 l a 2 _ a 2 _ 2 A - 2‘. ‘t ('7) ('2 + 2 ) —2—(° 5.) Y 0 Y o 2 2 ° 2 2 28 720 and 2 2 2 8 5 Y 8 _ a a 2 2 _ a 2 B - —72 (Y2 + m2 ) + (o —-0 ) . (A6) In these expressions a number of higher order terms and terms that are negligible because of the assumed magnitude of 8. and u have been omitted. 44 To siaplify Eqs. (A5) and (A6) we lake use of the fact that ISaI - o. This leads to 2 2 A848. ‘b/Yz (A7) and 8.2 (to " 8a)2 (u + 8a)2 2 B s + 41 (58) Y2 m2 2 Finally, the desired third order contribution to V0 is (3) _ xn° A n sz‘h (” 5n) (° + 5s) 2 0 2a B 2 2 2 0 28a 40 This result is in essential agreement with that derived previously by another method(10). The conclusion is that infrared microwave two-photon absorption in symmetric top molecules without inversion can be viewed as the result of a high-frequency Stark effect created by the microwave electric field. This Stark effect causes absorption sidebands in the molecules such that a resonance occurs when the laser frequency coincides with one of these sidebands. The denominator in Eq. (A9) shows resonances when 8a = "l - "be = to, or when a! = ”be t u. 10. ll. 12. 13. 14. 15. 16. 45 REFERENCES E. Arimondo, P. Glorieux, and T. Oka, Phys. Rev. A17, 1375-1393 (1978). S. H. Autler and C. H. Townes, Phys. Rev. 78, 340 (1950). J. Brossel and F. Bitter, Phys. Rev. 86, 308-316 (1952). R. F. Curl, Jr. and T. Oka, J. Chem. Phys. 58, 4908-4911 (1973). F. Herlemont, M. Lyszyk, J. Lemaire, and J. Deaaison, Z. Naturforsch. 36a, 944-947 (1981). S. M. Freund, G. Duxbury, M. Romheld, J. I. Tiedje, and T. Oka, J. Mol. Spectrosc. 52, 38-57 (1974). J. C. McGurk, T. G. Schmalz, and l. H. Flygare, Adv. Chem. Phys. 25, 1-68 (1974). S. H. Autler and C. H. Townes, Phys. Rev. 100, 703-722 (1955). A. Jacques and R. H. Schwendeman. "An infrared zero .frequency double-resonance effect in CH F", Symposium on Molecular Spectroscopy, 37th, Columb s, Ohio, 1982. T. Oka and T. Shimizu, Phys. Rev. A2, 587-593 (1970). T. Oka, in ”Proceedings of the Summer School of Theoretical Physics”, Les Houches, France, 1975. S. M. Freund, M. Romheld, and T. Oka, Phys. Rev. Lett. 35, 1497-1500 (1975). T. Amano and R. H. Schwendeman. J. Chem. Phys. 68, 530-537 (1978). C. Freed and A. Javan, Appl. Phys. Lett. 17, 53-56 (1970). J. l. Russel, C. D. Needham, and J. Overend, J. Chem. Phys. 45, 3383-3398 (1966). C. D. Barnett and D. F. Eggers, Jr. ( private comaunication, cited in Ref.l5 ) ' 17. 18. 19. 20. 46 S. Saeki, M. Mizuno, and S. Eondo, Spectrochim. Acta Part A 32, 403-413 (1976). J. Aldous and I. M. Mills, Spectrochim. Acta 18, 1079-1091 (1962). C. H. Townes and A. L. Schawlow, ”Microwave Spectroscopy”, McGraw-Hill, New York, NY, 1955. G. Magerl, l. Schupita, E. Bonek, and l. Ereiner, J. Mol. Spectrosc. 83, 431-439 (1980). 47 - PART II - INFRARED-MICRONAVE SIDEBAND LASER SPECTROSCOPY OF 13 12 THE v3 AND 2V3 * v BANDS OF CH F AND CH F 3 3 3 48 CHAPTER I INTRODUCTION This thesis is concerned with studies of the v3 and 2V3 ~ v3 bands of 12CH3F and 13CH3F by infrared microwave sideband laser spectroscopy. Methyl fluoride is a typical prolate symmetric top aolecule with 03v symmetry. This molecule possesses six fundaaental vibrational modes, three totally symmetric (Al) and three doubly degenerate (E), all infrared active. The v3 mode is of totally symnetric species A1, associated mainly with the C-F stretching vibration. Since the v3 band of CH3F is in coincidence with 10 pm 002 laser lines and its rotational fine structure is a good exanple for a symmetric top molecule, it has been the subject of many publications and has played a key role in the development of molecular microwave and infrared spectroscopy(l,2). The measurements of pure rotational transitions in 12CH3F were done by Gilliam et al.(3), Johnson et al.(4), Thomas et al.(5), linton and Gordy(6), Sullivan and Frenkel(7), Tanaka and Hirota(8), and Hirota et al.(9) by means of microwave spectroscopy. The most precise measurements were obtained by a microwave Lash-dip method(6), and high J transitions in the ground state were observed by Sullivan and Frenkel(7). Tanaka and Hirota(8) 49 and Hirota et al.(9) measured rotational transitions.in excited vibrational states. The infrared spectrum of CH3F was first reported by Bennett and Meyer(10). Yates and Nielson(ll) examined all the fundamental bands with moderate resolving power, and Anderson et al.(12) analyzed all of the perpendicular fundamental bands with relatively low resolution. A detailed high resolution study of the 93 hand of CH3F with a conventional infrared spectrometer has been carried out by Smith and Mills(13). lith the advent of lasers, methyl fluoride has been used for various laser spectroscopic experiments because of its near coincidences with laser lines and large intensity of absorption. Laser spectroscopy using these coincidences. has been reported by Luntz and Brewer(l4), leitz et al.(15) and Freund et al.(16) who used 10 p- CO2 lasers for a radiation source. Chang and Bridges(l7) and Chang and McGee(18) observed far infrared maser action between the rotational levels in the v3 state. Nonlinear spectroscopy of CH3F and measureaent of the dipole moment in the ground and excited states have been reported by Brewer(l9,20). Additional nonlinear experiaents include infrared-infrared two-photon spectroscopy by Bischel et al.(2l) and the use of an infrared-submilliaeter wave double resonance technique by Blumberg et al.(22). More recently, further high precision spectroscopy of 50 12CH3F has been reported. This includes application of tunable 002 laser sideband radiation(23), diode laser measurement(24,25,26), IR-RF two-photon Lamb-dip technique(27,28), and Lamb-dip spectroscopy(29). In addition, methyl fluoride has been of fundamental importance in the development of optically pumped far-infrared lasers(17,18,30,31). The analysis of the 2V3 band was first reported by Pickworth and Thompson(32) without resolving the E rotational structure. Smith and Mills(13) performed a study of 203 o 03 transitions by a conventional grating spectrometer. Recently, a very accurate study of the overtone band 2V3 by using an interferometric spectrometer was done by Betrencourt(33), and Freund et al.(16) observed several 293 v v3 transitions by means of laser Stark method. But the number of transitions was insufficient to determine the higher order centrifugal distortion constants(16). The natural abundance of 13 CH3F is composed of 1.12 of 083F so that its spectroscopic interest should be emphasized. But relatively little work was done by infrared laser spectroscopy compared to its isotope 12CH3F. Pure rotational transitions in the ground state and in the v3 = 1 excited state were observed by Gilliam et al.(3) and Tanaka and Hirota(8), by means of microwave spectroscopy. Recently, Matterson and DeLucia reported a number of frequencies measured in the ailliaeter wave region(35). The 51 conventional grating infrared spectrum of the v3 band of 13 CH F was first reported by Smith and Mills(13) and Duncan 3 et al.(34) aeasured the overtone 2V3 band. The first study of the 2v3 overtone band with resolved E structure was made by Betrencourt(33) from an FT-IR spectrum. The actual application of laser spectroscopy to the 13 CH3F molecule was carried out by Freund et al.(16) by aeans of laser Stark spectroscopy, by Shoja-Chaghervand and Schwendeman(29) by means of IR-Ml two photon spectroscopy, and by Romheld(27) and Freund et al.(28) by IR-RF two photon Lash-dip spectroscopy. Only quartic centrifugal distortion constants could be obtained because of the relatively limited data (44 transitions, J i 8)(29). There has been no previous measurement of the 2V3 r v3 13 hot band of CH3F with or without E structure resolution. Centrifugal distortion constants for the ground and v3 = l and 2 states of 12 CH3F have been reported by a nuaber of authors.. Gordy and his group published several progressively improved sets of rotational constants in the ground state(4,5,36,37,38). linton and Gordy(6) reported sextic centrifugal distortion constants derived from their precise Lamb-dip measurements. Graner(39) has determined the ground state rotational constants, including A0 and (0) DE , FT-IR spectra. Betrencourt(33) obtained aolecular by analysis of ground state conbination differences in parameters for the second excited state from an analysis of 52 the 293 overtone band of 12CH3F and 13CH3F. And Freund et al.(16) also analyzed the rotational constants of v3 = 2 for 12CH3F from the observation of saall number of transitions. Recently, Arimondo and Inguscio(40), Magerl et al.(23), Herlemont at al.(24), Shoja-Chaghervand and Schwendeman(29), and Arimondo et al.(26) all obtained 12 rotational constants for CH3F from their observations and conpared them to previously reported values. Additional data needed to analyze the v3 - v6 Coriolis interaction have been given by DiLauro and Mills(4l) and by Hirota(42). 13 For CH F, Freund et al.(16), Shoja-Chaghervand and 3 Schwendeman(29), Romheld(27), and Matterson and DeLucia(35) all reported molecular parameters from their observations, just up to quartic centrifugal distortion constants. In this work, the v3 and 2V3 o v3 transitions of 12CH F and 13 3 laser spectrometer, in which the spectra were obtained by CH3F were measured by a 002 laser-Ml sideband tuning the laser_to sore than 60 CO2 laser lines and sweeping a microwave source from 8.2 - 12.2 and 12.4 - 18.0 GHz on each 002 laser line. From the analysis of these spectra, the molecular parameters including quartic, sextic, and octic centrifugal distortion constants were detersined and will be given. The next chapter describes the theory used for vibration-rotation interaction (Coriolis interaction), centrifugal distortion, and absorption intensity. Chapter 53 III gives the theory and its application to the generation of an infrared-microwave sideband laser system. In Chapter IV, the experimental diagram and method for this work will be summarized. Finally the experimental results and their quantum number assignment will be presented with a detailed discussion in Chapter V. 54 CHAPTER II THEORY I t o ctio The study of molecular spectra is the most useful of all methods for experimental investigation of molecular structure and notion in free molecules. It affords information on the possible molecular energy levels as well as on the diaensions of aolecules. Spectra arise from the emission or absorption of definite quanta of radiation when transitions occur between certain energy levels. In the theory of solecular spectroscopy, it is custonary, according to the Born-Oppenheimer approximation,— to consider that the energy of a molecule can be expressed simply as the sum of electronic, vibrational, and rotational contributions; 8 = 8else + Evib + 8rot (1) where Belec is electronic energy, Bvib is vibrational energy, and Er0 is rotational energy. t The observed spectra correspond to transitions between two energy levels according to the Bohr frequency condition, 55 by = E’ - E” , (2) where the ’ and " refer to the upper and lower states, respectively, and v is the frequency. The transition probabilities are determined by the eigenfunctions of the Schrodinger equation by way of the matrix eleaents of the dipole moment n such as I w’u 0" d1 . (3) Rotational Energy - General Theory For a body rotating about a fixed axis, the moment of inertia about that axis is given by I a 2 mi r. (4) i where r1 and mi represent the distance and the mass of the i-th particle from the axis, respectively. If a aolecule is considered as a rigid body of point masses, its structure can be described by a tensor whose diagonal elements are the moments of inertia about Cartesian axes. For a Cartesian coordinate system fixed at the center of sass (COM), the diagonal eleaents of the inertia tensor are 56 2) <5) _ 2 Ixx ’ f‘i‘fl + "i where Iyy and I2 can be forned by a permutation of x, y, z and z; the m1 are atomic masses whose coordinates are xi, yi, and zi. The off-diagonal elements, called products of inertia, are given by I = - 2 mi x. y. . (6) The inertia tensor can be simplified because it is synaetric leaving only 6 independent tensor elements. The orientation of the coordinate system used to define the inertia system will determine the values of the moments defined above. There is always at least one proper orientation of the coordinate system which forces the off-diagonal elements of the tensor to vanish. The diagonal elements'become the principal moaents of inertia, and the axis system is termed the principal axis system. As the Cartesian system is rotated into the principal axis system, the moments of inertia approach either maximum or minimum values. The three principal moments of inertia are designated as Ia’ Ib’ and Ic such that In S Ib S Ic’ For any general orientation of the molecule-fixed axes with origin at the COM, the principal moments of inertia can be obtained by diagonalizing the initial tensor. This is 57 done by solving the detersinantal equation, as follows: Ixx - x Ixy Ixz Iyx Iyy - x Iyz = 0 (7) I zx zy 22 where the roots x are the principal moments of inertia. Since the trace, which is the sum of the diagonal elements is a constant for the diagonalization procedure, I + I + I = I + I + I . (8) lhen the principal axis system of a rigid rotor is employed, the energy can be expressed in a simple form in terms of the angular somenta Pi about the three principal axes. Determination of the energy levels in a quantum mechanical system follows from 110 =. 30 ' (9) where H is the Hamiltonian operator for the system, 0 is an eigenfunction, and E is an eigenvalue. Since the Hamiltonian operator and eigenfunctions are independent of time, the E values are constants which are the only stationary state energy values of the system. The Hamiltonian is given by 58 .__, , ___.__ ___-___ .‘s. P N N sz + 21— + 'U 1 lo (10) N b Ic .1: which is commonly written as follows: 1 2 1 a = -§— (1982 + npbz + area) (11) l .h where A, B, and C are rotational constants which are defined in frequency units as A: 2 ,3: 2 ,C=—§—. (12) Since Ia i Ib S Ic , A 2 B 2 C . (13) The operator for momentua about the principal axes is related to the total angular momentum of the systea P by P = P + P + P = P + P + P . (14) The axes x, y, z say be identified with the principal axes a, b, c in any of 6 possible ways. For any identification, P2 is conventionally chosen as the component of angular 59 momentum for which there exists simultaneous eigenstates with P2 as shown in Fig. l. The matrix elements are 2 - 2 = §— {(§- + -}—)[J(J+1)-22] + ii.) (17) x y z (kalHleth) = "2 {(-1—- — -1-—)[(J$k)(J$k-l) 6— Iy Ix (th+l)(th+2)]1/2 } . (18) Eizid_§zsaatris_122_helzsulsa lhen a nonlinear molecule possesses two equal moments of inertia, it is classified as a symaetric top aolecule. There are two possible identifications for the two equal moments. If I. is equal to Ib' Ic is the unique moment and is by definition greater than I. or lb. The molecule is then designated as an oblate symmetric rotor. If I is b equal to Ic’ the molecule is called as a prolate symmetric Figure 1. 60 Classical motiom of a symmetric top. This is a combined rotation around the molecular axis associated with P2 and a precession of this axis around the total angular momentum P. The molecule represented is CH3F. 61 top molecule. For a prolate rotor, the matrix elements of the Hamiltonian are = (19) (kalHle12m> = o . (20) The energy matrix is diagonal in k, since k is a good quantum number for a true symmetric rotor. In terms of the rotational constants, the energy for a prolate rotor is E = hBJ(J + 1) + h(A - B)k2. (21) For an oblate top, the energy is 3 = hBJ(J + 1) + h(C - B)k2. (22) By convention A -‘B 2 0 and C - B i 0. The energy levels for a symaetric top are shown in Fig. 2. Because k is the projection of J on the figure axis, J 2 lkl. For a given value of J, however, k may have a number of values, as follows: k = J, J-I’ eee g-J (23) a total of 2J+l different values.‘ Since the energy is 2"; 1“; _. 62 --l0 -l0 9 IO-lo l0 -0" — " —n I 9—3 o_lo "9 -l0 --8 _ " -IO _3-8 “’7 6 —8 —-3 “'9 -7 -5 -8 —6 —9 ._ -7 —7_ _ J ‘6 -5 -4 —6"5 -5-7'8 —5-5_4 —3 -5-5 _6_7 —4-4-3 -4_4 ‘6 -3 :3_2 -3 _3 -4-5 -5 :221-l :221"2 -+3.—m4 —4 K=o l 2 3 4 o I 2 3 4 Figure 2. Energy levels of typical symmetric top molecules (A) prolate, (B) oblate symmetric top. 63 independent of the sign of k, levels with the same absolute magnitude of k coincide, so that all levels for which k is greater than zero are doubly degenerate, and there are only J+l different energy values for each possible value of J. For each particular k, there is an infinite series of levels with different values of J. Symmetric Top Wave Functions In terms of the Bulerian angles a. O. and x, the Schrodinger equation for a prolate symmetric top is l a . aw 1 a w cos a A a w . —— (sin e -) + + ( + -)-—— ‘1” 9 3° 3° sin a 86 sin a B axz 2cos a 32W 8 - -————— + SE W = 0 (24) sin 0 3x 30 The variables in Eq. (24) may be separated, and the solutions written in the form _ 1.0 ikx ka. - 8(a) e e . (25) Because 9 and x only appear in the differential terms, they are known as cyclic coordinates and always appear in the wave function as exponential terms. The quantum number m 64 and k must be integers for w to be single-valued. The 9 equation has the form 2 2 l d_ (sin e degez) _ [ m2 + (cos a + A)k2 sin a do do sin a sin a B - 222%.: km - %§]e(e) = o . (26) sin a By introducing the variable _ l x - §(l- cos a) (27) and letting 6(a) = x'k"'/2 (1-x)"“""/2 F(x) , (28) the equation for F is found to be 2 d F d! _ x(l-x);—§ + (a - Bx)3; + if - 0 (29) x a = Ik-ml + l , (30) B = |k+lI + lk'll +2 . (31) and w ckz 2 1 Y = hi ’ -i— + k ‘(§|k+ll + Ik‘ll) (%|k+m| + %|k--| + 1) . (32) 65 The equation for F can be solved by using the polynomial F(x) = E a x . , (33) The resulting recursion relation is _ n(n-l) + 8n - Y a . (34) an+1 ’ (n+l)(n+u) n For w to be a satisfactory normalizable wave function, the series must terminate and become Just a polynomial, which requires that the energy W is w = hBJ(J+l) + h(A-B)k2 (35) with J = n + l |k+m| + l-lk-ml (36) max 2 2 nmax is the largest value for which an does not vanish. From Eq. (36), J must be a positive integer which is equal to or larger than lkl or lml, so that k = 0, £1, 22,..., tJ (37) m = 0, 11, 12,..., tJ The symmetric top wave functions can be written in terms of the hypergeometric series and a normalization factor, 66 = N X'k-.'/2(1-x)lk+.l/zei-. eikx kam ka r(—J+g -1; 3+3; l-lk-ml; x) (38) where N - t(23+1)(J+lk+-I/2+|k-Il/2)! ka Buz (J’|k+l|/2)‘|k-l|/2)! (J-1k+m|/2+|k-m|/2)! 11/2 (lk-ml!)2(J+|k+m|/2-lk-m|/2)! ° (39) Nonr d mmetr c To Molecules No real molecule is a rigid rotor. The molecules in a sample cell which are subjected to electromagnetic radiation are vibrating as well as colliding with other molecules and the sample cell walls. Thus the molecular energy levels cannot be predicted exactly by rigid rotor theory but are influenced by perturbations such as those resulting from vibration-rotation interactions (Coriolis interaction) and centrifugal distortion. The Coriolis force is a vibration-rotation- interaction, and vanishes when rotation and vibration are completely separated. If 3 is the linear velocity of the molecule relative to the molecule-fixed axis system and 5 is 67 the angular velocity of rotation of the molecule-fixed system with respect to a space-fixed axis system, the Coriolis force is defined as F = 2.3 x u . (40) Under the proper conditions, the Coriolis force can produce large changes in the rigid rotor energy levels. These deviations may occur as an energy level splitting resulting from the removal of a degeneracy or as a shift of energy levels due to a near degeneracy. In order to visualize the influence of the Coriolis force more clearly, let us consider classically its effect in a linear symmetric XYZ molecule. Consider the vibration v3 in the rotating molecule. The displacement vectors (solid arrows in Fig. 3) also give the relative velocities at the instant when the nuclei pass through the equilibrium position, The Coriolis force on each nucleus is proportional to this velocity but perpendicular to it, and, for a counterclockwise direction of rotation, always toward the right when looking in the direction of motion. From Fig. 3 it is seen that during the vibration v3, these forces tend to excite the perpendicular vibration v2, but with the frequency of v3. Conversely, when the vibration Va is excited in the rotating molecule, the Coriolis forces are as given in Fig. 3 and tend to excite Figure 3. 68 ‘\ 6.; 4? 4» v2 Normal vibrations of a linear XYZ molecule and the effects of Coriolis coupling. v2 is a degenerate bending vibration and the arrows attached to the atoms represent one component of the vibration. The other component (not shown) results from identical motions perpendicular to the plane of the paper. 69 the parallel vibration v3 but with the frequency v2. If the frequencies of v2 and us were nearly the same accidently, a strong excitation of one of the two vibrations would take place if the other were first excited, in consequence of this Coriolis coupling. However, this excitation will be very weak when v2 and ya have widely different frequencies. No coupling takes place between v1 and v3 or between the two components of v2. This results froa the effective absence of rotation about the figure axis in a linear molecule. This coupling is called the second- order Coriolis interaction. These two components of the degenerate bending mode can couple in a symmetric top molecule where rotation about the figure axis is allowed. Figure 4 illustrates the effects of a Coriolis force on the degenerate bending mode in a symmetric top molecule. When one of the degenerate components is excited, rotation about the figure axis produces vibrational components which excite the other component. Since the two frequencies are identical, the interaction may be very strong. This is called the first-order interaction because it does not vanish in the absence of rotation about the figure axis (k=0). Even when rotation ceases, a vibrational angular momentum coupling the two degenerate components is present. However, the degeneracy is only lifted by the second-order terms in the vibration-rotation Hamiltonian when rotation is present (k n 0) because the two modes of vibration still 70 (8) Figure 4. Coriolis coupling of the degenerate bending vibrations in e X123 symmetric top. (A) and (B) illustrate two components of the degenerate bending mode. (C) shows the coupling effect of the Coriolis force on the (A) mode as it tends to induce the (B) mode. In all three illustrations, the figure axis is perpendicular to the plane of the paper and only off-axis atoms are shown. 71 have the same energy when k = 0. For one level k = 1 and for the other level k = -l, the relative positions of these two levels will depend on the sign of the Coriolis coupling constant. For 03v molecules, the first excited state of a degenerate bending vibration must belong to the degenerate irreducible representation 3, and the rotational wave functions belong to the representations of the subgroup 03. The important case results when k = :l, 1 = :1. The rotational wave functions for k = t1 belong to B with the resulting symmetry of over coming from the product B x B = 2A + B . (41) Of the four levels produced by k = t1, 1 = :1 permutations, two will be nondegenerate and two form a degenerate pair whose degeneracy cannot be lifted by any internal permutations of C3 symmetry. For k = l the value of lk-ll may be either 0 or 2. From the symmetry consideration of the group 03v, the levels of A symmetry for a given k must have a value of lk-Al = 3n; if lk-ll is not a multiple of three, the level belongs to the representation 8. In this case the levels with k = l have A symmetry and can be split by i-type doubling. flith interaction between an A1 species normal coordinate Or and an 8 species pair of coordinates (0.1.0.2) due to rotation about the x and y axes, each pair of 72 degenerate symmetry coordinates or normal coordinates satisfy the following equations: A = e-iZn/3 A c3(°s1 + 10.2) (0.1 + 10.2)03 ’ (42) " (xx) _ _ . " (xz) av (0.1 +iQ.z) - (0'1 10.2)0v . (43) Bquation(42) defines the relative sense of each pair of degenerate coordinates and Eq. (43) fixes their coordination in the (x,y) plane. The Al - B interaction is characterized by a single seta constant for the above coordinate conventions y -_x =y {r,s1 - {r,s2 (rs (44a) and X - y - {r,s1 - +{r,s2 0 (44b) The interaction between the pair of coordinates 0.1 and 0.3 due to rotation about the z axis is characterized by the constant (45) If the normal coordinate vectors are known, the zeta constants may be conveniently calculated from C matrix 73 elements defined according to Ref. 47 e“ = L'lc“(L’1)’ (46) where a = x, y or 2. Considering the matrix representing H in the via . O J, vibration-rotation basis functions, denoted by lvr, k), the important selection rules for interaction between the first two excited vibrational levels in 0r (A1 species) and 0.1, 0.2 (B species) are ok = 61. = 11; translated into terms of K = lkl these become: B(+l), k+l interacts with Al, k which interacts with B(-i), k-l. The interaction is illustrated in Fig. 5. Thus if the interaction is large, k and I. are not good quantum numbers; the true rovibrational states are some mixture of the basis functions which cannot. be characterized by particular values of k and 1.. For each value of J the Hamiltonian matrix factorises into a number of (3x3) blocks, according to the scheme of Fig. 6, each block being characterised by a particular value of (k-l.), so that (k-i.) remains a good quantum number. In addition to the (3x3) blocks there will be two (2x2) blocks, for which (k-i.) 8 2J, and two (lxl) blocks (unperturbed states) for which (k-i.) = :(J+l). A typical (3x3) block of the Hamiltonian has the form 74 (+0 (-I) — A . ground state I O Figure 5. Allowed transitions and interactions for an A1 and an H fundamental of a 03v molecule. 75 Vibrational E A, E 23:22:: Me. v,=. v.=: ls =+l IS = ls =-I k = +3 0 +2 \‘s H \ O \ -l \\ —2 .3 0 Figure 6. Diagrammetric representation of interaction between an Al and an I vibrational state for J 8 3. Iach dot represents a basis function characterised by particular values of k and 1.; the lines represent Coriolis interactions, connecting states of the same (k - 1.). Except for the extreme values of (k - l.) the secular equation factors into (3x3) blocks. 76 ll,0;J,k> l0,l-1;J,k-l) o 1/2 o y 1/2 v.+F (J,k+l) 2 a 0r.£r.[J,k] o -2A’{:(k+l) . _1/2. y vr+F (3.x) 2 3 nr.:r. (47) (Hermitian) [J,k-l]1/2 v.+F’(J,k-l) az_ +2A {.(k l) where F’(J,k) = B’J(J+1) + (A’-B’)k2 (43) or. = % [(vrxv,)1/2 + ]4 53 = 3 (51) [V6(J.K-1,‘1)‘V3(J,K)] where = iB{§2)[(J+K)(J-K+1)]l/2 [Va/v6)1/2+(v6/v3)1/2)]/ 2“2 (52) and v6(J,K-l,-l)-v3(J,K) = vg-vg-A(ZK-l+{)(1-{) +2n(2x-1) . (53) In modern calculations, the 3x3 matrix in Eq. (47) is diagonalized numerically rather than relying on perturbation theory. The centrifugal force differs from the Coriolis force in that it does not vanish in the absence of a perturbing vibrational mode. The centrifugal force on a mass m at a distance r from the axis of rotation is 78 i = m 32 P . (54) The effects of centrifugal distortion are generally small for low J values but can reach the order of hundreds of megahertz for transitions between levels of high J. Rotation in a symmetric top is accompanied by centrifugal forces which tend to alter the effective moments of inertia. For rotation about any axis in the molecule, this dynamic effect forces the atom away from the axis of rotation and increases the moment of inertia about that axis. The centrifugal effects enter the energy level expression as higher powers of J(J+l) and K. For a prolate rotor, the first correction due to centrifugal distortion leads to the energy expression B/h = BJ(J+1) + (A-B)K2 - DJJ2(J+1)2 2 4 - DJKJ(J+1)K - DKK . (55) Here, D D and D are centrifugal distortion constants. J’ JK’ K Dependence of the rotational and centrifugal distortion constants on the vibrational state is assumed implicitly. The correction terms for centrifugal distortion are found to depend only on even powers of the angular momentum because the distortion effects do not depend on the direction of rotation about any axis. The frequencies of a 79 symmetric top nolecule (selection rules oJ=l, ok=0) exhibiting detectable centrifugal distortion effects are hv(J+l,k . J,k) = 2B(J+l) - szK(J+1)x2 - 4DJ(J+1)3 . (56) Since the effective rotational constants tend to decrease due to the centrifugal force, DJ is normally positive, but DJK may have either sign. The centrifugal distortion constants can be expressed in terms of the moments of inertia (molecular structure) and molecular force constants of the molecule. However, a theoretical calculation of these constants is very difficult except for the simplest structures. Wilson(49) has given explicit formulas for the D distortion constants D and ”K for a symmetric top J’ JK’ molecule with 03v symmetry in the harmonic oscillator approximation. The formulas are given in terms of the constants, I = I +I = 2 m (x 2+y 2+22 2), (57) 1 headstone: _ _ _ 2_ 2 12 - Ib Ic- E .¢(xa ya ), (58) 13 = 2 . (x 2+y 2) , (59) “a“ 80 I = 22 . y z s (60) “a“ where the z axis corresponds with the a axis(figure axis). The formulas are as follows: 4 al 31 al 31 -8» 4 l -l 1 2 -l 2 ”J“E"e [igj aS (F )1) a' *1?) 5‘"(F )1) a§_]’ (61) i J i J 32u4AiBE 313 1 313 314 _1 314 DJK=-ZDJ+ h [igj 3§:(F )iJ 3_; +i§j s_;(F )ij Egg]! (62) 32.4A: a13 1 a13 DK=-DJ-DJH+ h 1?) asi‘F )ij 3§3 ' (63) In these equations Ib and Ic are regarded as instantaneous moments of inertia. The 81 are internal symmetry coordinates, and the Pi) are elements of the force constant matrix consistent with the Si and 83’ The derivatives of II and 13 are non-zero only for internal symmetry coordinates which have the symmetry A1 of C3v‘ Similarly, the derivatives of I2 and I4 vanish unless the Si have symmetry 3. For large J and K values and/or light molecules, the distortion correction must be extended to higher order. The present study required centrifugal distortion constants that multiplied the eighth power of the angular momentum quantum 81 numbers. The energy level expression used was B(J,K) = BJ(J+1) + (A-B)HZ — DJJ2(J+1)2 — anJ(J+1)x2 4 3 3 2 2 2 4 - nxx + BJJ (J+l) + HJKJ (J+1) K + HKJJ(J+1)X 6 4 4 3 3 2 + BK! + L4JJ (J+l) + LSJBJ (J+1) K 2 2 4 6 8 + LZJKKJ (J+l) K + LJKKKJ(J+1)K + LKX (64) "h°'° BJ’ BJK’ HKJ’ nx’ L4.1: L3JH’ Lszx' LJHKK’ and Lu “re additional distortion constants. Intensities of Symgetric Top Transitions The intensity of a vibration-rotation transition for a symmetric top molecule interacting with plane polarizing radiation may be calculated from the basic formula given as followsz' BuszluilIzvzbv r = 2 2 (65) 3ckT[(v-vo) +(Ov) ] Here N = the number of molecules per unit volume in the absorption cell, f = the fraction of the molecules in the lower of the two states involved in the transition, 82 lpul2 = the square of the dipole moment matrix element for the transition, summed over m components, v = the source frequency, v0 = the resonant frequency or, to a good approximation, the center frequency of the absorption line, by = the half width of the line at half maximum, or the line-breadth parameter, c = velocity of light, k = Boltzmann constant, and T = absolute temperature. The selection rule for a parallel band, in which the dipole moment matrix element is non-zero only for the component along the molecular axis may be written for a nonplanar symmetric top without inversion, as follows: oJ'= 0, :1, ok = 0. (66) The matrix elements, which are non-zero only for transitions given by the above selection rules, are as follows; 2 2 + - a: = +1. ck = o; luijlz = u2 (:11 J21) <67) 2 OJ: 2 2 k 00 6k : 0; luijl = U J 3+1) (68) 83 2 Jz-kz OJ = —1. ok = o; '"13'2 = u ‘JTEJITT . (69) The fraction of the molecules in a particular initial state is the product of the fraction fv in the vibrational state of interest and the fraction of these fJx in a particular rotational state. If the statistical weight due to nuclear spin is neglected, the probability of a molecule being in a state (J,K) is proportional to -B /kT (2J+1) e J“ (70) where B is the rotational energy level given by Bq.(64) JK and 2J+l is the statistical weight due to the different orientations of J (different a states). The fraction of molecules in this rotational state is ~8JK/kT f = (19“) ° 1, ._ (71) JK A o J 'EJK/kT Z Z (2J+l)e J=0 k=-J If B and A in BJK are small compared to kT/h and if the small contribution due to centrifugal force can be neglected, the sum may be replaced by integrals giving -3 /kT 2 3 fJK = (2J+l)e 3‘ 5—59—3 . (72) u(kT) Bquation(72) applies to one particular value of H, and does 84 not allow for H degeneracy. For a 03v symmetric top without inversion, the degeneracy due to spin and K degeneracy for each value of J and K is giving by the following rules: For H a multiple of 3, but not 0 S(I,H) = 2(412+41+3)(21+1)/3 (736) For K = 0 S(I,H) = (412+41+3)(21+1)/3 (735) For X not a multiple of 3 s<1,x) = 2(412+41)(21+1)/3 (73c) Allowing for this degeneracy, Eq. (71) becomes -2 /kT f g S(I,H)(2J+l) e J“ _ JK . J ~3JK . Z 2 S(I,H)(2J+l) e J=0 x=o /kT (74) With the assumption that B and A are much smaller than kT/h, Eq. (74) becomes 2 3 -B /kT fJK = S(I,:)(2J+l)lB Ahi 6 JK . (75) 41 +41+1 «(k7) For low values of J and K 85 2 3 _ 3(1,x)(23+1)l3 Ah f - - (76) JR 412+41+1 "(k7)3 The fraction of molecules in a given vibrational state may be obtained as ‘0 /kT -fio /kT d r = e n H (l-e " ) n (77) where dn is the degeneracy of a vibrational mode of frequency on. By substituting Eqs. (67) and (76) into (65), and setting 2B(J+l) = hvo, the intensity for a transition J+l r J, K . K is found to be 2 4nh vaS(I,K) nAh 2 r = [1- (412+4I+l)3c(kT)2 -FT " K2 vov26v .(73) (7+1)2 (v-vo)§+(6v)2 86 CHAPTER III INSTRUMENTATION I t ductio The infrared spectrometer is one of the most useful instruments for study of the molecular dynamics such as vibration-rotation interaction, nuclear spin-rotation interaction, effects of molecular collisions, etc. About 15 years ago it became possible to obtain high resolution spectra in the IR region by using a tunable narrow linewidth laser — the semiconductor diode laser(50). Since that time, several high resolution tunable IR lasers have been developed. Among these are the difference frequency laser(51), the color center laser(52), the spin- flip Raman laser(53), the waveguide laser(54,55,56), and magnetically tuned gas lasers(57,58). The most useful laser in the mid-IR region is still the CO2 laser, which provides coherent output radiation of high intensity at a multitude of lines spaced ~2 cm.1 apart. The only drawback to the CO2 laser is its fixed frequency nature, limiting its spectroscopic applications to accidental coincidences between a laser frequency and some feature of spectroscopic interest. Several methods have been developed to increase the tunable range of the CO2 laser. One such method is the 87 waveguide 002 laser which uses the molecular collisional broadening of CO2 to increase the tuning range. In practice, the tunability of a waveguide laser is limited to 3500 MHz around each laser line which, although useful, is too narrow for general molecular spectroscopy. A second method for increasing the tuning range is infrared microwave two-photon spectroscopy which uses the simultaneous interaction of an infrared photon, a microwave photon, and an absorbing molecule. This technique has wide tunability but.has low sensitivity since it involves a nonlinear absorption. In this method, the transition moment is inversely proportional to the square of the laser frequency mismatch(59). For a symmetric top molecule, <1 * ‘ 1> - <2 * ‘ 2> <1 * ‘ 2> M = ( lup€r| luPErl ) luv€1| (79) 2 2 Zfi ”r where 3p and 3v are the permanent and vibrational dipole moment, respectively; er and c are the amplitudes of the A microwave and laser electric fields, respectively; and at is the angular frequency of the MW radiation. A third method for increasing the tunability of a CO2 laser is the infrared microwave sideband technique which is the subject of this thesis. With this method the radiation has a frequency of "IR 1 vM"(60) and has the tunability of the microwave frequency "MW’ Generation of IR-gfl Sideband Radiation Franken et al.(61) observed the first nonlinear optical effect generated from a dielectric crystal. In this experiment second harmonic energy (~3472 A) was produced upon projection of a beam of 6943 A light through . crystalline quartz. The sum frequency from two beams at different frequencies was observed by Base at al.(62), in which two ruby lasers at different temperatures were used for radiation sources. Corcoran et al.(60) observed the first CO laser-MW 2 sideband radiation by using a GaAs loaded waveguide cell as a modulator to measure CO2 gain profiles. Since then there. have been many developments to increase the tunability and the power for general molecular spectroscopy(63-68). However, the CO2 laser-MW sideband laser system most useful for molecular spectroscopy was developed by Magerl et al.(69). They described a device that operates in a traveling wave mode with low power and wide tunability, or in a cavity mode with high power and narrow tunability. The first application of the sideband laser technique to molecular spectroscopy was a report by Magerl et al.(70) in 1977 on the fundamental 93 band of the SiH4 molecule. Even though the sideband power is very weak due to low coupling efficiency between the two kinds of radiation, 89 sub-Doppler spectroscopy has been performed on the NH3 molecule(7l) by employing modulated sidebands in an optical double resonance experiment and in a saturated Lamb-dip experiment. Structure of thg,Modulator The expression for the sideband power PSB generated by an electrooptic crystal with cubic symmetry (CdTe single crystal) is given by(72) _ 2 PSB - PL F /16 (80) Here, PL is the incident laser carrier power and r is the single-pass phase retardation induced by the transverse electrooptic effect. The latter can be written as(73,74) F = R. L. SINC (u. L -/2W) (81) (‘)“03’ 41 where XL stands for the free-space wavelength of the CO2 laser, E. denotes the peak microwave electric field strength within the modulator crystal, no is the refractive index, r41 is the electrooptic coefficient, and L. is the length of the modulator crystal. The abbreviation SINC(x) is used for (sin x)/x, u. is the angular frequency of the modulator 90 signal, and l/W characterizes the mismatch of the microwave phase velocity (VM) and of the laser group velocity (vi) within the modulator, that is, _ = __ - _— (82) For optimum electrooptic interaction, the laser group velocity (vt) should be same as the microwave phase velocity (vM). Since the refractive index of the modulator crystal (CdTe) in the IR region is appreciably smaller than the square root of the microwave dielectric constant, it is necessary to accelerate the microwave signal. The easiest way to do this is to insert the modulator crystal inside a closely fitting rectangular waveguide. The width of the crystal a can be obtained as follows: 2 a 0 ) = CO/(Zfflolir - n (83) where fMo is the microwave frequency where exact velocity match occurs, co is the speed of light, and Er is the relative dielectric constant of the electrooptic crystal. Figure 7 shows the modulator diagram designed by G. Magerl of the Technical University of Vienna, which is optimized for microwave frequency modulation at 8.2 - 18.0 GHz. In this design, the CdTe crystal (Er = 10) is partly replaced by two less expensive and stronger alumina (A1203) 91 Cd Te CRYSTAL Figure 7. Diagram of the sideband modulator, in which the CdTe crystal is embedded between two A1203 slabs to achieve velocity match. The tapered double- ridged waveguide section (upper half removed) provides impedance match to incoming/outgoing standard waveguide sizes. 92 strips with about the same microwave dielectric constant (Er = 9.5). The crystal cross section is designed to be a square with side b", which is chosen as small as possible for high modulating field 8., but large enough to permit unimpeded laser beam focusing through the modulator. The excess length of the A1203 slabs permitted improved coupling of the microwave energy into the modulator. By altering the relative positions of the CdTe and A1203 in a trial and error process, it is possible to obtain with different arrangements of the crystals either an almost perfectly matched traveling wave modulator (terminated by a power load) or a critically coupled resonant modulator (terminated by a sliding short section for frequency tuning). Adjugtgegt of the Crystal Position in the Modulator Since the sideband power depends mainly on the velocity mismatch (l/W) within the modulator, the adjustment of the position of the CdTe and A1203 crystal is crucial in generating the optimum sideband power over a desirable modulation frequency range for a given laser and microwave power. Figure 8 is a diagram of the microwave setup used for the adjustment of crystal within the modulator. For this M00 93 TERM 10dB PM"! METER pm- 1068 PWR METER I REF. oscj SYNC Figure 8. Experimental diagram for adjusting the position of crystal inside modulator. 94 experiment, 10 dB-directional couplers P2 and P1 monitor the input microwave power and the reflected microwave power from the modulator, respectively. By trial and error adjustment of the position of the crystal and of the length of the modulator housing, the almost optimum condition shown in Fig. 9(C) was obtained. In this configuration, the housing is 23 mm long, the CdTe crystal is 0.5 mm behind the edge of modulator and the two alumina slabs are 3.0 mm in front of the modulator. 95 (A) (B) (C) | 8.0 |2.4 FREQ. (GHz) Figure 9. Variation of coupling efficiency with the crystal position. (A) represents input microwave power with frequency. (B) and (C) indicate the reflected microwave power from the modulator with improper position and optimum position, respectively. 96 CHAPTER IV EXPERIMENT Figure 10 shows the experimental diagram of a C02 laser-microwave sideband laser spectrometer in the configuration for linear absorption spectroscopy used in the early stages of this work. The laser medium is a 2.2 a water cooled plasma discharge containing less than 10 torr of a flowing gas mixture of COZ, N2, and He. The plasma tube is in a 4 m cavity mounted on an invar frame. The laser tube is a 25 mm inner diameter Pyrex glass tube sealed with NaCl windows at the Brewster angle at each end. The windows are oriented such that the output radiation is plane polarized with the electric field of the radiation parallel to the floor. One end of the cavity is a rotatable plane grating of 50 mm diameter ruled with 150 lines/mm. The other end of the cavity is a partially transmitting (953 reflection) concave spherical Ge mirror (50 mm diameter, 10 m radius of curvature) which is mounted on a piezoelectric translator (PZT) to control the length of the laser cavity. For stabilization of the laser frequency the position of the cavity mirror is sinusoidally modulated at 250 Hz, causing modulation of the laser cavity length and therefore modulation of the laser frequency. A cell containing CO2 at a pressure ranging from 30-100 mTorr, depending on the CO2 97 I l 1* STAR .Jfli POWER SUPPLY DET * 1 I’iL____J Al is lJ GRATING PZT SAMPLE CELL 051' fi _:_.._:_fi)! seems ’ Pwa ISO ATT PIN METER )l TWTA Figure 10. Block diagram of IR-Mfl sideband laser spectrometer used for the measurement of 13cn3r. set for linear absorption spectroscopy of gases. 98 laser line, is inserted in the cavity(29). The frequency modulation of the laser causes amplitude modulation of the saturation-dip in the fluorescence from this cell at ~4.3 pl wavelength. The fluorescence is detected by a liquid N2 cooled InSb photovoltaic detector and is processed at 250 Hz by a phase sensitive detector (PSD). The output of the PSD controls the output of a high voltage operational power supply (OPS) which sets the length of the PZT. By this means the laser frequency is controlled to 3300 kHz (1 part in 108). An Optical Engineering Model 16-A CO2 laser spectrum analyzer was used to identify the particular CO2 laser line. The frequency of the laser radiation depends on the orientation of the grating and the length of the laser cavity. The grating is rotated to select a particular laser line and the length of the cavity provides fine frequency control within the laser gain curve. The cavity length is controlled by the PZT crystal whose length is linearly proportional to the voltage applied to crystal. Figure 11 shows the relationship between the PZT voltage (laser cavity length) and the laser gain curve with a saturation Lamb-dip. Thus the laser optics can be adjusted for single frequency, single mode operation at the Lamb-dip of the gain curve with an output power of 10 watts on the strongest laser line. The laser output radiation is focussed by a ZnSe lens into a CdTe single crystal mounted in double ridge microwave cell where electrooptic interaction with the tunable 99 (A) as 3 a W .. (B) d) (D 3 4 ' PZT Voltage Figure 11. Variation of the output laser power (B) and the differential signal (A) displayed on screen with piezoelectric translator voltage. The signal due to Lamb-dip can be easily distinguished from that due to the end of mode. 100 microwave signals is accomplished. The infrared power at the entrance of the modulator is kept less than 2 watts by adjusting the size of the diaphragms in the laser to prevent damage to the crystal or to its anti-reflective coating. The microwave source is either one of two Varian Backward Wave Oscillators (BWO) operating in the 8.0-12.4 GHz or the 12.4-18.0 GHz region. The voltages for the BWO are obtained from a power supply designed at MSU, except for the frequency controlling helix voltage. This voltage is obtained from a Kepco Model 2000 operational power supply, which is controlled by the output from a digital/analog converter that is in turn controlled by a minicomputer. The microwave frequency is brought into the lock range of a phase sensitive synchronizer (Hewlett Packard Model 8709A) by the OPS output. The synchronizer locks the microwave frequency to 20 MHz above a harmonic of a synthesized frequency also controlled by the computer, so that the frequency sweep of the BWO is under complete control of the computer. The attenuated output power of the BWO enters a 3 dB directional coupler, where it is divided into two parts; one part is sent to a diode mixer-multiplier for comparison with a harmonic of a precisely known reference frequency, the other part which has around 1 mW power, is switched at a frequency of 33.3 kHz square wave by a PIN diode. The modulated MW signal is then amplified to more than 20 watts 101 by means of a traveling wave tube amplifier (Varian Model VZM-6991Bl TWTA). The output of the TWTA with the polarization of the MW adjusted to be perpendicular to that of the CO2 laser radiation, is applied directly to the modulator. With the aid of the TWTA, we can access a tunable range of 8.2-18.0 GHz on either side of each 002 laser line. Four kinds of radiation are emitted from the modulator: (l) slightly modulated carrier radiation which has almost the same power as the input radiation but whose phase is rotated 900 from that of the sidebands, (2) fully modulated carrier with the same polarization as the sidebands and with comparable amplitude, (3) the fully modulated positive sideband whose frequency is the sum of the CO2 laser and microwave frequencies, and (4) the fully modulated negative sideband whose frequency is the difference of the CO2 laser and microwave frequencies. Both sidebands have the same polarization as that of microwave radiation. The fraction of negative sideband within the total sideband power increases with decreasing microwave frequency, reaching almost 1003 of total sideband power in the 8-9 GHz region. This appears to be an unexplained property of our particular modulator. A ZnSe focusing lens with a 20 cm radius of curvature is located ~25 cm from the modulator. A second comparable lens recollimates the radiation. A II-VI Model PAZ-6-AC 102 polarizer, which consists of six ZnSe windows placed at the Brewster angle substantially attenuates the carrier radiation. A Ge beam splitter divides the sideband radiation into a probe beam, which passes through a sample cell containing the sample gas, and into a reference beam. The sideband radiation that passes through the cell is monitored by a liquid N2 cooled Santa Barbara Research Center Hg-Cd-Te photoconductive detector, and the reference beam is monitored by a liquid N2 cooled Honeywell Radiation Center Hg-Cd-Te photovoltaic detector. The outputs of the two detectors are amplified and processed by two phase sensitive lock-in amplifiers whose reference frequencies are obtained from the square wave that drives the PIN switch in the microwave circuit. The power and the beam direction of the sideband radiation depend on the modulator temperature which is strongly affected by the microwave power and by the alignment of the 002 laser beam in the crystal. In order to maintain a constant temperature at the modulator, it was air-cooled by means of a fan. In addition, the modulator position was adjusted to obtain the maximum signal to noise ratio. For the measurements in this work, less than 200 mTorr of sample pressure for the fundamental band and less than 2 Torr of sample pressure for the hot band were used. For some experiments, the sample cell was heated to ~lOO 0C to 103 increase the population of the first excited state, causing increased intensity on the hot band transition. The pressure was measured by our MHS Model 220BHS-2A5-B-10 Baratron. The spectra were taken by stepping the BWO frequency at l or 2 MHz intervals through a range of 500-1000 MHz. The output of the phase sensitive detectors was digitized and recorded almost simultaneously by the PDP8/E computer. Usually 5 sweeps were used and 5 readings at each frequency were averaged during each sweep. The time constants on the phase sensitive detectors ranged from 30-100 ms and the time between readings was 100 ms. After normalizing the signal spectrum by the reference spectrum, a Gaussian lineshape fitting program was used to determine the peak frequency of the observed transition. Most of the transitions that were not overlapped showed a reproducibility from spectrum to spectrum within :1 MHz. The large fluctuation of microwave power inside the modulator, as shown in Fig. 12, caused a fluctuation in the baseline and the lineshapes of the normalized spectrum. We therefore took steps to modify the microwave pin diode control system to include a feedback loop that maintained constant sideband power as the frequency was changed. The new system includes an absorptive modulator and a feedback control circuit designed by Mr. Martin Rabb at Michigan State University. 104 4) 0 1: C0 .33. E m C 3 I41) ISJ) Signal Reference FREQ. (GHz ) Figure 12. Unnormalized spectrum obtained by IR-MW sideband laser spectrometer. The signal and the reference show the large fluctuation in amplitude with frequency. The lower sideband generated from the lOR(20)CO2 laser line used with ~200 mTorr of 13CH F for the v3 P(27,H) transition. 3 105 According to the experimental diagram shown in Fig. 13, the reference detector monitors the sideband power generated from the modulator. Then, the output of phase sensitive detector No. 2 is fed to an electronic circuit that controls the current to the PIN diode during the "on" position of the on-off cycle. Thus, the input MW power depends on the sideband power monitored by the reference detector. The necessary conditions for lineshape study are that the radiation should be highly monochromatic relative to the linewidth, that it should have precise frequency control, and that it should have very good amplitude and frequency stability. Since the MW feedback controlled IR-MW sideband laser satisfies all of these conditions, it is a promising radiation source for lineshape study. Figure 14 shows the lineshape obtained by the modified spectrometer for the 12 CH3F molecule. CH3F measurements were done with Q0(5,5) transition in the v3 band of the In this work, all 13 the normal IR-MW sideband laser spectrometer, while all 12CH3F measurements were made with the MW feedback controlled IR-MW sideband laser spectrometer. 106 sue rowan suppu DET / / W /' L—————A Al' \_ TJ GRATIMG 927 SAMPLE ceu. DET { } ‘ O I I I enema ‘— H PREAMP H DET mm ISO A‘I’T Pm . METER — i go; TWTA STAB SYNCH MW MOD Contr AID! 7 COMPUTE ‘ TTY All) 1 Figure 13. Block diagram of MW feedback controlled IR-MW sideband laser spectrometer set for linear absorption spectroscopy of gases used for 12 cnap O 107 x J / {a / \‘1 1:” a. 5 C .9 a 9 O 3 12 < CHaF Va°O(5.s) P=L5|8 Torr “J! l0.30 l0.40 l0.50 l0.60 l0.70 l0.80 FREQ.(GHz) Figure 14. Typical spectrum obtained by feedback controlled IR-MW sideband system for lineshape experiment. The lower sideband generated from the 9P(18)CO2 laser line used with a 3.2 cm long sample cell with 0.1 see. time constant. 108 CHAPTER V RESULTS AND DISCUSSION v3 Fundamental and 2V3 ~ v3 Hot Bands of 13CH3F In the present study, the spectrometer was operated for more than 60 CO2 laser lines ranging from 10P(10) - 9R(26). The microwave sources were tuned from 8.2-12.2 GHz and from 12.4-18.0 GHz for each CO2 laser line so that it was possible to observe a total of 386 v3 fundamental band transitions involving J values up to 47 and K values up to 16. Of these transitions, the peak frequencies of 305 transitions could be accurately measured by a Gaussian lineshape fitting program with a good reproducibility, while the others could not be resolved due to overlapping of several transitions. A typical spectrum of the v3 13 fundamental band of CH F obtained by the IR-MW sideband 3 spectrometer is shown in Fig. 15. In this spectrum, the intensity doubling for K = 3n that results from nuclear spin statistics is clearly seen. For the measurement of the frequencies of transitions in the 2V3 ~ v3 hot band, more than 16 C02 laser lines were tuned ranging from 10R(4) - 9P(20) and the microwave sources were scanned from 8.2-12.2 GHz and from 12.4-18.0 GHz. Since there were no previous data, it was very difficult to predict the frequencies of the 2V3 ~ v3 transitions. .seea unassuo on use aesusb a c» usavsooos sass huaeseusu on» .ISsaosas swan loam .Hueo equine used I A as s« ousaasha summon no shoal cow: and: use: as: scan eased Nooaouvnon on» loan veussosem vssaev«s heron can .soaelosaoeae semen vssaov«a Ilium as» as“: eoasaaao masons e6 ease as us» no sausage. guesses .os ass-4s A NIG V .Ommu O.w_ . m.m_ N.m_ 0.3 TV— 0.3 0.. av. MD.” .....2... max . . . m . .../MI . . wflx Av-NNVQO MA V U ..s.. 0 a mu" mm n__annF ...... .... Bu .1 . . ... >_. ... .. .....2. fist. /) \ .1 4.. f/Inl/Ilk I .... uondJosqv 110 Fortunately, during the measurement of the v3 fundamental band, several 2V3 . v3 hot band transitions were observed even though they were very weak and noisy. From these observations it was possible to extend the prediction of the 2V3 ~ v3 frequencies. Finally, a total of 101 transitions could be observed, of which 81 transitions could be resolved. Figure 16 shows a typical spectrum of 2v3 v v3 13 transitions of CH F obtained by the IR-MW sideband laser 3 spectrometer. For the least squares fitting, a total of 296 IR-MW sideband laser frequencies of the v3 fundamental band were fitted to Eq. (64) together with the previously reported data listed in Table I. The frequencies of the v3 transitions measured in this work are shown with their estimated uncertainties in Table II. For the 2V3 . v3 hot band the frequencies shown in Table III were fit, also to Eq. (64). For the least squares fits, the data were weighted by the inverse of the square of the uncertainties shown in Tables I - III. The parameters obtained from the fitting are given for the ground state and the v = 1 state 3 in the first two columns and for the v3 = 2 state in the last column of Table IV. In these fits, the L constants were constrained to zero for the ground state, but allowed to vary for v3 = l and 2. Also, the v3 = 1 parameters obtained from the fit of the fundamental frequencies were constrained in the fit of the hot band transitions. The .aueo eagles mesa I u as aw susaasua sun-me no such o.~1 saws tees as: saws seas“ Nooaonvmcm adv mosh veusueasw cassavae boson can .souslouuooas hosed vssAOVua sauna on» new: voswsuao halo no vasa as 1 man one no lasuooae usofiaha .mu shaman MA 3.9de Ow; mm; Nm._ of. Val 01. AV— .NFvQO GAUGKN m ”.9102 o .3. nu Nun 1.3).... >. vuv. mu mu ...... sw/\\/.../ \A/ h n" V. ... \x/ 4. / aouemwsueJl 112 Table I. IR-MW Sideband This work, Table II Laser IR-MW Two-Photon Ref. 29, IR Laser Stark Ref. 16, Ref. 27, IR Laser Stark Ref. 16, Lamb Dips Ref. 27, IR-RF Two-Photon Ref. 16, Lamb Dips Ref. 27, mm Wave Ref. 8 Ref. 35 Table IV Table IV Appendix A6 Table IV Appendix A6 Table IV Appendix A6 High and low J,H: P,O,R. Low J,K: P,0,R. Low J,K: P,O,R. Q(J,E), J = 1-3; R(4,H). 0(3.x). 1101,11). R(0,0), pure rot., v3 = 0, l. R(J,K), pure rot., J = 3.5. V3 3 0, 1e 1.0- 3.0 2.0 2.0 0.2 .Uncertainty assumed in least squares fits. 113 Table II. Comparison of Observed and Calculated frequencies P(3?, 5) P(37, 6) P(37, 7) P(37. 8) P(37, 9) P(3?,10) P(3?,11) P(37,12) P(35,11) P(36,12) P(35,l3) P(36,l4) P(36,15) P(32, 7) P(32, 8) P(32, 9) P(32.10) P(32.11) P(32,12) P(32,l3) P(32,14) P(32,16) P(32,16) P(32,17) P(32,18) P(30, 0) P(30, 1) P(30, 2) P(30, 3) P(30, 4) P(30, 5) P(30, 7) P(30, 8) P(30, 9) P(30,10) lOR(10) 10P(10) 10P(10) 10P(10) 10P(10) 10P(10) lOR(10) 10P(10) lOR(10) 10P(10) 10P(10) 10P(10) 10P(10) 10P( 4) 10P( 4) 10P( 4) 10P( 4) 10P( 4) 10R( 4) 10R( 4) 108( 4) 108(.4) 108( 4) lOR( 4) 108( 4) 108( 4) 108( 4) lOR( 4) 108( 4) 108( 4) 108(10) lOR(10) lOR(10) lOR(10) 108(10) lOR(10) lOR(10) 108(10) lOR(10) lOR(10) -13736.0 -13?36.0 -13735.0 -13735.0 -13735.0 -13735.0 -13672.0 -13502.0 -13424.0 -13326.0 -13236.0' -13l26.0 -13010.0 -17836.0 -17600.0 -17356.0 -17080.0 -16784.0 -l7954.1 -17724.9 -17453.6 -17144.2 -16784.8 -16378.0 -15915.4 -15406.0 -14818.4 -14196.3 -13305.8 -12481.0 -13002.0 -13002.0 -13002.0 -12874.0 -12766.0 -12601.1 -12156.4 -11877.1 -11539.7 -11146.0 28552914.2 28652914.2 28662914.2 28562914.2 28552914.2 28552914.2 28553077.2 28553147.2 28553225.2 28563323.2 28563413.2 28553523.2 28553639.2 28696301.? 28696537.? 28696781.? 28697057.? 28697363.7 28905092.4 28906321.6 28905592.8 28905902.2 28906261.6 28906668.5 28907131.0 28907640.4 28908228.1 28908860.2 28909?40.6 28910666.4 29041070.? 29041070.? 29041070.? 29041198.? 29041316.? 29041471.6 29041916.3 29042196.6 29042533.0 29042926.? 1303 r o—cc Unc.d 24.3 OVERLAP 19.3 OVERLAP 4.3 OVERLAP -21.1 OVBRLAP -57.1 OVERLAP -104.2 OVRRLAP 0.5 2.0 0.8 3.0 -l.8 2.0 5.5 2.0 -3.7 3.0 1.1 3.0 9.1 3.0 -302 1.0 4.2 1.0 -1.1 3.0 5.7 3.0 13.5 OMIT -2.8 1.0 -3.6 1.0 -1.7 1.0 -3.7 1.0 -1.3 1.0 -0.4 1.0 3.0 1.0 -5.0 2.0 0.3 3.0 -32.9 0x11 118.0 OVERLAP 104.5 OVERLAP 23.5 OVRRLAP 7.0 OVRRLAP -42.7 OVERLAP 1.3 2.0 -0.2 1.0 -2.4 1.0 5.0 1.0 -2.7 1.0 -2.7 1.0 -l.8 1.0 962.42270( 962.42270( 962.42270( 952.42270( 962.42270(- 952.42270(- 952.42814( 962.4304?( 952.4330?( 952.43634( 962.43934( 952.44301( 952.44688( 967.20659( 967.21346( 957.22160( 957.23081( 967.24068( 964.17010( 964.17774( 964.18679( 964.19?11( 964.20910( 964.22267( 964.23810( 964.25509( 964.2?469( 964.29645(- 964.32515( 964.35266( 968.70686( 968.70586( 968.70685(- 968.71012( 968.71405( 968.71922( 968.73405( '968.?433?( 968.76463( 968.76776( 81) 64) 14) -70) 190) ' 34?) 1) z) -5) 18) -12) 3) 30) -10) 13) -3) I9) 44) -16) 1) 109) 393) 348) 78) 23) 142) 4) 0) -7) 16) -3) -9) -5) 114 Trans. Laser v.b v/MR: o-c Unc. v/cm ° P(30,11) lOR(10) -10692.6 29043380.l 1.0 968.78288( -6) P(30,12) lOR(10) -10172.7 29043900.0 1.0 968.80022( -7) P(30,l3) lOR(10) -9682.0 29044490.? 1.0 968.81993( —19) P(30,14) lOR(10) -8917.2 29045166.6' OHIT 968.84210( -62) P(29, 4) lOR(12) 12638.0 29108812.4 2.0 970.96647( 18) P(29, 6) lOR(12) 12708.0 29108982.4 2.0 970.97114( 12) P(29, 6) lOR(12) 12924.1 29109198.6 2.0 970.97834( 14) P(29, 7) lOR(12) 13187.2 29109461.6 1.0 970.98712( l4) P(29, 8) lOR(12) 13600.9 29109776.3 1.0 970.99769( 11) P(29, 9) lOR(12) 13872.8 29110147.2 1.0 97l.00999( 16) P(29,10) lOR(12) 14301.4 29110676.8 1.0 97l.02429( 3) P(29,11) lOR(12) 14806.1 29111079.6 1.0 971.04109( l6) P(29,12) lOR(12) 16382.6 29111667.0 1.0 971.06036( 20) P(29,13) lOR(12) 16040.0 29112314.4 1.0 97l.08228( 10) P(29,14) lOR(12) 16772.0 29113046.4 OMIT 971.10670( -67) P(29,l6) lOR(12) 17666.0 29113930.4 2.0 971.13619( 0) P(27, 0) lOR(20) -16942.9 29241716.7 OVRRLAP 976.39864( 22) P(27, l) lOR(20) -l6942.9 29241716.6 OVERLAP 976.39864( -47) P(27, 2) lOR(20) -l6864.6 29241794.0 2.0 976.40126( 3) P(27, 3) lOR(20) -15760.3 29241898.2 1.0 976.40473( -4) P(27, 4) lOR(20) -16608.7 29242049.8 1.0 976.40979( -4) P(27, 6) lOR(20) -l6409.6 29242248.9 1.0 976.41643( ~7) P(27, 6) lOR(20) -16168.2 29242500.3 1.0 976.42482( -6) P(27, 7) lOR(20) -l4861.6 29242807.0 1.0 976.43606( -6) P(27, 8) lOR(20) -14484.4 29243174.1 1.0 976.44729( -8) P(27, 9) lOR(20) -l4049.4 29243609.2 l.0 976.46180( -6) P(27,10) lOR(20) -l3642.3 29244116.2 1.0 976.47872( -ll) P(27,11) lOR(20) -12962.6 29244706.0 1.0 976.49839( -14) P(27,13) lOR(20) -11479.9 29246178.? 1.0 976.6476l( -8) P(27,14) lOR(20) -10678.0 29247080.6 3.0 976.67760( -23) P(27,16) lOR(20) -9641.l 29248117.6 OMIT 976.61218( -41) P(27,16) lOR(20) -8366.0 29249302.6 OMIT 976.66171( -90) P(26, 0) 10R(22) 11312.6 29307448.9 OVERLAP 977.69127( 47) P(26, l) 10R(22) 11312.6 29307448.9 OVERLAP 977.69127( -26) P(26, 2) 10R(22) 11396.6 29307632.9 2.0 977.69407( 28) P(26, 3) 10R(22) 11606.7 29307643.l 1.0 977.69776( 17) P(26, 4) 10R(22) 11668.8 29307805.2 1.0 977.60316( 18) P(26, 6) 10R(22) 11880.8 29308017.1 1.0 977.61022( 14) P(26, 6) 10R(22) 12141.3 29308277.6 1.0 977.6189l( -11) 9(26, 7) 108(22) 12476.1 29308612.6 1.0 977.63008( 12) 116 P(26, P(26, P(26, P(26, P(26, P(26, P(26, P(23, P(23, P(23, P(23. P(23, P(23, P(23, P(23, P(22, P(22, P(22, P(22, P(22, P(22, P(22, P(22, P(22, P(22, P(22, P(ZI. P(21, P(21, P(21, P(21, P(21, P(21, P(2l, P(21, P(21, P(21, P(20, P(20, P(20, 8) 9) 10) ll) 12) 13) 14) 0) l) 2) 3) 4) 6) 6) 7) 108(22) 108(22) 10R(22) 108(22) 108(22) 108(22) 10R(22) 10R(34) 10R(34) 10R(34) 108(34) 10R(34) 108(34) 108(34) 108(34) 108(38) 108(38) 10R(38) 10R(38) 108(38) 10R(38) 10R(38) 10R(38) 10R(38) 10R(38) 108(38) 108(42) 10R(42) 108(42) 108(42) 108(42) 10R(42) 10R(42) 10R(42) 108(42) 108(42) 108(42) 108(46) 10R(46) 108(46) 12868.3 13334.2 13878.3 14612.6 16247.6 16096.7 17076.0 -9968.1 -9968.1 -9872.9 -9742.3 -9663.0 -9301.9 -898?.2 -8601.3 -12078.6 -120?8.6 -11981.3 -11843.7 -11643.7 -11384.2 -11063.3 -10661.1 -10164.9 -9688.9 -8910.6 -11643.0 -11643.0 -11638.9 -11402.4 -11189.4 -10919.2 -106?6.1 -10166.3 -9649.9 -9048.0 -8336.0 -8620.7 -8620.7 -8616.9 v/Hflz 0-0 29309004.6 2.8 293094?0.6 3.? 29310014.6 2.8 29310649.0 2.8 29311383.8 2.6 29312233.1 3.4 29313211.4 3.0 29601098.6 11.4 29601098.6 -14.8 29601193.8 1.6 29601324.4 -1.2 29601613.? -1.? 29601?64.8 -1.0 296020?9.6 -l.6 29602466.4 -1.6 29664466.6 12.3 29664466.6 -16.0 29664663.8 -0.2 29664701.4 -1.6 29664901.4 -0.1 29666161.0 -2.1 29666491.8 -0.8 29666894.1 -2.3 29666380.3 -1.7 29666966.3 -2.2 2966?634.6 -2.2 2962?23?.2 12.4 2962?23?.2 -16.9 2962?341.3 2.4 296274??.8 -6.8 2962?690.8 0.? 29627961.0 -1.3 29628304.1 -1.2 29628?24.9 -1.0 29629230.3 -1.? 29629832.2 -1.1 29630644.2 2.7 29689408.? 12.4 29689408.? -17.0 29689613.4 -1.1 OOOOOOO OVERLAP OVERLAP 2.0 0? 0V AP AP 0? 07 AP AP ' N” 0906000 OOFHOOOOOO OOOHHOOOOO wwHI-IHHH HNNNI—HHHHH HHNINNNo—Hw O O OVERLAP OVERLAP 3.0 977.64316( 9??.668?0( 977.67686( 97?.69801( 977.72262( 977.76086( 977.78348( 984.06073( 984.06073( 984.06390( 984.06826( 984.0646?( 984.0?296( 984.08346( 984.09632( 986.16446( 986.16446( 986.16770( 986.17229( 986.1?896( 986.18?62( 986.19866( 986.21207( 986.22829( 986.24760( 986.27013( 988.26826( 988.26826( 988.26173( 988.26628( 988.27339( 988.28240( .988.29386( 988.30786( 988.32474( 988.34482( 988.3686?( 990.3320?( 990.3320?( 990.3366?( 9) 41) -66) -3) 116 P(20, 3) 10R(46)- -8367.9 29689661.6 -3.0 3.0 990.34061( -9) P( 6, 0) 9P(60) 16060.? 30496677.? 20.3 OVERLAP 1017.22298( 6?) P( 6, 1) 9P(60) 16060.? 30496677.? 1017.22298( -48) P( 6, 2) 9P(60) 16174.0 30496701.0 0 1.0 1017.22709( 10) P( 6, 3) 9P(60) 16364.2 30496881.2 4 1.0 1017.23310( 14) P( 6, 4) 9P(60) 16609.9 30496136.9 0 1.0 1017.24163( 13) P( 6, 6) 9P(60) 16948.6 30496476.6 1 1.0 1017.26293( 10) P( 4, 0) 9P(46) -9764.7 30600761.4 1 1 OVERLAP 1020.73120( 37) P( 4, 1) 9P(46) -9764.7 30600761.4 -2 0 OVRRLAP 1020.73120( ~76) 7 9 8 3 I ...: uh ‘3 O < I I l" > "U P( 4, 2) 9P(46) -9636.6 30600880.6 2.0 1020.73660( 8) P( 4, 3) 9P(46) -9468.1 30601048.0 - P( 1, 0) 9P(42) 16089.0 30763746.? - 0( 6, 6) 9P(40) -8989.6 30791163.0 - Q( 6, 6) 9P(40) -9366.2 30790786.6 -0.4 Q( 6, 4) 9P(40) -9644.8 30790497.9 -1.3 0( 6, 3) 9P(40) -9860.? 30790281.9 —1.3 0( 6, 2) 9P(40) -10011.9 30790130.8 -2.2 0( 6, 1) 9P(40) -10102.0 30790040.6 -3.9 0( 7, 7) 9P(40) -13064.6 3078?088.2 -2.0 0( 7, 6) 9P(40) -13601.1 30786641.6 -1.8 1020.74109( -16) 1026.83464( -6) 1027.08231( -4) 1027.07008( -1) 1027.06046( -4) 1027.06326( -4) 1027.04821( -7) 1027.04620( -13) 1026.94672( -6) 1026.93182( -6) 0( 7, 6) 9P(40) -13869.4 30786283.3 -1.2 0( 7, 4) 9P(40) -14141.0 30786001.6 -2.0 0( 7, 3) 9P(40) -14361.2 30786791.4 -1.6 0( 7, 2) 9P(40) -14498.3 30786644.3 -2.1 O( 7, 1) 9P(40) -14686.0 30786666.6 -3.6 0( 8, 8) 9P(40) -1?687.4 30782466.3 -l.7 0(12, 2) 9P(42) 16974.0 30763630.? 0. 0(12, 3) 9P(42) 16096.0 30763762.? 0(12, 4) 9P(42) 16270.? 3076392?.4 0(12, 6) 9P(42) 16498.0 30764164.? 1026.91987( -4) 1026.91048( -6) 1026.90347( -4) 1026.89866( -7) 1026.89663( -11) 1026.79218( -6) 1026.83070( 2) 1026.83477( 7) 1026.84060( 9) 1026.84818( -8) 1 0000000000 0900000900 0000000000 flOHNOQwQNN NNN 0(12, 6) 9P(42) 16796.0 30764462.? 0(12, 7) 9P(42) 17170.0 30764826.? 0(12, 8) 9P(42) 17637.2 30766293.9 0(13, 8) 9P(42) 9234.8 30746891.6 0(13, 9) 9P(42) 9771.3 30747428.0 0(13,10) 9P(42) 10408.0 30748064.? 0(13,11) 9P(42) 11183.9 30748840.6 0(13,12) 9P(42) 12110.0 30749766.? 0(13,13) 9P(42) 13218.0 30760874.? 0(16, 2) 9P(42) -108?8.0 30726778.? 1026.86812( -9) 1026.87069( -7) 1026.88618( 19) 1026.60690( 11) 1026.62380( 26) 1026.64604( 2) 1026.67092( 7) 1026.70181( 3) 1026.?3877( 2) 1024.93601( 4) WWWNWNwr-‘fdfl “waHflNh-‘Hl-i HHwNHHHNwI-i IbDOIDQQQQN” hmwd 0(1 9(1 0(2 117 0(16, 3) 9P(42) -10779.9 30?26876.9 0.2 1024.93829( 0) 0(16, 4) 9P(42) -10638.2 30727018.6 -2.0 1024.94301( -6) 0(16, 6) 9P(42) -10446.0 30727210.? -3.1 1024.94942( ‘10) 0(16, 6) 9P(42) -10189.4 3072746?.3 4.3 1024.96798( 14) 0(16, 7) 9P(42) -9881.6 307277?6.2 -1.3 1024;96826( -4) 0(16, 8) 9P(42) -9493.2 30728163.6 -0.7 1024.98121( -2) , 9) 9P(42) -9019.4 30728637.4 -1.2 1024.99701( -4) 0(16,10) 9P(42) -8434.1 30729222.6 8.1 1026.01663( 27) 0(16,12) 9P(42) -17394.1 30720262.6 - 1024.71766( -3) 0(16,13) 9P(42) -16448.0 30721208.? 1024.74922( 1) 000009000 0000090900 0060000000 0(16,14) 9P(42) -16317.0 30722339.? 0(16,16) 9P(42) -13967.6 30723699.2 0(19, 9) 9P(44) 8946.0 30683391.8 0(19,10) 9P(44) 9369.4 30683816.2 0(19,11) 9P(44) 9880.9 30684326.? 0(19,12) 9P(44) 10601.1 30684946.8 0(19,13) 9P(44) 11263.3 30686699.1 Q(19,14) 9P(44) 12160.0 30686605.8 0(19,16) 9P(44) 13260.0 30687706.8 0(19,l6) 9P(44) 14697.1 30689042.8 1024.78694( -4) 1024.83229( 8) 1023.48778( -8) 1023.60191( 12) 1023.61897( 14) 1023.63966( 7) 1023.66474( 0) 1023.69499( -22) 1023.63168( -29) 1023.67628( 2) I O O C O I O O Numhnuoaqu OQNOQODQNG dddfdflfidadfl #0 O O O O O O O O O O 0 0(21, 7) 9P(44) -17966.6 30666480.2 0(21, 8) 9P(44) -17766.4 30666690.4 0(21, 9) 9P(44) -17494.0 30666961.8 0(21,10) 9P(44) -17169.2 30667276.6 0(21,11) 9P(44) -16761.9 30667683.9 0(21,12) 9P(44) -16263.9 30668191.9 0(21,13) 9P(44) -16648.3 30668797.6 0(21,14) 9P(44) -14896.6 30669649.2 0(21,16) 9P(44) -l3986.0 30660469.8 0(23, 1) 9P(46) 16883.0 30627399.1 1022.69011( -8) 1022.69712( 0) 1022.60684( -2) 1022.61667( -12) 1022.63026( -10) 1022.64720( 12) 1022.66740( -18) 1022.69248( -17) 1022.72286( -32) OVERLAP 1021.62007( 181) II I l ”unuqownboo 05000447000000” OQOONfiwNNI-I 0° wwwpwwwwn waNHNNw—H WHNNHNHwHw 0(23, 2) 9P(46) 16883.0 3062?399.1 4 0(23, 3) 9P(46) 16883.0 30627399.1 1 0(23, 4) 9P(46) 16883.0 30627399. 1 -2 0(23 , 6) 9P(46) 16966.0 30627482. 1 0(23 , 6) 9P(46) 17041.4 30627667.6 0(23 , 7) 9P(46) 17162.9 30627669.0 0(23 , 8) 9P(46) 17287.6 30627803.? “(23 , 9) 9P(46) 17469.2 30627986.3 0(23 , 10) 9P(46) 17699.8 30628216.0 0(23,11) 9P(46) 17994.0 30628610.1 OVBRLAP 1021.62007( 134) OVERLAP 1021.62007( 48) OVERLAP 1021.62007( -81) 3.0 1021.62284( 8) 0 1021.62636( 1) 0 1021.62907( 23) 0 1021.63366( 11) 0 0 0 1021.63962( 16) 1021.64731( 10) 1021.66713( 7) 118 Trans. Laser v.b v/HR: O-Cc Unc. v/cm l . 0(26, 1) 9P(46) -l4264.0 30696262.1 OVRRLAP 1020.68146( 100) 0(26, 2) 9P(46) -l4264.0 30696262.1 OVERLAP 1020.68146( 96) 0(26, 3) 9P(46) -14264.0 30696262.1 OVERLAP 1020.68146( 83) 0(26, 4) 9P(46) -14264.0 30696262.1 OVERLAP 1020.68146( 66) 0(26, 6) 9P(46) -14264.0 30696262.1 OVRRLAP 1020.68146( 2) 0(26, 6) 9P(46) -14264.0 30696262.1 OVERLAP 1020.68146( -8?) 0(26, 7) 9P(46) -14264.0 30696262.1 OVRRLAP 1020.68146(-231) 0(26, 8) 9P(46) -14122.0 30696394.1 3.0 1020.68686( -9) 0(26, 9 9P(46) -l4026.0 30696490.1 3.0 1020.68906( -2) 0(26,10) 9P(46) -13900.3 30696616.8 2.0 1020.69326( -20) 0(26,11) 99(46) -13718.6 30696?97.6 1.0 1020.69931( -7) 0(26,l2) 9P(46) -l3481.8 3069?034.3 1.0 1020.60721( -4) Q(26,13) 9P(46) -1317?.6 3069?338.6 1.0 1020.61736( -16) 0(26,14) 9P(46) -12?72.? 30697743.6 1.0 1020.63086( 14) 0(2?, 1) 9P(48) 16647.0 30662621.3 OVRRLAP 1019.46698(-371) 0(27, 2) 9P(48) 16647.0 30662621.3 OVERLAP 1019.45698(-331) 0(27, 3) 9P(48) 16647.0 30662621.3 OVERLAP 1019.46598(-268) 0(27, 4) 9P(48) 16647.0 30662621.3 OVBRLAP 1019.46698(-188) 0(27, 6) 9P(48) 16647.0 30662621.3 OVRRLAP 1019.46698(-100) 0(27, 6) 9P(48) 16647.0 30662621.3 OVRRLAP 1019.46698( -l4) 0(27, 7) .9P(48) 16647.0 30662621.3 OVERLAP 1019.46698( 66) 0(27, 8) 9P(48) 16647.0 30662621.3 OVERLAP 1019.46698( 93) 0(27, 9) 9P(48) 16647.0 30662621.3 OVERLAP 1019.46698( 80) 0(27,10) 9P(48) 16647.0 30662621.3 OVERLAP 1019.45698( -4) 0(27,11) 9P(48) 16647.0 30662621.3 OVERLAP 1019.46698(-18?) 0(27,12) 9P(48) 16647.0 30662621.3 OVERLAP 1019.46698(-499) 0(27,13) 9P(48) 16940.0 30662814.3 2.0 1019.466?6( 2) O(27,l4) 9P(48) 17142.0 30663016.3 2.0 1019.47249( -6) O(2?,16) 9P(48) 17423.0 3066329?.3 1.0 1019.48186( -10) 0(27,16) 9P(48) 17807.0 30663681.3 3.0 1019.49467( 4) 0(32, 3) 9P(60) -12822.0 3046??06.0 2.0 1016.29326( -7) 0(32, 4) 9P(60) -12930.0 3046?697.0 3.0 1016.28964( -2) 0(32, 6) 9P(60) -l3066.0 30467461.0 3.0 1016.28611( 6) 0(32, 6) 9P(60) -13234.0 3046?293.0 1.0 1016.27960( -2) 0(32, 7) 99(60) -13422.0 30467106.0 1.0 1016.2?323( 7) 0(32, 8) 9P(60) -13637.9 30466889.l 1.0 1016.26603( 0) 0(32, 9) 9P(60) -138?6.6 30466661.4 1.0 1016.26810( -8) 0(32,10) 9P(60) -l4130.0 30466397.0 2.0 1016.24962( -10) 0(32,11) 9P(60) -14400.0 30466127.0 2.0 1016.24061( -9) 0(32,12) 9P(60) -14688.0 30466839.0 2.0 1016.23100( -23) 119 R( 6, 1) R( 6, 0) R(12, 1) R(12,12) 8(14.11) R(14,12) R(14,13) 3(14,14) R(19, 0) R(19, 1) R(19, 2) R(19, 3) R(19, 4) R(19, 6) R(19, 6) R(19, 7) R(19, 8) R(19, 9) R(19,10) R(19,11) R(19.12) R(19,13) R(19,14) R(19,16) R(19,16) R(21, 0) R(21, 1) R(21, 2) R(21, 3) R(21, 4) 9P(60) 9P(38) 9P(34) 9P(34) 9P(34) 9P(34) 9P(30) 9P(30) 9P(30) 9P(30) 9P(30) 9P(30) 9P(20) 9P(20) 9P(16) 9P(16) 9P(16) 9P(16) 99(10) 9P(10) 9P(10) 9P(10) 9P(10) 9P(10) 9P(10) 9P(10) 9P(10) 9P(10) 9P(10) 9P(10) 9P(10) 9P(10) 9P(10) 9P(10) 9P(10) 9P( 6) 9P( 6) 9P( 6) 9P( 6) 9P( 6) -14970.0 -934l.8 12777.0 12777.0 12872.0 13012.2 -12634.0 -127?4.4 -12964.9 -13077.8 -13166.0 -13166.0 9636.4 10214.0 -17960.0 -17412.4 -16724.0 ~16862.0 16000.0 16000.0 16000.0 16000.0 16000.0 16000.0 16000.0 16000.0 16000.0 16000.0 16000.0 16000.0 16278.0 16644.6 16934.3 16464.0 17162.0 -13042.0 -13042.0 -13042.0 -13132.0 -13208.0 30466667.0 30862666.? 30996967.8 30996967.8 30996062.8 30996202.9 31088968.2 31088717.8 31088637.3 31088414.4 31088327.2 31088327.2 31393436.8 31394114.4 31473477.4 31474026.0 31474713.4 31476676.4 31661843.4 31661843.4 31661843.4 31661843.4 31661843.4 31661843.4 31661843.4 31661843.4 31661843.4 31661843.4 31661843.4 31661843.4 31662121.4 31662387.9 31662777.6 31663307.4 31664006.4 31733441.8 31733441.8 31733441.8 31733361.8 31733276.8 I Ih-l O O O O O 0 I bun . O C O C O O I I¢NHHh9fiJflChh Owflhiflfllflflnflbcflfi hiOMdGM°¢DC>OW¢ HMDGDGWDOHflfifimflfl I ...; EDI II I 0" -124.8 -106.4 -77.6 -41.3 -1.7 36.0 66.0 76.8 61.7 7.4 -100.3 -O.4 -20 Ibhfifidb 2. 3. -7. -13.2 -1.2 34.1 1.1 1.4 1.0 OVERLAP OVERLAP 2.0 ODHWHFHH O OMDC>OM3 OVERLAP OVERLAP 2.0 3 2 1 2 OVERLAP OVERLAP OVERLAP OVERLAP OVERLAP OVERLAP OVERLAP OVERLAP OVERLAP OVERLAP OVERLAP OVERLAP 2.0 2.0 1.0 1.0 3.0 OVERLAP OVERLAP OVERLAP 2.0 2.0 v/cm-l . 1016.22160( 18) 1029.13048( -2) 1033.91419( 60) 1033.91419( -29) 1033.91736( 14) 1033.92204( 18) 1037.01602( -11) 1037.00800( -6) 103?.00198( -6) .1036.99788( 0) 1036.99497( -47) 1036.99497( 33) 1047.17230( 9) 1047.19494( 16) 1049.84220( -6) 1049.86047( -6) 1049.88343( -7) 1049.91218( -6) 1066.12641(-437) 1066.12641(-416) 1066.12641(-364) 1066.12641(-268) 1066.12641(-137) 1066.12641( -6) 1066.12641( 120) 1066.12641( 216) 1066.12641( 266) 1066.12641( 206) 1066.12641( 24) 1066.12641(-334) 1066.13469( -1) 1066.14368( -9) 1066.16668( 8) 1066.17426( 10) 1066.19763( -24) 1068.61368( -43) 1068.61368( -4) 1068.61368( 113) 1068.61068( 3) 1068.60814( 4) 120 R(29,13) R(30, R(30, R(30, R(30, R(30, 8) R(30, 9) R(30,10) R(30,11) R(30,12) R(32, 0) 4) 5) 6) 7) R(32, R(32, R(32, R(32, R(32, R(32, R(32, R(32, R(32o R(32,10) 9R( 9R( 9R( 9R( 9R( 9R(. 9R( 9R( 9R( 9R( 9R( 9R( 9R( 9R( 9R( 9R( 9R( 91H 9R( 9R( 9R( -13302.0 -13406.0 -13614.0 -13618.0 -13711.0 -13786.0 -10908.1 -10908.1 -11037.2 -11219.3 -11469.0 -11788.2 -121?3.6 -12626.2 -13134.3 -l3699.4 -14316.1 -149?6.8 -16679.1 -16420.4 17990.1 17640.2 17217.9 16722.2 16168.9 16636.0 14846.4 14100.0 13297.7 -11992.0 -11992.0 -12166.0 -12380.0 -12706.4 -13116.0 -13617.9 -14208.7 -14870.0 -16626.0 -16460.7 31733181.8 31733077.8 31732969.8 31732866.8 31732772.8 31732697.8 31993109.3 31993109.3 31992980.2 31992798.1 31992648.4 31992229.2 31991843.8 31991391.2 31990883.1 31990318.0 31989702.2 31989040.6 31988338.3 31987697.0 32022007.4 32021667.6 32021236.3 32020739.6 32020176.3 32019663.4 32018862.? 32018117.4 32017316.1 32079660.? 32079660.? 32079497.? 32079272.? 32078946.3 32078636.? 32078034.8 32077444.0 32076782.? 32076027.? 32076192.0 N QwOICDHNQOQw OQQOINQIDQWID NG NI OHNONOHQNH GQGQQHNWNH OH OVERLAP OVERLAP O < O < waHer-Iwwfl HNHHHHHHt-uw Nl-‘NI-‘I-IHHHI-IH H 2.0 O O O O weeeeeeeee 1:: 000000000!” E‘OOOOOOOOO 0006000000 0 O O O O O O O O 0 > '0 > '0 1068.60601( 1068.60164( 1068.49794( 1068.49447( 1068.49136( 1068.48886( 1067.17526( 1067.17626( 1067.17096( 1067.16487( 1067.16664( 1067.14590( 1067.13304( 1067.11796( 1067.10100( 1067.08216( 1067.06161( 1067.03964( 106?.01611( 1066.99139( 1068.13919( 1068.12762( 1068.11344( 1068.09690( 1068.07811( 1068.06734( 1068.03430( 1068.00943( 1067.98267( 1070.06230( 1070.06230( 1070.06686( 1070.04936( '1070.03847( 1070.02481( 1070.0080?( 1069.98836( 1069.96630( 1069.94111( 1069.91324( 121 Trans. Laser v-b v/Rflz o-c Unc.d v/cm l . R(32,ll) 9R( 8) ~17376.6 320?4277.1 0.9 2.0 1069.88272( 3) R(33, 0) 9R( 8) 16660.0 32107212.? ~16.1 OVERLAP 1070.98133( ~60) R(33, 1) 9R( 8) 16660.0 32107212.? 34.6 OVERLAP 1070.98133( 116) R(33, 2) 9R( 8) 16380.1 32107032.8 3.6 1.0 10?0.97633( 12) R(33, 3) 9R( 8) 16132.9 32106786.6 4.0 1.0 10?0.96?09( 13) R(33, 4) 9R( 8) 14784.0 32106436.? 0.6 3.0 1070.96646( 1) R(33, 6) 9R( 8) 14346.2 3210599?.9 4.0 1.0 1070.94081( 13) R(33, 6) 9R( 8) 13807.6 32106460.2 4.2 1.0 1070.92288( 13) R(33, 7) 9R( 8) 13176.0 32104828.? 4.9 3.0 1070.90181( 16) R(33, 8) 9R( 8) 12460.0 32104102.? 4.3 3.0 10?0.8?760( 14) R(36, 0) 9R(12) ~16?66.6 32160314.0 ~34.9 OVERLAP 10?2.76260(~116) R(36, 1) 9R(12) ~16766.6 32160314.0 21.6 OVERLAP 10?2.?6260( 71) R(36, 2) 9R(12) ~16961.4 32160118.1 ~6.3 1.0 1072.7460?( ~17) R(36, 3) 9R(12) ~16239.8 32169839.? ~2.3 1.0 1072.736?8( ~7) R(36, 4) 9R(12) ~16631.6 32169447.9 ~0.8 1.0 10?2.723?2( ~2) R(36, 6) 9R(12) ~17136.6 32168943.0 ~l.3 1.0 1072.?068?( ~4) R(36, 6) 9R(12) ~17763.1 32158326.4 ~2.9 1.0 1072.68630( ~9) R(37, 6) 9R(14) ~8606.2 32208686.1 ~0.1 1.0 1074.36279( 0) R(37, 7) 9R(14) ~9326.9 3220??64.3 ~3.2 1.0 10?4.33638( ~10) R(37, 8) 9R(14) ~102?3.4 32206817.9 ~4.1 1.0 1074.3038l( ~13) R(37, 9) 9R(14) ~11340.1 32206761.l 3.4 1.0 1074.26822( 11) R(37,10) 9R(14) ~12666.2 32204636.0 ~6.8 1.0 10?4.22766( ~22) R(37,11) 9R(14) ~13893.4 32203197.9 ~2.? 2.0 10?4.18306( ~8) R(37,12) 9R(14) ~16384.0 32201?07.3 -11.2 OMIT 1074.13334( ~37) R(38, 0) 9R(14) 17982.0 32236073.3 ~66.6 OVERLAP 1076.24631(~184) R(38, 1) 9R(14) 17982.0 32236073.3 11.1 OVERLAP 1076.24631( 3?) R(38, 2) 9R(14) 17776.6 32234866.8 4.2 1.0 1076.23942( 14) R(38, 3) 9R(14) 17443.2 32234634.6 4.6 1.0 1076.22833( 16) R(38, 4) 9R(14) 16972.0 32234063.3 ~1.2 2.0 1076.21262( ~4) R(38, 6) 9R(14) 16378.0 32233469.3 3.1 3.0 1076.19280( 10) R(38, 6) 9R(14) 16648.? 32232?40.0 6.2 1.0 1076.16848( 1?) R(38, 7) 9R(14) 14780.1 32231871.4 1.9 1.0 10?6.13960( 6) R(38, 8) 9R(14) 13779.6 322308?0.8 2.1 1.0 1076.10613( 7) R(38, 9) 98(14) 12640.0 32229731.3 1.2 3.0 1076.06812( 3) R(40, 0) 9R(18) ~16004.0 32281?13.1 ~6.3 3.0 1076.80204( ~20) R(40, 1) 9R(18) ~160?2.0 32281646.1 ~0.9 3.0 1076.?997?( ~2) R(40, 2) 9R(18) ~16292.? 32281424.4 ~1.6 1.0 1076.79241( ~4) R(40, 3) 9R(18) ~16659.0 32281058.0 ~1.0 1.0 10?6.78019( ~3) R(40, 4) 9R(18) ~16174.0 32280643.1 ~2.2 1.0 1076.76302( ~7) R(40, 6) 9R(18) ~16832.6 322?9884.6 0.2 1.0 1076.74106( 0) 122 Trans. Lasera v.b v/MRa o-c Unc. v/cm . R(40, 6) 9R(18) ~17641.0 32279076.1 0.8 2. 10?6.71408( 2) R(42, 0) 9R(20) ~9633.9 32326700.1 ~4.4 2. 1078.26929( ~14) R(42, l) 9R(20) ~9714.6 32326619.6 ~4.8 2. 1078.26660( ~16) R(42, 2) 9R(20) ~9966.2 32325378.9 ~6.0 1. 1078.26868( ~16) R(42, 3) 9R(20) ~10363.0 32324981.1 ~1.? 1. 1078324631( ~6) R(42, 4) 9R(20) ~109l4.9 32324419.1 ~1.7 1. 1078.22666( ~6) R(42, 6) 9R(20) ~11636.8 32323697.2 0.0 l. 1078.20248( 0) R(42, 6) 9R(20) ~12623.3 32322810.? 0.0 2. 1078.17291( 0) R(42, 7) 9R(20) ~13673.2 32321760.8 1.8 2. 1078.13789( 6) R(42, 8) 9R(20) ~14796.0 32320638.0 -0.6 3. 1078.09710( ~1) R(42, 9) 9R(20) ~16196.6 32319138.4 ~6.8 2. 1078.06042( ~19) R(42,10) 9R(20) -17763.2 32317670.9 1.8 2. 1077.99813( 6) R(43, 0) 9R(20) 11392.0 32346726.0 4.6 2. 1078.97064( 14) R(43, 1) 9R(20) 11310.1 32346644.1 6.1 2. 1078.96791( 20) R(43, 2) 9R(20) 11063.4 32346387.4 0.2 2. 1078.96934( 0) R(43, 3) 98(20) 10642.0 32346976.0 7.0 1. 1078.94662( 23) R(43, 4) 9R(20) 10066.0 32346390.0 7.0 3. 1078.92608( 23) R(46, 3) 9R(22) 12839.7 32386996.9 2.2 2. 1080.28064( 7) R(46, 4) 9R(22) 12200.0 32386356.2 ~3.4 3. 1080.26920( ~11) R(46, 6) 9R(22) 11394.0 32384660.2 7.6 2. 1080.23232( 24) R(46, 6) 9R(22) 10366.0 32383622.2 ~18.7 1080.19803( ~62) R(47, 0) 9R(24) 14110.0 32424296.? ~4.6 1081.66809( ~16) R(47, 1) 9R(24) 14008.0 32424193.? ~9.4 108l.66468( ~31) R(47, 2) 9R(24) 13718.8 32423904.6 ~7.1 1081.64604( ~23) R(47, 3) 9R(24) 13246.6 32423431.2 6.9 1081.62926( 19) R(47, 4) 9R(24) 12668.0 32422763.? 10.1 1081.60666( 33) .002 laser line used. bMicrowave frequency in M82. The signed microwave frequency is added to the laser frequency to obtain the absorption frequency. cObserved minus calculated frequency in MHz. d Estimated uncertainty in the observed frequency in M82. The parameters for the calculation are in the last two columns of Table IV. An "0M1T" and an "0V3RLAP" mean that the frequency was omitted from the least squares fits and the transition was overlapped by another transition(s), respectively. °0bserved frequency in cm_1. The numbers in parentheses are _1 the observed minus calculated frequencies in units of 0.00001 cm . 123 Table III. Comparison of Observed and Calculated Frequencies in the 2V3 ~ V3 Band of 1303311 Trans. Laser v.b v/MRs 0~Cc Unc.d v/cm ° P(26, 3) 10R( 4) 12492.0 28936638.4 ~3.8 3.0 966.18667( ~12) P(26, 4) lOR( 4) 12691.? 28936738.1 ~6.2 2.0 966.19233( ~17) P(26, 6) lOR( 4) 12961.4 28936007.8 ~2.3 2.0 966.20133( ~7) P(26, 6) 10R( 4) 13306.9 28936362.3 4.1 2.0 966.21282( 13) P(26, 7) 10R( 4) 13722.0 28936?68.4 4.? 3.0 966.226?0( 16) P(26, 8) lOR( 4) 14196.3 28937242.? ~19.7 OMIT 966.24262( ~66) P(26, 9) 10R( 4) 14818.4 28937864.8 16.6 OMIT 966.2632?( 66) P(24, 3) 10R( 8) ~12131.0 28999001.0 ~2.2 2.0 967.30266( ~7) P(24, 4) 10R( 8) ~11923.0 28999210.0 ~1.1 2.0 96?.30962( ~3) P(24, 6) 10R( 8) ~11646.0 28999487.0 0.8 2.0 967.31876( 2) P(24, 6) 10R( 8) ~11298.0 28999836.0 0.8 2.0 967.3303?( 2) P(24, 7) 10R( 8) ~10870.0 29000263.0 1.8 2.0 96?.34466( 6) P(24, 9) 10R( 8) ~9760.0 29001373.0 ~0.7 2.0 967.38167( ~2) P(22, 0) 10R(14) ~13793.1 29123943.0 9.6 OVERLAP 971.4701?( 32) P(22, 1) 10R(14) ~13?93.1 29123943.0 -20.3 OVBRLAP 971.4701?( ~67) P(22, 2) 10R(14) ~13680.3 29124066.9 2.1 2.0 971.4?393( 6) P(22, 3) 10R(14) ~13629.6 29124206.6 -0.2 1.0 9?1.47896( 0) P(22, 4) 10R(14) ~13311.7 29124424.4 ~0.8 1.0 971.48623( ~2) P(22, 6) 10R(14) ~13023.8 29124712.4 ~1.2 3.0 971.49683( ~4) P(22, 6) 10R(14) ~12667.1 29126079.0 1.6 3.0 971.60806( 6) P(22, 8) 10R(14) ~11682.0 29126064.1 ~1.8 2.0 971.64069( ~6) P(22, 9) 10R(14) ~11066.0 29126680.1 ~1.2 3.0 9?1.6614?( ~4) P(22,10) 10R(14) ~10336.0 29127400.1 -0.3 3.0 971.68649( ~1) P(21, 8) 10R(16) 9366.0 29187821.? ~0.7 3.0 973.60093( ~2) P(21, 9) 10R(16) 9997.6 29188463.3 ~4.7 3.0 973.62200( ~16) P(21,10) 10R(16) 10736.6 29189192.2 2.8 3.0 973.64666( 9) P(20, 0) lOR(20) ~10833.8 29246824.? 13.9 OVERLAP 9?6.66906( 46) P(20, 1) lOR(20) ~10833.8 29246824.? ~17.2 OVERLAP 976.66906( ~67) P(20, 2) lOR(20) ~10722.3 29246936.3 0.4 2.0 976.67278( 1) P(20, 3) lOR(20) ~10662.1 29247096.4 2.1 1.0 9?6.67812( 6) P(20, 4) lOR(20) ~10337.7 2924?320.9 0.4 2.0 976.68661( 1) P(20, 6) lOR(20) ~10041.5 29247617.0 ~1.6 1.0 976.69649( ~4) P(20, 6) lOR(20) ~9666.7 29247991.9 ~2.l 2.0 976.60799( ~6) P(20, 7) lOR(20) ~9206.0 29248462.6 -0.4 3.0 976.62336( ~1) P(20, 8) lOR(20) ~8667.9 29249000.6 ~1.4 3.0 976.64164( ~4) P(19, 6) 10R(22) 12440.0 29308676.4 3.7 3.0 977.62888( 12) P(19, 8) 10R(22) 13460.0 29309696.4 4.1 3.0 97?.66290( 13) P(l9, 9) 10R(22) 14108.0 29310244.4 ~0.1 2.0 ‘97?.68461( 0) P(17, 0) 10R(30) ~16?27.6 29426756.8 1 .0 OVERLAP 981.67092( 63) P(17, 1) 10R(30) ~16727.6 29426766.8 ~16.2 OVERLAP 981.67092( ~63) 124 P(17, 9) P(17,12) P(16, 6) P(16, 6) P(16, 7) P(16, 8) P(16, 9) P(16,12) P(13, 0) NH. 1) P(13, 2) P(13, 3) P(13, 4) 9(13. 5) P(13, 6) P(13, 7) P(12, 0) P(12, 1) P(12, 2) P(12, 3) P(12, 4) P(12, 6) P(12, 6) P(12, 7) 9(12. 8) n( 3. 0) n( 3, 1) n( 3, 2) n( 3, 3) n( 5, 0) n( 5. 1) n( 5, 2) n( 5. 3) 108(30) 10R(30) 10R(30) 108(30) 108(30) 108(30) 108(30) 108(30) 10R(30) 10R(32) 108(32) 108(32) 10R(32) 108(32) 108(32) 10R(44) 108(44) 108(44) 10R(44) 108(44) 10R(44) 108(44) 10R(44) 108(48) 10R(48) 108(48) 10R(48) 10R(48) 108(48) 108(48) 10R(48) 108(48) 9P(48) 9P(48) 9P(48) 9P(48) 9P(46) 9P(46) 9P(46) 9P(46) ~16613.7 ~16462.2 ~16218.2 ~14909.7 ~14626.8 ~14064.3 ~13490.0 ~12823.6 ~10218.0 9216.0 9606.4 10082.0 10646.1 11316.9 13938.0 ~10481.3 ~10481.3 ~10367.4 ~10202.0 ~9966.0 ~9666.6 ~9266.2 ~8787.4 ~11611.8 ~11611.8 ~11496.8 ~11336.1 ~11100.4 ~10788.4 ~10398.2 ~9921.0 ~9360.0 ~11426.7 ~11426.7 ~11366.9 ~11260.6 16249.8 16249.8 16249.8 16393.6 29426869.6 29427031.2 29427266.1 2942?673.6 29427967.6 29428429.0 29428993.3 29429669.? 29432266.3 29486376.9 29486767.3 29487242.9 29487807.0 29488477.8 29491098.9 29668374.6 29668374.6 29668488.4 29668663.8 29668889.8 29669200.3 29669689.6 29660068.4 29714782.9 29714782.9 29714897.9 29716068.? 29716294.4 29716606.4 29716996.6 29716473.8 29717044.8 30634448.6 30634448.6 30634607.6 30634613.? 30626766.0 30626766.0 30626766.0 30626909.? o-c one.d 0.7 2.0 -1.4 1.0 -o.7 1.0 0.8 1.0 ~1.6 1.0 -2.3 1.0 -3.o 3.0 -o.9 2.0 3.2 3.0 2.8 3.0 4.8 2.0 5.5 2.0 1.2 3.0 3.2 3.0 -4.0 3.0 18.6 OVERLAP -14.o OVBRLAP 1.8 2.0 1.7 3.0 2.0 1.0 2.1 1.0 0.7 2.0 1.5 3.0 16.8 OVERLAP -15.7 OVERLAP 1.4 2.0 -2.9 1.0 -2.5 2.0 -o.3 1.0 -o.1 1.0 -o.2 2.0 —2.0 3.0 29.2 OVBRLAP 7.8 OVERLAP 1.8 2.0 ~1.8 2.0 31.7 OVERLAP 13.0 OVRRLAP -43.5 OVERLAP 4.1 2.0 981.67471( 981.68010( 981.68791( 981.69820( 981.61100( 981.62673( 981.64666( 981.66778( 981.76470( 983.66966( 983.6?268( 983.68866( 983.60737( 983.62974( 983.71717( 989.29689( 989.29689( 989.30068( 989.30620( 989.31407( 989.32443( 989.33742( 989.36339( 991.1784?( 991.1784?( 991.18230( 991.18767( 991.19663( 991.20693( 991.21896( 991.23487( 991.26391( 1018.61967( 1018.61967( 1018.62164( 1018.62608( 1021.66669( 106) 1021.66669( 1021.66669(~146) 1021.67039( 43) 13) 126 R(13, 8) R(13, 9) R(13,10) R(13,11) R(20, 0) R(20, R(20, R(20, R(20, R(26, 9P(46) 9P(46) 9P(38) 9P(38) 9P(34) 9P(34) 9P(34) 9P(34) 9P(34) 9P(34) 9P(34) 9P(34) 99(34) 9P(34) 9P(26) 9P(26) 9P(26) 9P(26) 9P(26) 9P(20) 9P(20) 16626.0 16713.0 ~17994.0 ~17696.0 ~17340.0 ~17340.0 ~17340.0 ~17312.0 ~17120.0 ~17002.0 ~16860.0 ~16644.0 ~16398.0 ~16102.8 13388.0 13388.0 13178.0 13096.0 12863.0 16940.0 16226.9 30626041.1 30626229.2 30843903.6 30844201.6 30966860.8 30966860.8 30966860.8 30966878.8 30966070.8 30966188.8 30966340.8 30966646.8 30966792.8 30967088.0 31230149.3 31230149.3 31229939.3 31229867.3 31229624.3 31399840.4 31399126.3 O-C Unc. ~3.1 2.0 ~0.6 3.0 ~0.6 3.0 ~2.2 3.0 17.3 OVERLAP 12.3 OVERLAP ~3.3 OVERLAP ~3.1 3.0 ~2.0 3.0 ~1.1 3.0 ~3.9 3.0 3.1 2.0 1.3 3.0 0.3 2.0 ~14.3 OVERLAP ~3.9 OVERLAP 6.4 2.0 6.0 2.0 ~0.2 2.0 3.1 2.0 ~2.l 2.0 1021.6747?( 1021.68104( 1028.84188( 1028.86182( 1032.90960( 1032.90960( 1032.90960( 1032.91063( 1032.91694( 1032.92087( 1032.92694( 1032.93282( 1032.94102( 1032.96087( 1041.72666( 1041.72666( 1041.71864( 1041.?1691( 1041.70814( 1047.38694( 1047.36212( 2 laser line used. bMicrowave frequency in M82. The signed microwave frequency is added to the laser frequency to obtain the absorption frequency. cObserved minus calculated frequency in M82. calculation are in the last two columns of Table IV. d The parameters for the Estimated uncertainty in the observed frequency in M82. An ”0H1?” and an ”OVRRLAP” mean that the frequency was onitted from the least squares fits and the transition was overlapped by another transition(s), respectively. °Observed frequency in cm- the observed minus calculated frequencies in units of 0.00001 CI- . 1 The nunbers in parentheses are 1 126 Table IV. Vibration-Rotation Parameters for 13083?. Parameter v3 = 0b v3 = 1b v3 2c,e 8v /682 0 0000d 30803.4726(8) 61147.??1(3) 8v /M82 .24862.6460(34) 24542.1246(36) 24231.981(36) 0(Av-Bv) /M82 0.0000 31.3483(660) 57.308(294) DJ /k82 57.7386(166) 55.0634(147) 52.808(193) DJ! /k82 424.7361(2862) 477.5682(3141) 616.664(1968) ADK /k8z 0.0000 ~69.8691(10668) ~115.?18(6968) HJ /82 ~0.0172(100) ~0.1349(97) ~1.443(417) HJR /82 1.5816(1426) 9.8696(1894) 23.931(4992) HRJ /82 20.3809(13806) ~40.2484(l6926) ~64.366(23928) 08x /82 0.0000 56.9988(62308) 208.862(61690) LJ /m82 . 0.0000d 0.0078(16) 1.600(303) LJJJK /m82 0.0000d ~0.7666(433) ~17.569(4004) LJJRR /m82 0.0000d 11.3394(6012) 64.984(23322) I.Jxxx /m82 0.0000d ~81.6816(27627) ~362.961(101561) AL /m82 0.0000 49.2839(118569) ~700.266(204238) aVibration-rotation parameter. 0? = P(va) ~ P(v3=0). 127 bObtained from fit of frequencies indicated in Table I and listed in Table 11. Number in parenthesis is one standard error in units of last digit in the parameter. cObtained from fit of frequencies in Table III. Parameters for v =1 were constrained to values shown in this table. Number 16 parenthesis is one standard error in units of last digit of the parameter. dConstrained to zero in the least squares fit 8It should be noted that the parameters for v =2 are given to one less significant figure than the paramet rs for v3=0 and 1. 128 standard deviations for an object of unit weight (SD) were 2.46 and 1.37 M82 (r.m.s. deviations 3.38 and 2.49 M82) for the fits to the fundamental and hot band frequencies, respectively. If the L constants for the v3 = 1 state were constrained to zero for the fundamental frequencies, the SD rose to 9.77 M82. In addition, there was a definite increase in the residual for increasing J and K. On the other hand, allowing the L constants to vary for the ground state led to only a slight improvement in the $0 (from 2.46 to 2.44 M82). These findings are probably a result of the v3 ~ "6 Coriolis coupling, which strongly affects the energies for v3 = 1 and 2. The effect of this coupling can 2 and be expanded in a power series in J(J+1) and 8 apparently L constants are required to calculate the frequencies to within a few M82 for the high J’s($47) and K’s($16) in the present study. The standard deviation for an object of unit weight obtained from the fit of the 03 fundamental band (2.45 M82) is more than twice the value expected (1.00 M82) if the uncertainties are accurately estimated. This large value of the SD is probably the result of model error rather than underestimation of the experimental uncertainty. The SD for the 2V3 ~ v3 hot band (1.37 M82) was much closer to the expected value, which can be explained as being a result of smaller effects of model error for the lower J’s and 8’s 129 included in the fits of the hot band. The least squares fits to Eq. (64), although providing an accurate representation of the experiaental frequencies, are not entirely satisfactory. Part of the problem is the unexpectedly large SD just discussed. In addition, however, there is a question of convergence of that part of the Zn expansion having to do with K This is best seen by calculating the contributions from the terms involving 00K, 8’ and ALK. For the largest K(=16) value studied, there 8 is slow convergence in these terms (e.g., oRKKG/OLKK - OH 4.5). For large K values, however, the convergence rapidly decreases and for 8:40, which is still snaller than the largest J values studied, these terms are diverging. For these reasons, the values in Table IV, especially the L constants, should be regarded as fitting constants for the range of J and K values studied (Tables II and III). In order to try to obtain a convergent set of parameters to represent the experimental frequencies for the fundamental band, several fittings to equations in the forms of a Pade approximant(76), which is famous for fits of the 883 inversion frequencies, were applied. The first Pade form tried was similar to Young’s form(76,77), which was applied to the 883 inversion frequencies with a great success. This can be expressed as 130 m+n$3 . n Bp(v.J.x) = t 50 nEOB-n f g 1/[1 + blof + bale] (84) where f = J(J+l) and g = 82. Least squares fits with this Pade approximant form of the energy showed exceptionally high correlations between the parameters, even when the denominator and the coefficients of K2n were omitted for the ground state. The second Pade approximant tried is Burenin’s form(78) given by a + z z n f'g” 0 mu 8 : 1$n+n$2 (85) 1 + R Z Z 8 f g 1$m+n$3 And the last one tried is Watson’s form(79,80), which is z z 8 f'gn n+822 mn f + B g + 01 1+b10f+b E = R0 + B10 (86) 018 The application of Watson’s form of Pade approximant to the experimental frequencies worked very well for the case of m+n i 3. Of a total of 24 parameters used for this fit, 6 parameters (80, 801, 802, 803, blo, and b01) for the ground state were fixed to zero. The least squares fits to Eq. (86) showed good convergence and small deviation in the 131 region of high J and K values. Also, the fitting uncertainty is much better compared to the fits to Eq. (64). Moreover, the SD was improved to 2.99 M82 (r.m.s. deviation 3.77 M82) for these fits, which proves that the Watson’s form of Pade approximant is very useful for high J and 8 region. The fitting parameters to Eq. (86) are given in Table V. No attempt was made to include the Coriolis interaction explicitly because there is not enough information available for the interacting bands (v6 or 03 + v6). The data in Table IV are sufficient to allow estimation of the first 3 constants in an expansion of the 13 vibration-rotation parameters for 083F in powers of v3. If a parameter P(v) is expressed as P(v) = p(0) + clv + czvz (87) then c1 = [9(0) - 29(1) + p(2)]/2 (88) and c2 = -[3p(0) - 49(1) + p(2)]/2 . (89) The values of P(O), c1, and c2 for the vibrational energy, 132 Table V The Fitting Parameters of Watson’s Form of Pade Approximant for 93 Band of CHSF Parameters v3 = 08 v3 = la n /682 0.00000” 30803.47561(0) 910 /M82 24862.64766(0) 24542.11570(0) 801 /MHz 0.00000” 31.05489(4) 820 /k82 57.72178(2) ~55.04668(2) ”11 /k82 424.7889?(34) ~476.49688(33) 302 /k82 0.00000” 72.73522(42) 830 /82 -0.03717(1) -2.46022(30) 321 /82 1.86983(17) 55.65918(355) 812 /82 19.3511?(165) 528.1?178(1466) 803 /82 0.00000” ~41.25928(266) blo x 103 0.00000” 41.93419(550) 501 x 103 0.00000” ~120.51669(2989) 8Obtained from fit of frequencies indicated Table I and listed in Table 11. Number in parenthesis is one standard error in units of last digit in the parameter. bConstrained to zero in the least squares fit. 133 Table VI. Vibrational Dependence of Vibration-Rotation Parameters for 130831‘ 9(v)a 9(0)” c1” c2” Ev /082 0 000 v3 = 31033.060(2) x33 = ~229.587(1) av /M82 24862.646(3) -23 = -325.710(20) 5.189(18) oAv /an 0.000 -ag = -291.668(197) 2.494(162) DJ /k82 57.739(15) -2.885(103) 0.210(98) DJK /k82 424.736(285) 59.730(1239) ~6.908(1038) 0DK /k82 0.000 -81.859(4081) 12.000(3639) aVibration-rotation parameter. P(v) = P(O) + c v + c v2. P(O), c1, and c2 were derived from the parametgrs in Table IV. bUncertainties in parentheses, in units of the last digit in the parameter, were propagated from one standard error in the parameters. ' 134 rotational constants, and quartic distortion paraneters are given in Table VI together with the more conventional symbols for some of them. v3 Fundamental and 203 ~ 03 Hot Bands of 12C83? By using 8 MW feedback controlled 002 infrared laser- MH sideband laser, more than 30 C02 laser lines ranging from 108(40) ~ 98(26) were tuned according to the predictions of approximate frequencies for the v3 fundamental band of 12083? obtained from many transitions observed previously. However, the predictions turned out to be not so accurate, particularly for high J and K transitions in the P branch. By scanning the M8 frequency from 8.2-12.2 682 and fro- 12.4-18.0 682 for each CO2 laser line, a total of 266 v3 fundamental band transitions could be observed, of which 212 transitions could be resolved, and of which 206 transitions were used for the vibration-rotation analysis. The estimated accuracy of these frequencies is 1~3 M82, depending on the signal to noise ratio of the spectra. Figure 17 shows a typical spectrum from the v3 band of 12C831? obtained by the MW feedback controlled IR-MW sideband system. For the least squares fits, the data were weighted by the inverse of the square of the uncertainties shown in 136 .vees as: sewn seasn Nooauuvua one loan veueuessu unencume sets" ssh .easaessuu was sauna-ea assess-a floss stone Issuoeae sank .aamus on» as Issaooas one son anon! an: ass omen ena as Issuosaa one son shoal ecu: -esseeess asseeuuav as veausaao one: snooeae 029 .seuelosaosaa hosed vssaev«e 381nm ve~nosasoo musavoeu :2 sad: soagasso same no was; a. .28 no .9220... 2.0-ass «- .e- cuss-s A NIGV .Ommn- 00.9 mh.¢_ Nmé. mwé. #40:! Om.n_ Qua.- Eo na- 1 mux a mux mu m.. \xz. “u .inv .\1 xxx. ,\ H . \\/m . . aouemwsueu 136 Table VII, and the present data were combined with the available millimeter wave and laser-based frequencies and fitted by least squares adjustment of the parameters. 12683F was observed with the same instrument as the v3 fundamental band. According to The 293 ~ 03 hot band of the rough predictions based on the data from a previously published IR laser Stark experiment(16), a total of 11 CO2 laser lines were tuned while sweeping the microwave frequency from 8.2-12.2 682 and/or from 12.4-18.0 682. From these measurements, a total of 84 transitions in the 293 ~ 93 hot band could be observed, of which 70 transitions were resolved and used for the least squares fits. The estimated accuracy was again 1~3 M82 depending on the S/N. In the fit of the 203 ~ v3 transitions the energy levels of the v3 = 1 state were assumed from the fit of the v3 = 1 ~ 0 transitions. With the same method as 13 683?, the transitions of v3 fundamental and 203 ~ v3 hot bands were fitted to Eq. (64). With the L constants being constrained to zero for the ground state and allowed to vary for v3 = l and 2 state, the standard deviations for an object of unit weight were 1.33 and 1.37 M82 (r.m.s. deviations 7.43 and 2.22 M82) for the fits to the fundamental and hot bands frequencies, respectively. If the L constants are allowed to vary for the ground state, the SD was slightly decreased to 1.29 M82. Tables 13? Tab1e 711. This work, Table VIII IR-MM Sideband Laser IR-MM Two-Photon IR Laser Stark IR Laser Stark Lamb Dips IR~RT Two-Photon Waveguide Laser Diode Laser FIR Emission mm lave Lamb Dips ms lave Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. Ref. 23, 29, 16, 16, 16, 40, 24, 24, 26, 17, 7. Table Table Table Table Table Table Table Table Table Table Table Table Table Table III III III III 2 1 71 I High and low J,K; P,Q,R. 8igh J,E; Low J; 0,R. P,R. Low J; P,0,R. Low J; P,0,R. 0(1.l). 0(2.2)- 0(12,2). 0(12,3). 0(12,l), 0(12,2). nigh J,l; 0, High J,I; P, B. High J, pure rot., v3 = 0 and l. R(l-3ox)0 pure rot., v3 = 0. R(4,l), pure rot., v3 = . R(0.0). v3 = 1. pure rot., R(l.l). v3 = 1. pure rot., High and low J; pure rot., v3 = R. 0. P(l,0). 3.0 ' 10.0 10.0 6.0 6.0 1.0 1.0 1.0 0.6 10.0 30.0 6.0 0.01 0.1 0.6 ---------------------------------------------------‘----—---------- .Uncertainty assumed in least squares fits. 138 VIII and IX show the measured frequencies with their estimated uncertainties for the v3 and 293 ~ v3 transitions, respectively. The parameters in Table X were obtained from fits to Eq. (64) in which the L constants were constrained to zero for the ground state. 12 13 The small SD for 683? compared to CR3! can be explained as being the result of the lower maximum J(=39) value (J S 4? on 13 1268 683F) and a larger number of data for 3?. The molecular parameters for the vibrational ground state were conpared with the data obtained from combination difference of several thousand transitions by Graner(39). Table XI shows the comparison between two data, in which the present parameters are in very good agreement with the previous ones. The least squares fits of the v3 = 1 transitions to 13 Eq. (86) were done by the same method as for C8 F by 3 constraining 6 parameters for the ground state to zero and allowing the other parameters to vary. The results show that the SD decreased to 1.63 M82 (r.m.s. deviation 7.39 M82) and the fitting uncertainties are much improved. This phenomenon can be explained in the same way as for 13C83F. The fitting parameters to Eq. (86) are shown on Table XII. Also the vibrational dependence of vibration-rotation 12 parameters for C83? is given in Table XIII. 139 Table VIII. Comparison of Observed and Calculated Frequencies in the v3 Band of 12 08 F P(30,10) P(30,11) P(30,12) P(30,13) P(30,14) P(30,16) P(29, P(29, P(29, P(29, P(29, P(29, P(29, P(29, P(29, P(29, P(l6, P(l6, P(l6, P(l6, P(l6, P(l6, P(15. P(l4, P(l4, P(l4, P(l4, P(l4, P(l4, P(l4, 108(40) 10R(40) 108(40) 108(40) 108(40) 108(40) 108(40) 108(40) 108(40) 108(40) 108(40) 108(40) 10R(40) 108(40) 10R(40) 108(40) 108(46) 108(46) 108(46) 108(46) 108(46) 108(46) 10R(46) 108(46) 108(46) 108(46) 9P(46) 9P(46) 9P(46) 9P(46) 9P(46) 9P(46) 9P(46) 9P(44) 9P(44) 9P(44) 9P(44) 9P(44) 9P(44) 9P(44) 10610.0 10610.0 10610.0 10708.0 10791.0 10896.0 11036.0 11196.0 11396.6 11616.4 11870.6 12162.0 12481.8 12830.0 13209.9 13618.0 ~9630.6 ~9630.5 ~9630.6 ~9418.8 ~9313.4 ~9182.0 ~9014.6 ~8813.6 ~86?6.1 ~8294.0 ~10176.8 ~10176.8 ~10031.6 ~9820.3 ~9616.1 ~9113.1 ~8604.6 ~13761.7 ~13761.7 ~13693.9 ~13374.0 ~13069.9 ~12647.9 ~12124.6 29618718.1 29618718.1 29618718.1 29618816.1 29618899.1 29619003.1 29619143.1 29619304.1 29619604.? 29619?23.6 29619978.? 29620270.1 29620689.9 29620938.1 29621318.1 29621?26.1 29688498.8 29688498.8 29688498.8 29688610.6 29688?16.0 29688847.3 29689014.? 29689216.? 29689463.2 29689736.3 30600340.3 30600340.3 30600484.? 30600696.8 30601000.1 30601403.1 30601911.6 30660684.1 30660684.l 30660851.9 30661071.? 30661386.8 30661797.9 30662321.2 6.8 ~6.3 ~39.0 2.0 I ah! H NMHHH00 H0~3000HHON NOHN~IGO0NG 0000003 HNIII I uh 40000000 H0000001~00 NIFQHQGQQQO 0000000 I 0 II hiH NCO OVERLAP OVERLAP OVERLAP 3.0 ashu—n5wi hndnawueha 00000 000000 OVERLAP OVERLAP OVIRLAP 2.0 HHNN coco 2. OVERLAP OVERLAP OVERLAP 1.0 1.0 hahud 000 OVERLAP OVERLAP 1.0 thhiF' 0000 987.97409( 987.97409( 987.97409(- 987.97736( 987.98013( 98?.98360( 987.98827( 987.99364( 988.00033( 988.00763( 988.01614( 988.02686( 988.03663( 988.04814( 988.06082( 988.07443( 990.30173( 990.30173( 990.30173(~ 990.30646( 990.30897( 990.31336( 990.31893( 990.32564( 990.33366( 990.34297( 1020.71748( 1020.71748( 1020.72230( 1020.72934( 1020.73949( 1020.76293( 1020.76990( 1022.73033( 1022.73033(~ 1022.73693( 1022.74326( 1022.76374( 1022.76749( 1022.78494( 1m ~17) 129) 6) ID ~1) 12) ~1) 16) ~10) ~19) ~9) ~3) 2) 18) 26) 40) -5) 144) -7) 8) 2) 3) -4) ~20) ~20) 79) ~69) 1) -3) -2) 1) 4) 5) 13?) ~10) ~6) -2) -5) -3) 140 P(l4, 7) 9P(44) ~11480.8 30662964.9 ~ 0 1022.80642( ~2) P(l4, 8) 9P(44) ~10701.3 30663744.6 0 1022.83242( 1) 0 0 P(l4, 9) 9P(44) ~9769.6 30664676.l 1022.86360( 2) P(14,10) 9P(44) -8664.0 30665781.8 P(l3, 0) 9P(42) ~17238.8 30720417.9 P(l3, 1) 9P(42) ~17238.8 30720417.9 P(l3, 2) 9P(42) ~17079.2 30720677.6 P(l3, 3) 9P(42) ~16867.8 30720798.9 P(l3, 4) 9P(42) ~16637.2 30721119.6 P(l3, 6) 9P(42) ~16112.8 30721643.9 . 1022.90038( 0) OVERLAP 1024.72284( 64) OVERLAP 1024.72284( ~82) 1.0 1024.72816( 7) 1024.73666( ~1) 1024.74624( ~1) 1024.76040( 0) I N 1- P(13, 6) 9P(42) ~16676.7 30722080.0 P(l3, 7) 9P(42) ~14916.6 30722740.2 P(l3, 8) 9P(42) ~14117.0 30723639.8 P(l3, 9) 9P(42) ~13159.7 30?24497.0 P(l3,10) 9P(42) ~12022.6 30725633.9 P(l3,11) 9P(42) ~10676.0 30726981.? P(l3,12) 9P(42) ~9078.1 30728678.6 P(12, 8) 9P(40) ~17469.l 30782673.6 P(12, 9) 9P(40) ~16488.2 30783664.6 P(12,10) 9P(40) ~16321.6 30784821.2 1024.77828( 0) 1024.80030( 0) 1024.82697( 0) 1024.86890( 0) 1024.89683( ~4) 1024.941?8( ~6) 1024.99606( 3) 1026.79947( 0) 1026.83219( 0) 1026.87110( 0) I HwOQmmmHI—O HOthHOOINN 0000I-iI-‘0000 OOON-hmoooo [03000000000 0O000I—‘NI—‘N0 HHN00000H0 HQONQQOQhQ r-I I-‘I-‘I-flI-‘HI-‘HHHH I-u-n-I 0 0000000000 000 P(12,11) 9P(40) ~13940.6 30786202.1 P( 6, 0) 9P(28) 14967.8 31174476.0 P( 6, 1) 9P(28) 14967.8 31174476.0 P( 6, 2) 9P(28) 16136.0 31174644.2 P( 6, 3) 9P(28) 16378.8 311?4887.0 P( 6, 4) 9P(28) 16724.3 31175232.4 P( 4, 0) 9P(26) 11481.4 31228242.? P( 4, l) 9P(26) 11481.4 31228242.? P( 4, 2) 9P(26) 11648.0 31228409.3 P( 4, 3) 9P(26) 11889.3 31228660.6 1026.91716( ~9) OVBRLAP 1039.86869( 74) OVERLAP 1039.86869( ~83) 1.0 1039.87420( 0) 1.0 1039.88230( 3) 2.0 1039.89382( 0) OVERLAP 1041.66206( 76) OVERLAP 1041.66206( ~80) 1.0 1041.66761( 1) 1.0 1041.67666( 3) NNI I I N N 0(39,12) 9P(36) ~16133.6 30907781.9 0(38, 9) 9P(36) 14669.9 30937686.3 0(33, 3) 9P(32) 17624.0 31060342.l 0(33, 4) 9P(32) 17420.0 31060138.1 0(33, 6) 9P(32) 17168.0 31069876.l 0(33, 6) 9P(32) 16839.1 31069667.2 0(33, 7) 9P(32) 16470.6 31069188.6 0(33, 8) 9P(32) 16029.2 31068747.3 0(33, 9) 9P(32) 16623.3 31068241.4 0(33,10) 9P(32) 14946.6 31067664.6 2.0 1030.97263( 1) 2.0 1031.96676( 6) OMIT 1036.06149( ~39) 3.0 1036.05469( ~30) 2.0 1036.04696( ~21) 1.0 1036.03631( ~12) OMIT 1036.02302( 26) 1.0 1036.00829( 19) 1 0 1036.99142( 10) 1.0 1036.97218( ~3) I I I I H I O O O O O - u - 0000000000 CCCCC 11111 141 0(33,11) 0(33,12) 0(33,13) 0(29, 8) 0(29, 9) 0(29,10) 0(29,11) 0(29,12) 0(29,13) O(29,l4) 0(29,16) 0(26,14) 0(26,16) Q(26,l6) 0(26,l7) 0(23,17) 0(23,18) 0(21,11) 0(21,12) 0(21,13) 0(21,14) 0(21,16) 0(21,16) 0(21,17) 0(21.18) 0(19,11) 0(19,12) 0(19,13) Q(19,14) 0(19,l6) 0(19,16) O(19,17) 0(17,l3) 0(17,14) 0(17,16) 0(17,16) 0(17,17) 0(16, 2) 0(16, 3) 0(16, 4) 9P(32) 9P(32) 9P(32) 9P(28) 9P(28) 9P(28) 9P(28) 9P(28) 9P(28) 9P(28) 9P(28) 9P(26) 9P(26) 9P(26) 9P(26) 9P(24) 9P(24) 9P(24) 9P(24) 9P(24) 9P(24) 9P(24) 9P(24) 9P(24) 9P(24) 9P(22) 9P(22) 9P(22) 9P(22) 9P(22) 9P(22) 9P(22) 9P(22) 9P(22) 9P(22) 9P(22) 9P(22) 9P(22) 9P(22) 9P(22) 14297.3 13666.4 12711.8 ~16017.2 ~16236.6 ~16478.0 ~16721.7 ~17001.8 ~17293.0 ~17609.3 ~17962.2 ~16l74.0 ~1696l.4 ~16682.0 ~16332.0 ~17161.7 ~16662.1 9628.6 10212.0 10934.1 11809.8 12890.2 14216.0 16846.6 17926.2 ~17734.9 ~16966.6 ~16018.0 ~14870.7 ~13473.3 ~11766.1 ~9663.l 10017.4 11414.3 13111.6 16176.6 17680.0 16826.0 16966.1 16130.0 31067016.4 31066273.6 31066429.9 31143491.0 31143271.6 31143030.2 31142786.4 31142606.4 31142216.1 31141898.9 31141646.0 31200587.3 31200799.9 31201079.3 31201429.3 31266096.6 31267686.1 31282876.8 31283469.2 31284181.3 31285067.0 31286137.3 31287462.2 31289092.? 31291173.3 31311226.6 31311996.0 31312943.6 31314090.8 31316488.2 31317196.4 31319298.4 31338978.9 31340376.8 31342073.1 31344137.1 31346641.6 31344787.6 31344916.6 31345091.6 O~C Unc. ~0.1 1.0 ~3.1 1.0 ~5.4 2.0 0.7 2.0 ~3.4 1.0 ~9.6 OMIT 2.2 2.0 ~l.3 2.0 6.5 1.0 8.4 2.0 ~6.7 2.0 1.4 2.0 ~2.7 1.0 ~31.3 OVERLAP ~1l3.6 OVERLAP ~60.4 OVERLAP 38.4 OVERLAP 1.8 2.0 1.0 3.0 6.2 2.0 1.8 2.0 ~0.2 1.0 ~10.2 OMIT ~3l.l OVERLAP ~1.0 2.0 2.9 1.0 ~3.6 1.0 0.6 2.0 0.2 1.0 ~1.6 1.0 ~3.2 1.0 2.6 2.0 3.2 2.0 2.7 1.0 6.7 3.0 10.1 2.0 3.9 2.0 0.2 2.0 6.1 2.0 0.4 2.0 1036.96062( 1035.92678( 1036.89764( 1038.83604( 1038.82772( 1038.81967( 1038.81164( 1038.80220( 1038.79248( 1038.78193( 1038.77016( 1040.73967( 1040.74666( 1040.76698(~ 1040.?6766(~ 1042.69112(~ 1042.644l4( 1043.48442( 1043.60387( 1043.62796( 1043.66717( 1043.59321( 1043.63740( 1043.69179(~ 1043.76119( 1044.43010( 1044.466?6( 1044.48737( 1044.62664( 1044.67226( 1044.62923( 1044.69934( 1046.36681( 1046.40241( 1046.46903( 1046.62787( 1046.61141( 1046.64967( 1046.66388( 1046.66971( 0) ~10) ~17) 2) ~11) ~32) 7) ~4) 18) 28) ~22) 4) ~9) 104) 378) 201) 127) 5) 3) 20) 5) 0) ~33) 103) -3) 9) ~11) 1) 0) -4) ~10) 8) 10) 8) 18) 33) 13) 0) l7) 1) 142 Trans. Laser v-b v/M82 O~Cc Unc.d v/cm l . 0(16, 6) 9P(22) 16372.0 31346333.6 1.6 1.0 1046.56778( 6) 0(16, 6) 9P(22) 16682.1 31345643.6 2.0 1.0 1046.57812( 6) 0(16, 7) 9P(22) 17069.2 31346030.? 0.8 1.0 1045.59104( 2) 0(16, 8) 9P(22) 17550.2 31346511.? 2.2 2.0 1045.60708( 7) 0(14, 4) 9P(20) ~l7839.5 31366060.9 ~0.9 1.0 1046.25917( ~2) 0(14, 6) 9P(20) ~17656.8 31366343.6 ~1.5 1.0 1046.26860( ~4) 0(14, 6) 9P(20) ~l7192.8 3136670?.6 ~0.7 1.0 1046.28075( ~2) 0(14, 7) 9P(20) ~16738.0 31367162.4 0.0 2.0 1046.29691( 0) 0(14, 8) 9P(20) -16l79.6 31367?20.8 ~0.3 1.0 1046.31464( 0) 0(14, 9) 9P(20) ~l5496.0 31368406.4 3.9 2.0 1046.33738( 12) O(14,10) 9P(20) ~l4676.7 31369223.? ~l.3 1.0 1046.36467( ~4) O(l4,ll) 9P(20) ~13681.7 31370218.? 0.8 1.0 1046.39786( 2) 0(14,12) 9P(20) ~l2490.2 31371410.2 ~3.1 1.0 1046.43?60( ~10) 0(14,13) 9P(20) ~11049.5 313?2860.9 ~1.0 1.0 1046.48666( ~3) 0(14,l4) 9P(20) ~9313.0 31374587.4 2.6 3.0 1046.64369( 8) 0(13, 2) 9P(20) ~8745.1 31375155.3 ~1.5 2.0 1046.56253( ~5) 0(13, 3) 9P(20) ~8587.9 31375312.6 ~1.7 1.0 1046.66777( ~6) 0(13, 4) 9P(20) ~8361.4 31375539.0 ~2.0 1.0 1046.67533( ~6) 0(11, 6) 9P(20) 9326.3 31393226.? 27.1 OVERLAP 1047.16529( ~90) 0(11, 7) 9P(20) 9896.4 31393796.8 5.1 1.0 1047.18434( 1?) 0(11, 8) _9P(20) 10666.4 31394465.8 3.1 1.0 1047.20633( 10) 0(11, 9) 9P(20) 11366.9 31395257.3 1.8 1.0 1047.23306( 6) 0(ll,11) 9P(20) 13489.0 31397389.4 0.7 1.0 1047.30418( 2) 0(10, 2) 9P(20) 16591.1 31399491.5 0.6 2.0 1047.37430( 1) 0(10, 3) 9P(20) 15776.3 31399676.? 1.0 1.0 1047.38048( 3) 0(10, 4) 9P(20) 16042.3 31399942.? 1.2 1.0 1047.38936( 3) 0(10, 6) 9P(20) 16396.6 31400297.0 1.4 1.0 1047.40117( 4) 0(10, 6) 9P(20) 16849.1 31400749.5 1.5 2.0 1047.41626( 4) 0(10, 7) 9P(20) 17412.6 31401313.0 1.7 1.0 1047.43506( 5) O( 6, 1) 9P(18) ~l6679.2 31422381.0 0.3 2.0 1048.13781( 1) 0( 6, 2) 9P(18) ~16556.1 31422605.l ~0.2 1.0 1048.14195( 0) Q( 6, 3) 9P(18) ~15344.0 31422716.2 ~0.3 1.0 1048.14899( 0) O( 6, 4) 9P(18) ~16041.2 31423019.0 ~0.9 1.0 1048.16909( ~3) O( 6, 5) 9P(18) ~l4637.5 31423422.? ~l.0 1.0 1048.17266( ~3) O( 6, 6) 9P(18) ~14121.0 31423939.2 0.6 1.0 1048.189?9( 1) 0( 5, 2) 9P(18) ~ll49l.8 31426568.3 ~1.5 1.0 1048.27748( ~4) 0( 5, 3) 9P(18) ~112?5.8 31426784.3 ~1.5 1.0 1048.28469( ~4) O( 5, 4) 9P(18) ~10965.1 31427096.l ~0.9 1.0 1048.29606( ~2) O( 6, 6) 9P(18) ~10552.0 31427508.2 ~0.6 1.0 1048.30883( ~1) R( 2, 0) 9P(12) ~10109.9 31586721.9 18.0 OVERL 60) AP 1063.58627( 143 Trans. Laser 8( 2, l) 9P(12) R( 2, 2) 9P(12) R( 3, 0) 9P(10) R( 3, 1) 9P(10) R( 3, 2) 9R(10) R( 3. 3) 9R(10) R( 4, 0) 9P( 8) R( 4, 1) 9P( 8) R( 4, 2) 9P( 8) R( 4. 3) 9P( 8) R( 4. 4) 9P( 8) R( 5, 0) 9P( 6) R( 6, 1) 9R( 6) R( 5, 2) 9P( 6) R( 6, 3) 9P( 6) R( 5, 4) 9P( 6) R( 5, 5) 9R( 6) R(13, 0) 9R( 8) R(13, 1) 9R( 8) R(13, 2) 9R( 8) R(13, 3) 9R( 8) R(13, 4) 9R( 8) R(13, 5) 9R( 8) R(13, 6) 98( 8) R(13, 7) 9R( 8) R(13, 8) 9R( 8) R(13, 9) 9R( 8) R(13,10) 9R( 8) R(13,11) 9R( 8) R(14, 0) 9R(10) R(14, 1) 9R(10) R(14, 2) 9R(10) R(14, 3) 9R(10) R(14, 4) 9R(10) R(14, 5) 9R(10) R(14, 6) 9R(10) R(14, 7) 9R(10) R(14, 8) 9R(10) R(14, 9) 9R(10) R(14,10) 98(10) ~10109.9 ~9962.1 ~12766.4 ~12766.4 ~12623.9 ~12424.0 ~16313.0 ~16313.0 ~16176.6 ~14986.5 ~14706.3 ~l7746.2 ~l7746.2 ~17620.0 ~17433.9 ~17167.8 ~16809.9 ~11697.8 ~11697.8 ~11697.8 ~11663.0 ~ll436.0 ~11263.0 ~11034.8 ~10740.4 ~10364.1 ~9890.8 ~9298.9 ~8669.2 ~13608.6 ~13608.6 ~13608.6 ~13400.0 ~13294.8 ~13160.0 ~12968.6 ~12706.6 ~12404.0 ~11966.6 ~11447.3 31686721.9 31686869.? 31634077.0 31634077.0 31634219.6 31634419.4 31681748.4 31681748.4 31681886.9 316820?6.9 31682366.1 31728738.6 31728738.6 31728863.8 31729049.9 31729316.0 31729673.9 32079964.9 32079964.9 32079964.9 32080089.? 32080216.? 32080389.6 32080617.9 32080912.3 32081288.6 32081761.9 32082363.? 32083093.6 32120768.3 32120768.3 32120768.3 32120866.9 32120972.2 32121116.9 32121308.4 32121660.4 32121862.9 32122301.3 32122819.6 I I w ...: HONOHOOHQO bNOOOOOOGO I N abs-crdcanncu—CIO> hoamnsahdnhuwtsai OVERLAP 2.0 OVERLAP OVERLAP 1.0 1.0 OVERLAP OVERLAP 2.0 1.0 1.0 OVERLAP OVERLAP 2.0 1.0 1.0 1.0 OVERLAP OVERLAP OVERLAP 2.0 1.0 1.0 NHHI-Io-o 00000 3.0 OVERLAP OVERLAP OVERLAP 1063.68627( 1063.69120( 1066.19923( 1066.19923( 1066.20398( 1066.21066( 1066.78937( 1066.78937( 1066.79396( 1066.80030( 1066.80966( 1068.36680( 1068.36680( 1068.36097( 1068.367l8( 1068.37606( 1068.38800( 1070.07211( 10?0.07211( 1070.07211(~ 1070.07661( 1070.08084( 1070.08661( 1070.09423( 1070.10406( 1070.11660( 1070.13239( 1070.16213( 1070.17680( 1071.43317( 1071.43317( 1071.43317(- 1071.43679( 1071.44030( 1071.446l3( 1071.46162( 107l.45992( 1071.47001( 1071.48464( 1071.60192( -3) 6?) ~61) -7) ~2) -4) 0) 63) 0) 166) -1) 1) 1) 0) -1) 1) 2) 1) 8) 46) 2) 131) -3) 0) 0) -3) ~2) ~73) 13) 4) 144 R(14,11) R(14,12) R(16, 0) R(16, 1) R(16, 2) R(16, 3) R(16, 4) R(16, 6) R(16, 6) R(16, 7) R(16, 8) R(16, 9) R(16,10) R(16,11) R(16,12) R(16,13) R(15,14) R(16, 0) R(16, 1) R(16, 2) R(16, 3) R(16, 4) R(16, 6) R(16, 6) R(16, 7) R(16, 8) R(16, 9) R(16,10) R(16,11) R(16,12) R(16,13) R(16,14) R(16,16) R(17, 7) R(17, 8) R(17, 9) R(17,10) R(17,11) R(17,12) R(17,13) 98(10) 9R(10) 9R(12) 9R(12) 9R(12) 9R(12) 9R(12) 98(12) 9R(12) 9R(12) 9R(12) 9R(12) 9R(12) 9R(12) 9R(12) 9R(12) 9R(12) 9R(14) 98(14) 9R(14) 9R(14) 9R(14) 9R(14) 9R(14) 9R(14) 9R(14) 9R(14) 9R(14) 9R(14) 9R(14) 9R(14) 9R(14) 9R(14) 9R(16) 9R(16) 9R(16) 9R(16) 98(16) 9R(16) 98(16) ~10792.l ~9973.3 ~16205.0 ~16206.0 ~16206.0 ~16131.3 ~16044.0 ~14929.6 ~14773.7 ~14667.6 ~14296.3 ~l3947.0 ~13499.3 ~12930.1 ~12200.0 ~11301.6 ~10154.0 ~16800.0 ~16800.0 ~16800.0 ~16800.0 ~16800.0 ~l6601.5 ~16482.1 ~16321.7 ~16108.1 ~16824.3 ~16463.3 ~14972.6 ~14366.7 ~13667.l ~12668.3 ~11300.7 ~17972.4 ~17816.7 ~17601.6 ~17310.4 ~16922.0 ~16412.8 ~16736.3 32123474.8 32124293.6 32160874.6 32160874.6 32160874.6 32160948.2 32161036.6 32161149.9 32161306.8 32161611.9 32161783.1 32162132.6 32162680.2 32163149.4 32163879.5 32164777.9 32166926.5 32200291.3 32200291.3 32200291.3 32200291.3 32200291.3 32200489.8 32200609.2 32200769.6 32200983.2 32201266.9 32201638.0 32202118.? 32202734.6 32203624.2 32204623.0 32206790.6 32239330.9 32239486.? 32239701.8 32239993.0 32240381.3 32240890.6 32241667.0 H I II IIIIIN wawmmabow H H00000000 OONQQQQQGIO QHQOCDG-b-bflfl 1.0 1.0 OVERLAP OVERLAP OVERLAP OVERLAP 2.0 thha AP 008‘0000 000 N OVERLAP OVBRLAP OVERLAP OVERLAP OVERLAP 2.0 3rdhndhndwawwaw Hr-Hr-hudha HOOOOOOOOO OOOOOOO O “a 1071.52378( 1071.66109( 1072.77130( 1072.77130( M M 48) 14) 1072.77130( ~88) 1072.77376( ~22) 1072.77667( 1072.78049( 1072.78669( 1072.79256( 1072.80161( 1072.81326( 1072.82819( 1072.84718( 1072.87164( 1072.90160( 1072.93978( 1074.08610( 1074.08610( -3) ~“ -3) -m -5) 1074.08610( ~74) 1074.08610(-199) 1074.08610(-392) 1074.09272( ~10) 1074.09671( 1074.10206( 1074.10918( 1074.11866( 1074.13102( 1074.14706( 1074.16760( 1074.19394( 1074.22726( -3) -2) -5) -4) -2) U 0) U -3) 1074.26964( ~14) .1076.38832( 1076.39362( 1076.40070( 1076.41041( 1076.42336( 1076.44036( 1076.46291( m -5) -7) -7) -3) -1) 46) 146 Trans. Laser v.b v/M82 O~C Unc.d v/cm ° R(17,l4) 9R(16) ~l4890.8 32242412.6 2.8 1.0 1076.49112( 9) R(17,l6) 9R(16) ~l3?96.5 32243506.9 ~4.1 2.0 1075.52762( ~13) R(18,13) 9R(18) ~17838.0 32278879.0 6.? OMIT 1076.70751( 22) R(18,14) 9R(18) ~l7l41.3 32279575.? ~2.7 1.0 1076.73076( ~9) R(18,15) 9R(18) ~16208.3 32280508.9 4.4 2.0 1076.76187( 14) R(22, 0) 9R(24) 12150.0 32422335.? ~l3.9 OVERLAP 1081.4927l( ~46) R(22, 1) 9R(24) 12160.0 32422335.? 1.3 OVERLAP 1081.49271( 4) R(22, 2) 9R(24) 12150.0 32422335.? 46.6 OVERLAP 1081.4927l( 154) R(22, 3) 9R(24) 12028.0 32422213.? ~2.1 2.0 1081.48864( ~6) R(22, 4) 98(24) 11931.0 32422116.? 0.1 2.0 1081.48640( 0) R(22, 6) 9R(24) 11808.0 32421993.? ~1.6 2.0 1081.48130( ~5) R(22, 6) 9R(24) 11670.0 32421865.? ~1.0 2.0 1081.47670( ~3) R(22, 7) 9R(24) 11522.0 32421707.? 1.4 2.0 1081.47176( 4) R(22, 8) 9R(24) 11366.0 32421551.? 0.? 2.0 1081.46656( 2) R(22, 9) 9R(24) 11214.0 32421399.? 1.0 2.0 1081.46149( 3) R(22,10) 9R(24) 11074.0 32421259.? 0.5 2.0 1081.45682( 1) R(23, 0) 9R(26) 10500.0 32466925.0 ~20.4 OVERLAP 1082.64648( ~67) R(23, l) 9R(26) 10600.0 32466925.0 ~1.2 OVERLAP 1082.64648( ~3) R(23, 2) 9R(26) 10460.0 32456886.0 16.0 OVERLAP 1082.64515( 63) R(23, 3) 9R(26) 10350.0 32456775.0 -O.4 2.0 1082.64148( ~1) R(23, 4) 9R(26) 10222.1 32466647.1 ~0.6 1.0 1082.6372l( ~1) R(23, 5) 9R(26) 10067.? 32456492.6 3.4 1.0 1082.63206( 11) R(23, 6) 9R(26) 9880.0 32456304.9 0.? 1.0 1082.62580( 2) R(23, 7) 9R(26) 9673.7 32466098.6 0.9 1.0 1082.61892( 2) R(23, 8) 9R(26) 9460.6 32466875.6 0.0 1.0 1082.61148( 0) R(23, 9) 9R(26) 9222.7 32455647.6 2.9 1.0 1082.60387( 9) ‘COz laser line used. bMicrowave frequency in M82. The signed microwave frequency is added to the laser frequency to obtain the absorption frequency. cObserved minus calculated frequency in M82. calculation are in the last two columns of Table X. d The parameters for the Estimated uncertainty in the observed frequency in M82. An "OMIT” and an ”OVERLAP" mean that the frequency was omitted from the least squares fits and the transition was overlapped by another transition(s), °Observed frequency in cm- . _ the observed minus calculated frequencies in units of 0.00001 cm . respectively. 1 1110 1111-1101“. in parentheses 8P. 1 146 Table IX. Comparison of Observed and Calculated Frequencies in the 12 2V3 ~ 93 Band of 083! Trans. Laser v.b v/M82 O~Cc Unc. v/cm 1 ° R(17,12) 9P( 6) 10835.0 31?67318.8 ~0.7 2.0 1069.31013( ~2) R(17, 9) 9P( 6) 10006.0 31756489.8 14.6 OVERLAP 1059.28248( 48) R(15,12) 9P( 8) ~16500.0 31680561.4 16.4 OVBRLAP 1066.749?8( 64) R(16, 9) 9P( 8) ~l7765.0 316?9296.4 ~3.8 2.0 1066.70758( ~12) R(12,10) 9P(14) 14936.0 31568963.9 ~1.5 3.0 1062.69372( ~6) R(12, 9) 9P(14) 14453.4 31558482.3 1.? 2.0 1052.67766( 5) R(12, 8) 9P(14) 14057.9 31558086.8 ~2.2 2.0 1062.6644?( ~7) R(12, 7) 9P(14) 13749.0 315577??.9 2.6 1.0 1052.65416( 8) R(12, 6) 9P(14) 13494.9 31557523.8 ~2.6 1.0 1062.64569( ~8) R(12, 6) 9P(14) 13303.7 31557332.6 0.6 1.0 1052.63931( 1) R(12, 4) 9P(14) 13152.0 31657180.9 ~2.8 2.0 1052.63425( ~9) R(12, 3) 9P(14) 13045.0 31567073.9 ~0.8 3.0 1062.63068( ~2) R(12, 2) 9P(14) 12925.0 31556953.9 ~46.4 OVERLAP 1052.62668(~154) R(12, l) 9P(14) 12925.0 31556953.9 ~3.1 OVERLAP 1062.62668( ~10) R(12, 0) 9P(14) 12926.0 31556953.9 11.1 OVERLAP 1052.62668( 3?) R(10,10) 9P(16) ~l6282.7 31475154.? ~1.8 2.0 1049.89816( ~6) R(10, 9) 9P(16) ~16866.l 314?45?1.3 1.4 1.0 1049.87869( 4) R(10, 8) 9P(16) ~l7349.9 31474087.5 ~3.0 2.0 1049.86255( ~9) R(10, 7) 9P(16) ~17?37.1 31473700.3 ~l.3 1.0 1049.84964( ~4) R( 9, 3) 9P(18) ~8380.0 31429680.2 ~1.9 3.0 1048.38128( ~6) R( 9, 2) 9P(18) ~8488.0 31429672.2 ~2.3 2.0 1048.37?68( ~7) R( 9, 1) 9P(18) ~8662.0 31429498.2 ~13.2 OVERLAP 1048.37621( ~44) R( 9, 0) 9P(18) ~8562.0 31429498.2 7.6 OVERLAP 1048.37521( 26) R( 7, 6) 9P(22) 13218.7 31342180.2 0.7 2.0 1045.46260( 2) R( 7, 5) 9P(22) 12899.9 31341861.4 0.1 2.0 1045.45196( 0) R( 7, 4) 9P(22) 12651.7 31341613.2 ~0.6 1.0 1045.44368( ~1) R( 7, 3) 9P(22) 12463.7 31341425.2 ~3.? 1.0 1045.43742( ~12) R( 4, 4) 9P(26) ~12456.9 31204305.4 0.1 1.0 1040.86359( 0) R( 4, 3) 9P(26) ~126??.7 31204083.6 1.5 1.0 1040.86619( 4) R( 4, 2) 9P(26) ~12836.0 31203926.3 ~0.8 2.0 1040.85094( ~2) R( 4, 1) 9P(26) ~12938.9 31203822.4 ~l3.4 OVERLAP 1040.84748( ~44) R( 4, O) 9P(26) ~12938.9 31203822.4 16.? OVERLAP 1040.84748( 56) 0(23,12) 9P(40) ~15667.8 307844?4.9 0.0 1.0 1026.85955( 0) 0(23, 9) 9P(40) ~l6924.0 30783218.6 ~0.7 2.0 1026.81765( ~2) 0(21, 9) 9P(40) 12598.8 30812?41.6 3.6 2.0 1027.80242( 11) 0(18,10) 9P(38) ~9140.0 30852757.5 ~4.9 3.0 1029.13721( ~16) 0(18, 9) 9P(38) ~9701.4 30862196.1 ~1.2 1.0 1029.11849( ~3) 0(18, 8) 9P(38) ~10169.1 30851728.4 0.4 1.0 1029.10289( 1) 0(18, 7) 9P(38) ~10567.6 30851340.l ~0.9 1.0 1029.08993( ~3) 0(18, 6) 9P(38) ~10875.0 30851022.5 ~2.5 1.0 1029.07934( ~8) 14? 0(18, 6) 9P(38) ~11126.2 308607?2.3 1029.07099( 3) 0(18, 4) 9P(38) ~11326.0 30860672.5 1029.06433( 1) 0(18, 3) 9P(38) ~11476.0 30860422.6 1029.06933( 0) 0(16,12) 9P(38) 16683.1 3087?680.6 1029.96622( 1) 0(16,11) 9P(38) 14769.6 30876667.1 1029.93476( 2) 0(16,10) 9P(38) 13998.0 308?6896.6 1029.90902( ~9) 0(16, 9) 9P(38) 13368.2 30876266.? 1029.88767( 1) 0(16, 8) 9P(38) 12826.? 30874723. 1029.86991( 11) 0(16, 6) 9P(38) 12020.0 30873917. 1029.84304( 11) Q(13,13) 9P(36) ~l4028.6 30908886. 1031.00949( 0) 0(13,12) 9P(36) ~16278.9 30907636. 0(13,11) 9P(36) ~16323.4 30906692. 0(13,10) 9P(36) ~17224.0 30906691. 0(13, 9) 9P(36) ~17973.4 30904942. 0(12,10) 9P(36) ~8606.6 30914310. 0(12, 9) 9P(36) ~9388.1 30913627. 0(12, 8) 9P(36) ~10040.4 30912876. 0(12, 7) 9P(36) ~10679.0 30912336. 0(12, 6) 9P(36) ~11022.0 30911893. 0(12, 6) 9P(36) ~ll329.0 30911636. 1030.96778( ~4) 1030.93294( 36) 1030.90290( 2) 1030.87790( ~1) 1031.19038( 3) 1031.16428( ~4) 103l.14262( ~6) 1031.12466( 2) 1031.10978( 4) 1031.09787( 8) H I e e 0631-!th 0HONON000N NI-IOI-II-H-IOOOI-fi 0000N0000fl O < NHHNwHI-OHHN uwnuwwwr—Hw wwwHHNNNHN HNHHNHHNHH > '0 0000000000 0000000000 00000000150 0000000000 0(12, 4) 9P(36) ~11660.0 30911266. 0(12, 3) 9P(36) ~11874.0 30911041. 0( 9, 9) 9P(36) 12434.1 30936349. 0( 9, 8) 9P(36) 11710.0 30934626. 0( 9, 7) 9P(36) 11110.0 30934026.4 0( 9, 6) 9P(36) 10614.0 30933629.4 O( 9, 6) 9P(36) 10218.0 30933133.4 0( 9, 4) 9P(36) 9903.1 30932818.6 0( 9, 3) 9P(36) 9668.0 30932683.4 Q( 8, 8) 9P(36) 17647.0 30940662.6 1031.08849( 8) 1031.08136( 0) 1031.89219( 2) 1031.86803( 2) 1031.84802( 7) 1031.83148( 0) 1031.81827( 8) 1031.80776( 2) 1031.79992( 6) 1032.06607( 2) «sous-s 0&0Hfi00-fi00 00'” I 0QOQO0QO0H mqmocwmmwo bfiQQfiNQQOIN 0000~300NON 0( 8, 7) 9P(36) 17026.6 30939942.1 Q( 8, 6) 9P(36) 16621.4 30939436.8 0( 8, 6) 9P(36) 16112.0 30939027.6 Q( 8, 4) 9P(36) 16786.6 30938701.0 ~ . 0( 8, 3) 9P(36) 16647.4 30938462.9 Q( 8, 2) 9P(36) 16378.2 30938293.6 P( 1, 0) 9P(36) ~11660.0 30911265.4 ~1. P( 7, 6) 9P(46) ~13668.6 30596857.6 ~0. P( 7, 6) 9P(46) ~14171.0 30696346.2 ~2. P( 7, 4) 9P(46) ~14670.0 30696946.1 2. 1032.04638( ~3) 1032.02862( 6) 1032.01487( 7) 1032.00398( ~6) 1031.99604( 10) 1031.99039( 10) 1031.08849( ~6) 1020.60131( ~2) 1020.68422( ~8) 1020.67091( 6) 148 P( 7, 3) 9P(46) ~14877.0 30696639.1 0 6 1.0 1020.66067( 1) P( 7, 2) 9P(46) ~l6090.7 30696426.5 0 7 1.0 1020.66364( 2) P( 7, 1) 9P(46) ~16239.8 30696276.3 ~22 0 OVERLAP 1020.64867( ~73) P( 7, 0) 9P(46) ~16239.8 30696276.3 19 9 OVERLAP 1020.64857( 66) CO2 laser line used. Microwave frequency in M82. The signed microwave frequency is added to the laser frequency to obtain the absorption frequency. cObserved minus calculated frequency in M82. The parameters for the calculation are in the last two columns of Table X. dEstimated uncertainty in the observed frequency in M82. An ”OMIT" and an ”OVERLAP" mean that the frequency was omitted from the least squares fits and the transition was overlapped by another transition(s), respectively. °Observed frequency in cm—l. The numbers in parentheses are _1 the observed minus calculated frequencies in units of 0.00001 cm . 149 Table X. Vibration-Rotation Parameters for 120831' Parametera v3 = 0b v3 = 1b v3 2c,e Ev /682 0.0000d 31436.566?(3) 62398.209(l) 8v /an 25536.1498(7) 25197.5027(22) 248?0.976(40) 6(Av~8v) /882 0.0000 44.3433(214) 81.290(111) 0J /k82 60.2330(48) 56.8509(100) 53.434(376) an /k82 439.5279(488) 518.0548(739) 576.102(1074) ””3 /k82 0.0000 ~94.l387(3113) ~169.779(3174) HJ /82 ~0.0214(81) ~0.2737(166) ~6.672(1173) an /82 1.7321(951) 16.0470(1644) 57.728(5659) nxJ /82 21.4254(2708) ~93.10?8(8176) ~208.694(20427) “Ex /82 0.0000 106.7283(l7075) 1?3.320(39066) LJ /m82 0.0000“ 0.0795(73) 8.370(1603) LJJJK /m82 0.0000“ ~2.9636(825) ~46.610(l5279) I.“n /m82 0.0000“ 41.7067(5323) 107.530(50419) ”Jxxx /m82 0.0000d -237.9115(19977) ~238.983(57475) on /m82 0.0000 155.1981(32803) l42.063(105343) aVibration—rotation parameter. 0? = P(v3) ~ P(v3=0). 160 bObtained from fit of frequencies indicated in Table VII and listed in Table VIII. Number in parenthesis is one standard error in units of last digit in the parameter. ' cObtained from fit of frequencies in Table IX. Parameters for v =1 were constrained to values shown in this table. Number ii parenthesis is one standard error in units of last digit of the parameter. dConstrained to 2ero in the least squares fit. °It should be noted that the parameters for v§=2 are given to r one less significant figure than the paramet s for v3=0 and 1. 161 Table XI. Comparison of Ground-State Rotational Constants of 12C8312 Parameter This work. Cranerb Ao /M82 —— 166362.72 80 /M82 25536.1498 25636.14929 DJ /282 60.2330 60.228 DJ‘ /k82 439.6279 439.50 0‘ Am: — * 2108.4 8J /82 ~0.02l4 -—— RJ‘ /82 1.7321 1.29 8‘3 /82 21.4264 24.5 8‘ /82 —— —— .Obtained from fit of frequencies indicated in Table VII and listed in Table VIII. bObtained from the Table 3 in Ref. 39. 162 Table XII. The Fitting Parameters of Matson’s Form of Pade Approximant for v3 Band of 12683F Parameters v3 = 0. v3 = 1. s /682 0.00000” 30803.4756l(0) 810 /M82 25636.15001(0) 25197.49134(0) 301 /M82 0.00000” 44.16021(1) 820 /k82 60.22898(1) ~66.83832(1) '11 /k82 439.57479(6) ~6l7.36781(6) 802 /k82 0.00000” 97.12210(11) 930 /82 ~0.00863(l) -3.53175(20) 021 /82 1.44266(11) 63.66637(197) 812 /82 22.2?008(32) 624.42425(601) 003 /82 0.00000” -44.91134(126) 510 x 103 0.00000” 58.26188(353) 501 x 103 0.00000” ~l388.91964(1088) .Obtained from fit of frequencies indicated Table VII and listed in Table VIII. Number in parenthesis is one standard error in units of last digit in the parameter. bConstrained to 2ero in the least squares fit. 163 Table XIII. Vibrational Dependence of Vibration-Rotation Parameters for 126831‘ P(v). P(O)b c1b c2b 3' /682 0.000 03 = 31674.009(1) x33 = -237.452(1) 0' /M82 25536.160(1) -.g = ~344.708(2l) 6.060(21) OA' /M82 0.000 -.g = ~296.666(73) 2.362(63) nJ /k82 60.233(5) -3.365(190) -0.017(189) nJ‘ /k8s 439.628(49) '88.?67(562) -1o.240(543) 00‘ /h82 0.000 ~103.388(1705) 9.249(1618) .Vibration~rotation parameter. P(v) = P(O) + c v + c v2. P(O), cl, and c2 were derived from the paramet‘rs in Table X. bUncertainties in parentheses, in units of the last digit in the parameter, were propagated from one standard error in the parameters. 164 For the Coriolis interaction between v3 and ’6 bands, ShoJe~Chaghervand and Schwendeman(29) gave a detailed explanation on the formulas relating the perturbed state to unperturbed state. By using the formulas, they calculated the unperturbed molecular constants of the '3 and "6 states with assumption of ‘36 = 0.318. Finally, Tables XIV ~ XVII show the coincidences between the calculated frequencies of the 93 fundamental and the 293 r v3 hot band transitions of 13C83F and 12C83F and the 10 pm region fixed frequency gas laser 1ines(8l,82,83). In this comparison, the calculated frequencies were obtained by the parameters obtained from the fittings in which the v3 = 1 state parameters were fixed from the fits of the v3 = l r 0 transition and the L constants were constrained to 2ero for the ground state only. The results from the coincidences may be useful both for analysis of far infrared laser experiments and for the observation of the v3 = 3 state by an infrared-infrared double resonance experiment. 166 Table XIV. Coincidences Between Calculated Frequencies for 93 Band of 13C83F and CO2 Laser Frequencies. Trans. Frequency ”O-VLC Laserd P(44,16) 28034?26.1 58.9 nCl'Oz BAND 1 R(30) P(36, 9) 28624893.6 ~52.8 N20 R(19) P(36,10) 28625035.8 89.6 N20 R(19) P(30, 0) 29041047.2 ~21.8 N30 R(38) P(30, 1) 29041063.? ~6.3 NaO R(38) P(30, 2) 29041113.4 44.5 N20 R(38) P(26,13) 29312229.? 12.9 ‘3CI'02 BAND I R(16) P(25,15) 29379942.4 ~3.2 120100. BAND I R(20) P(24,10) 29440019.4 82.3 uCHOHO BAND I R(23) P(24,13) 29442634.9 61.6 uCl'Oa BAND I 8(30) P(23,12) 29505764.1 85.0 uCl'Os BAND I R(28) P(l6,12) 29938027.2 47.9 uCHOa BAND II P(36) P(l6,13) 29998669.? 19.6 laONO: BAND II P(20) P(l3, 0) 30107614.5 61.4 13CHOe BAND II P(l6) P(l3, 1) 30107648.9 95.8 nONO: BAND II P(l6) 0( 6, 6) 30791154.4 ~88.3 12Cl'Ol'O BAND II P(52) O(20,16) 30674416.2 ~29.6 13C1‘Oe BAND II P(44) O(21,13) 30658803.1 99.5 13C1'Oa BAND II P( 6) O(29,11) 3062586?.4 69.6 1“ONO: BAND II P(12) 0(29,12) 30625802.9 5.1 1301.03 BAND II P(12) 0(29,13) 306267?4.2 ~23.7 n61.0: BAND II P(12) O(29,l4) 30625780.4 ~l?.5 1301002 BAND II P(12) 0(29,15) 30525833.0 35.1 1301'02 BAND II P(12) B( 4, 3). 31042692.2 ~25.9 1301‘02 BAND II P(32) R(12, 7) 31391833.2 ~27.6 NCl'Os BAND II R(48) R(14, 9) 31472712.0 ~26.0 uCl'Oz BAND II R(38) R(21, l) 31733443.0 95.9 uCNOa BAND II R(68) R(21, 2) 31733407.? 60.6 1"C”Oe BAND II R(58) R(21, 3) 31733350.6 3.5 1301.0: BAND II R(68) R(21, 4) 317332?4.4 ~72.8 1301.03 BAND II R(58) .Transition in the v3 band of 13CR3F; J S 4?, E i 16. bFrequency of 93 band transition in M82. cFrequency of v band transition minus laser frequency in M82. in Refs. Laser frequencies calculated from constants 81, 82, and 83. dIdentification of CO Band I is 10 um band; Band II is 9 pi or N20 laser. bend. 166 Table XV. Coincidences Between Calculated Frequencies for 2v3 ~ v3 Band of 13C83F and CO2 Laser Frequencies. Trans. Frequency v0 ”L Laser P(26, 0) 2893529l.8 ~5.1 N20 R(33) P(26, l) 28935319.2 22.3 N20 R(33) P(24, 3) 28999003.2 ~80.6 NsO R(36) P(23, 3) 29061892.? ~6.3 NaO R(39) P(18, 7) 29369030.5 ~92.1 1261'0"0 BAND I P(l6, 4) 29644270.2 73.8 120’90: BAND I R(36) P(l4, 7) 29603067.1 48.8 1201‘01‘0 BAND I P(12, 9) 29717723.1 73.3 1301.02 BAND I R(44) P(ll, 0) 29770676.1 ~93.1 1301‘02 BAND II P(28) P(ll, 1) 29770607.4 ~60.8 laC"02 BAND II P(28) P(11, 2) 29770704.9 36.? 1361‘02 BAND II P(28) P(ll, 6) 29771800.? ~42.0 1361‘0130 BAND I R(46) P( 6, 4) 30093194.4 ~26.8 ‘301‘02 BAND II P(30) 0(13,12) 30291610.6 ~74.6 1361.02 BAND II P(22) 0(14, 7) 30280267.9 ~64.4 1361‘02 BAND II P(66) 0(26, 6) 30143668.8 ~87.6 1“(31002 BAND II P(28) 0(26, 6) 30143?28.2 ~28.2 1363.02 BAND II P(28) 0(26, 7) 30143814.3 67.9 1a61‘02 BAND II P(28) R(12,11) 30927031.0 38.0 1301.02 BAND II R( 6) R(13, 0) 30966833.6 ~36.2 1°61.02 BAND II R( 8) R(13, 1) 30966838.6 ~31.2 1303'02 BAND II R( 8) R(13, 2) 30966864.1 ~16.6 1301°02 BAND II R( 8) R(13, 3) 30966881.8 12.1 1361.02 BAND II R( 8) R(13, 4). 30966924.6 64.9 1:.61.02 BAND II R( 8) R(24, 9) 31366843.9 86.9 1303‘02 BAND II R(46) ‘Transition in the 293 e vs band of 1368 F; J S 25, 2:12. 3 bFrequency of 203 ~ v3 band transition in M82. cFrequency of 29 o v band transition minus laser frequency in M8 . Laser frequencies calculated from constants in Refs. 81, 82, and 83. dIdentification of CO or N20 laser. Band I is 10 um band: Band II is 9 pi bend. 167 Table XVI. Coincidences Between Calculated Frequencies for 03 Band of 12 C8 F and CO P(27,11) 0( 6, 4) 0(11, 1) 0(12, 1) 0(12, 2) 0(13,l3) 0(14, 2) 0(14. 3) 0(16.16) 0(21,16) 0(28, 3) 0(28, 4) 0(28, 6) 0(33. 8) 0(34,l5) 0(38, 2) 0(39, 8) R(10, 3) R(ll, 9) R(11,11) R(26.16) R(31, 4) R(34, 3) R(36,12). 29828909.0 31423019.9 31391948.0 31383841.? 31383940.1 31382764.9 31366702.8 31366849.8 31366845.0 31286137.6 31163602.8 31163626.6 31163432.1 31068741.4 31029723.8 30941471.6 30912621.1 31963616.9 31998687.9 32000206.2 32660672.? 32708073.? 32791607.1 32807743.3 24.6 2 Laser Frequencies. Laser 1‘ICI'Os BAND II P(26) uCHOl'O BAND II P(30) 1301‘09 BAND II R(48) uCl‘Os BAND II P(20) 1301‘02 BAND II P(20) 1361.011 BAND II R(32) 13C1'Oa BAND II R(46) 13C1‘Os BAND II R(46) nC1‘Os BAND II R(46) 1301‘01'0 BAND II P(35) uC1'Oe BAND II P(54) uCl'Os BAND II P(54) uCHOe BAND II P(54) uCHOI'O BAND II P(43) 120100100 BAND II P(44) 12CHOI'O BAND II P(4?) 193140. BAND II R(18) 130100100 BAND II P( 9) 13C100: BAND II P(22) uCl‘Ol'O BAND II P( 7) 1361'02 BAND II R( 2) 12Cl'Oe BAND II R(IO) 18c100100 BAND II R(32) 13C1'01'O BAND II R(33) CRan J S 40, X S 16. bFrequency of 93 hand transition in M82. cFrequency of v band transition minus laser frequency in M82. in Refs. Laser frequencies calculated from constants 81, 82, and 83. dIdentification of 00 Band I is 10 pm band; Band II is 9 p0 or N20 laser. band. 168 Table XVII. Coincidences Between Calculated Frequencies for 2V3 2 v3 Band of 12C83F and CO2 Laser Frequencies. P(22, 0) 29706011.1 ~96.2 I3(31‘01'0 BAND I R(40) P(22, 1) 29706048.0 ~68.3 la61°01'0 BAND 1 R(40) P(22, 2) 29706169.4 63.1 1361‘01‘0 BAND I R(40) P(2l, 7) 29770679.? 11.6 1301902 BAND II P(28) P(20, 6) 29833266.8 ~67.2 1a61‘01'0 BAND I 8(60) 0(10, 6) 30926970.0 ~23.0 1361902 BAND II R( 6) 0(16, 6) 30873622.0 ~68.4 1301'02 BAND II R(16) 0(17, 1) 30861966.1 68.6 1a01'02 BAND II P(38) 0(18, 8) 30861?28.0 ~37.0 1301901'0 BAND II P(60) 0(26,12) 30762061.6 ~7.3 1361°02 BAND II R(10) R( 7, 3) 31341429.0 6.7 ta01‘01'0 BAND II P(33) R(10, 0) 31472640.0 ~97.1 1301'02 BAND II R(38) R(10, 1) 31472668.6 ~78.4 1"01.02 BAND II R(38) R(10, 2) 31472716.3 ~21.7 1361.02 BAND II R(38) R(10, 3) 31472812.2 76.2 1361.02 BAND II R(38) R(12, 4) 31667183.? ~64.3 1361'02 BAND II R(44) R(12, 6) 31667332.0 94.1 1"61'02 BAND II R(44) R(13, 6) 31698691.2 36.1 1201‘02 BAND II P(38) 12 .Transition in the 2v v v band of CR F; J S 25, 2112. 3 3 3 bFrequency of 293 ~ v3 band transition in M82. cFrequency of 2v ~ v band transition minus laser frequency in M82. 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Misushima, ”The Theory of Rotating Diatomic Molecules”, Niley, New York, NY, 1982, p. 282. A. V. Burenin and V1. 6. Tyuterev, J. Mol. Spectrosc. 108, 153-154 (1984). J. E. G. Natson, J. Mol. Spectrosc. 103, 360-363 (1984). J. R. G. Natson, S. C. Foster, A. R. N. Mckellar, P. Berneth, T. Amano, F. S. Pan, M. N. Crofton, R. S. Altman, and T. Oka, Can. J. Phys. 62, 1875-1885 (1984). F. R. Peterson, B. C. Beaty, and C. R. Pollock, J. Mol. Spectrosc. 102, 112-122 (1983). B. G. Nhitford, X. J. Siemsen, H. D. Riccius, and G. R. Hanes, Opt. Commun. 14, 70-74 (1975). C. Freed, L. C. Bradley, and R. G. O’Donnell, 1888 J. Quantum Electron. QE~16, 1196-1206 (1980). 164 ~ PART 111 ~ 13 INFRARED-INFRARED DOUBLE RESONANCE 0F 08 F 3 BY MEANS OF A NAVEGUIDE 002 LASER AND AN INFRARED-MICROWAVE SIDEBAND LASER 166 CHAPTER I INTRODUCTION A molecule in a quantum state 0 collides with another molecule and changes its quantum state to 0’. For most molecules at room temperature, the energy transfer may be characteri2ed as being between vibration and rotation (V - R), between vibration and translation (V - T), between rotation and translation (R - T), between vibration and vibration (V - V), between rotation and rotation (R - R), and between translation and translation (T - T). Normally, the R - R processes have the highest rate constants with V - R and V - V processes being much slower. The experiments to be described in this section provide information about the relative rates of the various modes of energy transfer. Since the molecular interaction is a result of collision, the rates of energy transfer provide information about the mechanism of the collision process. In discussing the theoretical treatment of the collision process, we usually introduce the concept of strong and weak collisions. This is because, contrary to the situation for a radiative interaction in which the energy of interaction is much smaller than the energy spacing, a collision interaction has a wide range of energy values. For a limiting case of weak collisions, in which the intermolecular interaction is small and of long range, a 166 perturbation technique for the rotational energy changes can be used to a good approximation. For such collisions, the conversion from rotational energy to translational energy is small and the molecular path is not deflected significantly. Most of the N83 - N83 collisions at room temperature are examples of weak collisions(l). Also, when the interaction is weak, a molecule in a certain initial level has appreciable transition probabilities to only a few levels, and the selection rules can be understood by using the known symmetry properties of the long range potential. For strong collisions, for which the energy of interaction is larger than the rotational energy spacing, the molecular path is deflected by a large angle, and a molecule has transition probabilities to many rotational levels. For such collisions, no selection rules can be established. In reality, however, most collisions lie in a difficult region between these two extreme cases. For the study of collision processes, three experimental methods ~ molecular beams, optical fluorescence, and double resonance have been developed and used widely for the last two decades. In these methods a known non-Boltsmann distribution is established in some molecular levels of a gas at low pressure, and the consequence of collisions is obtained by monitoring populations of molecules in other levels. In the molecular beam method(2), a beam of molecules 167 in a single rotational level is selected by an inhomogeneous electric field and, after passing through a region in which collisions occur, is analysed by a second state selector. The advantage of this method is that the analysis of the results gives a single transition probability directly, and, further, it is possible to control the relative angle and velocity of the collision partners. The application of this method has been limited by the experimental difficulties. However, with the advance of molecular beam technique, this method may become a powerful tool for the study of collisions. In the optical fluorescence method(3), the molecules are pumped by monochromatic radiation into a single rotational level in an excited electronic or vibrational state and collision-induced rotational transitions in the excited state are detected in the fluorescence spectrum. So far, these experiments have been done by using accidental coincidences between the exciting radiation and the molecular absorption lines, but this method may become more generally applicable by using tunable lasers. One limitation of this method is that the lifetime of the excited state, which cannot be controlled, has to be of the order of collision time. The double resonance method uses two resonant one- photon interactions in a single molecule to probe molecular structure and relaxation properties. Figure 1 shows energy ‘Tqir—c a-T- c ”1 ”1 T I 750 ”2 Figure 1. 168 (o) 0:) (F) Diagrammatic representations of three-level double resonance spectroscopy (A)-(C) and four-level double resonance spectroscopy (D)-(F). 169 level diagrams for several kinds of double resonance. The fundamental double resonance process is that of three-level double resonance, in which fields at two different frequencies, v1 and v2, couple a given molecular energy level to two other levels. The common level may be either lower in energy than the other two, as in Fig. 1(A), higher than the other two, as in Fig. 1(8), or intermediate in energy, as in Fig. 1(C). A second process is four-level double resonance, in which the two radiation fields probe pairs of levels not having a level in common. For this kind of double resonance to occur, at least one level in each of the two pairs must be coupled to the other by collisional or other relaxation processes. This can occur by relaxation in the excited state, Fig. 1(D), in the ground state, Fig. 1(8), or both. Another variant is shown in Fig. 1(F), in which relaxation occurs to an intermediate level d. Figure 2 shows several kinds of pumping and monitoring schemes in four-level double resonance. Figure 2(A) is an energy diagram for microwave-microwave double resonance, in which strong and weak microwave fields are used for the pumping and probing radiation sources, respectively. The ease of handling microwave radiation has made this method widely applicable to many rotational levels of simple polyatomic molecule. Since the non-Boltsmann distribution is introduced into two rotational levels rather than in one level, the interpretation of the results is more complicated 170 MW- MW IR-MW l 3 V '4 l V, ”P 2 _ 2 V. I 3 V, 4 (A) (8) Figure 2. resonance experiments. Fl «6N (C) Energy level schemes in four-level double The light and heavy arrows represent low and high power radiation, respectively. The wavy arrows represent paths of collisional energy transfer. 171 than for other methods. Nevertheless, most of our information about selection rules for collision processes has been obtained by this technique(l). The infrared-microwave double resonance, Fig. 2(B) has usually used strong infrared and weak microwave radiation sources for the pumping and probing fields, respectively. This method has been widely used for the measurement of rotational frequencies and relaxation rates in the excited state because a large non-Boltzmann distribution is introduced in a single rotational level in an excited vibrational state by the infrared pumping. However, in most cases of infrared pumping, it has been necessary to rely on an accidental coincidence between a fixed frequency laser and the frequency of a molecular transition. Infrared- infrared double resonance of the type shown in Fig. 2(C) is even more difficult because it is necessary to rely on a double coincidence, in which strong infrared and weak infrared radiations are used for pumping and probing sources, respectively. Since in most cases the infrared source for pumping is a coherent radiation with a very narrow bandwidth, the molecules with a particular velocity component are depleted from the pumped level, that is, a hole is "burned" in the Doppler profile of the molecular absorption(l,4,6), as in Fig. 3. The first true double resonance was performed by Brossel and Bitter(8) in 1962. They used a mercury 172 Upper Level 52"]? 0 Vm Laser / E2 - E1 = h yo E1 ”Ill/MW/flW/l/flm. v Vres Figure 3. Change in the particle velocity distribution over two-levels of transition under the action of a - laser wave of frequency v. The 2-component of velocity of particles interacting with the light wave is 'res = C(v - vo)/v°. 173 resonance lamp to excite mercury atoms which were simultaneously subjected to a radiofrequency field. Double resonance as a general technique in molecular spectroscopy was first realised in the microwave spectroscopy of rotational levels by E. B. Nilson’s group at Rarvard 0niversity(7-ll) and by T. Oka at the National Research Council of Canada(12-20). Nith the introduction of the laser, it become possible to extend these techniques to the infrared and optical regions of the spectrum. For most infrared-microwave double resonance experiments(2l-37), coherent gas lasers in the 10 pm region, such as CO2 and N20 lasers, have been used for the pumping source. It would be very useful to be able to extend these techniques to a wide range of rotational energy levels in different vibrational states. Such studies would greatly increase our knowledge of molecular structure and the mechanism of collisional interaction. Until 1970, a true infrared-infrared double resonance experiment had not been done because of the limitation on the availability of a tunable infrared laser for the probing source. Rhodes et al.(38) had earlier tried to measure a collisional relaxation rate by using two fixed frequency CO2 lasers for pumping and probing sources on 002 molecules. In the early 1970’s, Lunts, working in Brewer’s laboratory(39~42), exploited the nonlinear behavior in three-level systems, which was originally worked out by 174 Schlossberg and Javan(43), to study double resonance in a molecular system. In these experiments, two laser radiations with slightly different frequencies were used in the presence of D.C. Stark field to measure the Stark shifts with high accuracy. At about the same time, Steinfeld and his collaboratores(44-47) and Preses and Flynn(48) measured the vibrational relaxation by monitoring the population change due to pumping in SF6, BC13, and CHaF molecules, respectively. In order to increase the tunability of an infrared source, Freund et al.(49) introduced the two-photon technique into infrared-infrared double resonance by carrying out a four-level double resonance experiment on 15N83. From this experiment, they observed not only the non-Boltzmann distribution, but also the hole being transferred to the signal levels. Shoemaker et al.(60,61) observed the same phenomenon in 13 C83F, by using two fixed- frequency C02 lasers and a D.C. Stark field. Although the two-photon technique has a wide range of tunability, the transition intensity is much weaker than that of one-photon spectroscopy, especially for the case of a large difference between the laser frequency and the one- photon allowed molecular transition(62). So, Orr and Oka(53,54) developed an infrared-infrared double resonance technique that employed the sidebands generated by passing CO2 laser radiation through an electro-optic modulator 176 driven by the combination of a radiofrequency and a D.C. Stark field. Nith this technique they could accurately measure the dipole moment for several symmetric top molecules. Nith the same method, Duxbury et al.(55,66) used isotopic CO2 laser radiation to measure the dipole moment of CHaF and its isotopes, Neber and Terhune(67) extended the infrared-infrared double resonance technique into the 6 pm wavelength region by employing a C0 laser as the pumping source and a tunable diode laser as the probing source. By using two laser sources in different frequency regions, they were able to see the double resonance effect in three different vibrational states in the N83 molecule. Recently, another infrared-infrared double resonance experiment on 15N8 14 vibrational energy transfer between 3 and NH3 was done by Euse et al.(68) by means of a CO2 and a tunable diode laser as pumping and probing sources, respectively. From the analysis of the experimental results, a preference for dipole-allowed (AJ = 0, :1, AB = 0) transitions and a prohibition of ortho-para conversion were confirmed, which is in agreement with the previous studies by microwave- microwave double resonance(l6) and by infrared-microwave double resonance(3?,59). The study of vibrational energy transfer is also very important to understanding the collisional process and its elementary mechanisms. Preses and Flynn(60) used an infrared-infrared double resonance technique to study the 176 vibration-vibration energy transfer between 12C83F and 13C83F with two-fixed frequency 602 lasers operating on different laser lines. The analysis of the experimental results showed that one quantum of 03 energy is transferred between 12C83F and 13C83F in every six collisions. In the study to be described in this thesis, a. waveguide CO2 laser and an infrared-microwave sideband laser were applied for the first time to infrared-infrared double resonance as pumping and probing radiation sources, respectively. The sample was 13 C83F and many kinds of three-level and four-level double resonance experiments were carried out. The results of the three-level double resonance measurements are in good agreement with the previous studies. However, four-level double resonance showed the evidence of indirect pumping to all rotational energy levels in the first excited state (v3 = 1), which is extremely useful for identification as well as observation of hot bands. The next chapter gives the theoretical background of saturation effects and double resonance. Chapter III provides an explanation of experimental details which is similar to that in the second part of this thesis. Finally, Chapter IV describes the experimental results and presents an analysis of the results and several spectra. 17? CHAPTER II THEORY isiszsiisn_zzgssssL§21 Nhen a molecular transition is subjected to high intensity radiation, the fraction of light absorbed by the molecule becomes less than that for low intensity light, that is, the absorption coefficient appears to saturate. Consider a two-level system, with states 1 and 2 coupled by electric-dipole radiation: where p12 is the dipole moment matrix element between states 1 and 2, o is the frequency of the radiation, and e is the amplitude of radiation field. Let the quantum mechanical amplitude of the upper state be 22, and that of the lower state he a1. Then d. 1(0 ' a )t ~i(o + a )t 011 ' 2 "‘2[° o * ° 0 (2) ds 1(0 - o )t ~i(0 + o )t a?! a %»x£a1[e ° + e o ] where x = plzlh and "o = (El-Ez)/h. As long as the Rabi 178 frequency '1 = x6 (< 00, we may neglect the high frequency terms (rotating wave approximation) to give 02.2 0.2 “e 2 Ft ‘1‘ 1(0 " 0°)a—t— + 4 I2 3 0 . (3) The solution to Eq. (3) is a2(t) 8 o-iAt/2(A.iflt/2 + Bo-iRt/Z) (4) and .1(t) a _ %E_.iAt/2[(° _ mA.iI'It/Z + (a + n>no““”/21 . (5) where A 8 e - o and fl = [02 + (x£)2]1/2. Let us assume the initial conditions a1(t°) = e1. and a2(t°) =‘0. This gives the coefficients [ie+io(t-t )/2] al(t) = e o [cosg(t-to)-i%sin%(t-to)] (6) and [ie-iA(t-t°)/21 e2(t) = iEE-e fl sin¥(t-t°) . (7) The corresponding expressions for the populations are 179 2 2 alct) = |I1(t)| 9; + i=$%— co .2 “(t- -t > (8) H H and 82(1) = Iaz(t)I2= £1§1—u z§.' = 71"] laz(t,t°)|2 ° 2 dto 2 ~11 2 = %_ g (If) _ . (11) (o-uo)z+(1/r§)§+<.e>z This expression indicates that the line shape is that of a Lorentsian, modified by power broadening proportional to (2. the intensity of the radiation field. Also this equation 180 45:0 N70 (1 (l-to) Figure 4. Time evolution of the population of the excited state of a two-level system subjected to a coherent dipole perturbation. On-resonance pumping (A = 0) results in the slowest oscillations having the greatest amplitude. 181 shows that a very intense field will eventually equalize populations between upper and lower levels of a transition 2 because (Iazl >av a 0.5 as G - s. The power absorbed, which is the observable in this system, can be written as 2 (0’wo)2+(l/Té)2+(x€)2 Here N1 and N2 are the equilibrium populations of states 1 and 2, respectively. As 6 - a, AP becomes a constant. Thus, the absorption coefficient, CI€I /8w "1. N2 4wu§20 = -—‘* (13) 2 cat(o-uo)2+(1/ré)2+(ue)§1 approaches zero and the medium saturates. Figure 3 shows the particle velocity distribution in the two levels of a transition subjected to a laser wave of frequency v, in which the laser light is intense enough to stimulate transitions of a considerable proporti0n of the molecules to an excited state. The excitation of particles with a certain velocity (vr°.) changes the equilibrium distribution of particle velocities in each level of the 182 transition. In the lower level there is a lack of particles whose velocity complies with the resonance condition, that is, a hole in the velocity distribution. By contrast, in the upper level there is an excess of particles with resonance velocities, or a peak in the velocity distribution. The hole depth and the peak height depend on the degree of absorption saturation by the radiation field. Nith a single propagating field, there will be no appearance of a Doppler free resonance as the frequency is tuned across the transition. The nonlinear dependence on the intensity of the strong (pumping) radiation requires a second transition to appear as a change in absorption coefficient of the weak (probing) radiation. Let us assume a pumping radiation at a fixed frequency a, saturating the Doppler broadened resonance, and the direction of propagation to be the +2 direction. Also, we assume that a probing radiation at the frequency up is propagating in the opposite direction of the strong radiation at the same time. This is the actual experimental scheme for most double resonance studies as shown in Fig. 6. For molecules with a velocity component vz = v, the frequency of the intense field at the molecules will be Doppler shifted to o - 0(1 - v/c). The weak probe field, however, will be Doppler shifted to up 4 "P(1 + v/c). Therefore, if v > 0, the intense field will be down-shifted in frequency, but the weak field will be up-shifted. 183 DET Figure 5. Schematic arrangement of pumping and probing radiation in many infrared-infrared double resonance experiments. 184 Consider the absorption of the probe field in the presence of an intense field at a fixed frequency a. The change in radiation power SIp due to molecules with a velocity v in a narrow range dv is given by(63) 81p = (dn1 - dnz)hopR(op) (14) where (dnl - dnz) is the change in the population difference between two states 1 and 2 over velocity distribution range dv, and R(op) is the transition rate induced by the probing field. Here, R(op) has the following form O ;(”12‘ )2 1' R(op) = 2 v“ 57— . (15) [09(1+3)-..°] 'r + 1 Thus, the probe field will show a Lorent2 shaped resonance at "p = 80/(l+v/c). b e e o nce in T ee- vel S ste Double resonance in a three-level system, as shown in Fig. l(A)~(C), means that two transitions induced by strong and weak fields share a common level. Consider a three- 1evel system of the type shown in Fig. 1(8), and let a1, a2, 186 and a3 be the quantum mechanical amplitudes of the states c, b, and a, respectively. Suppose that a strong field (P at frequency up is applied close to the transition frequency 031 = “ac’ and a weak field 6 is applied at frequency a close to 932 = 'ab' The equations of motion for the amplitudes are then a. I 1(0 ‘0 )t 1 a i p 31 a?- f spipiac (16) da 1(0 ’0 )t 333‘ ‘1’“ ‘ 73° 32 ”7’ da -i(o '0 )t ~i(o-w )t 3:1 3 %[xp£paae p 31 + xszs 32 ] (18) with xp = 2p13/h and x = 2p13/h. Let us impose the initial conditions al(to) = e1., a2(to) = a3(t°) = 0. The steady state solution for (p and 6 being constant may be found by setting dalldt = 0, yielding al(t) = Ale 1(0 ‘0 -x)t a2(t) = 12. P 32 (19) 83(8) = 130'1*‘ where 186 Xa-(Up-031+0-032 ) >52+[ (Up-031) (0-032)- ( ‘P€P) z ‘(x£)z]x+(xp£p)(o-o3z)+(x£)(op-031) = 0 (20) The complicated cubic expression for x can be solved approximately by recognising that (p >> 6 in typical experiments. Ne then find that x 6 is-i(u -o )(t+t )/2 fl (t-t ) 813(13) = I-g—P- e P 31 ° sin ° (21) P - _ 2 2 1/2 "her. up - [(09 031) + (‘p€p) ] 0nd 1(8 +8)(t-t ) x£x 6 P 0 _ p 2 e ~l a12(t) - 29 exp{ie[ n + 8 P P ~i(fl ~6)(t-t ) P 0 _ + ° ‘1} <22) flp~ 6 where 8 = 2(e~032)-(e~031)- 187 CHAPTER III EXPERIMENT Figure 6 shows the experimental diagram for the infrared-infrared double resonance studies described in this research. A waveguide 602 laser (Laakmann Electro-Optics Inc. Model RFG 88-8) and a microwave feedback controlled infrared-microwave sideband laser system were used for the pumping and the probing radiation sources, respectively. The system for the probing radiation was explained in detail in Chapter IV of the second part of this thesis. However, the sample cell was slightly modified to prevent the reflection of the pumping radiation from the window of sample cell to the detector. In order to do this, the NaCl window was sealed at the slant angle, in which the angle of window was rotated to let the probing radiation transmit more favorably. The pumping radiation, whose polarisation was perpendicular to that of the probing beam, passed through the sample cell after reflection by the beam splitter. In this experiment, the frequency of the pumping radiation was locked by means of its internal pyroelectric detector stabilising system. The amplitude of the frequency modulation required for this stabilisation was minimised to keep the fluctuation of the frequency of the pumping laser as small as possible. 188 _J I ~ rowan SUPPLY 067 ~ A/ 17“ /' 2______S ./ IGRAJNKS - l umuscuuxscthauu DET \ \. ' SAMPLE CELL PREAMP ,PREAuu’ 9001 Iso 477 PIM "STE" P501 P502 H:_——*— l ——-7 COMPUTER TTY A/DI ' Figure 6. Experimental diagram of infrared-infrared double resonance by means of a waveguide C02 laser for pumping and an infrared-microwave sideband laser for probing. 189 Naveguide CO2 Laser As a result of molecular collision broadening, it has been possible to increase the tunability of the frequency of a gas laser by developing small, high pressure, and sealed- off waveguide CO2 lasers. Since the CO2 Doppler full width at half maximum at 300 0! is approximately 50 M82 and the collision broadening is ~5.3 MHs/Torr(65), collision broadening will dominate the lineshape for operating pressures greater than about 10 Torr. At pressures above several hundred Torr, it is theoretically possible to increase the tunable range of a C02 laser to several 682. For most gas lasers, the electron temperature, and hence the characteristics of the discharge tube diameter are determined by the product of the pressure and the discharge tube diameter, so by going to small diameter tubes one can increase the pressure and still obtain high gain performance. These arguments led to the development of the waveguide 602 1aser(66,66), in which the discharge is contained in a hollow dielectric waveguide with an inside diameter of a millimeter or less. Since the individual vibration-rotation lines of CO2 in the ~10 pm region are separated by l to 2 cm-l, pressures of about 10 atm. are necessary to provide adequate overlap for continuous tuning. But it is difficult to obtain population inversion and gain in this pressure region, and 190 when laser action can be achieved the linewidths tend to be the order of a few tenths of a cm-l. Figure 7 shows a composite metal-ceramic waveguide laser structure, in which the tube is surrounded by two ceramic plates which are separated by precisely formed metal electrodes. The gas mixture in this small tube is RF- excited. The laser tube is bonded into a hermetically sealed aluminium tube and support structure, which also functions as the gas reservoir. The and mirror is mounted at the output end of the laser to seal the system, and a grating is placed inside the vacuum envelope at the other end. A single micrometer control allows the grating to rotate for tuning the system over a wide range of laser lines without causing any severe problem in optical alignment. 191 GAS CHAMBER CERAMIC WAVEGUIDE CAVITY ELECTRODE Figure 7. Cross sectional view of the waveguide CO2 laser used for this experiment. 192 CHAPTER IV RESULTS AND DISCUSSION For an infrared-infrared double resonance experiment, a waveguide CO2 laser and an infrared-microwave sideband laser were used for pumping and probing radiation sources, respectively. Figure 8 shows the energy level diagram for three-level double resonances within the tunable range of the sideband system, in which a microwave oscillator was swept from 8.2 to 18.0 682 for each CO2 laser line. The ’famous’ 9P(32)CO2 laser line of the waveguide CO2 laser was used for a pumping source because the frequency of the 13 QR(4,3) molecular transition of the 03 band of CH F is 3 just 25.8 M82 below the laser frequency.‘ Nithin the tunability of the sideband system, three kinds of three- level double resonances could be observed, all of which involved pumping the QR(4,3) transition (8 in Fig. 8). The signal transitions were A (intermediate common level), C (upper common level), and D (lower common level). In addition, two four-level double resonance experiments (combinations of B and E and B and F) were performed without observing any significant pumping effect, in agreement with the selection rules (AK = 0) for a collisional process. Since many transitions in the 203 ~ 03 band of 13683F could be observed by using the infrared-microwave sideband system(61), it was possible to observe many four-level Figure 8. 193 R(5.5) R (4.3) P (6.3) P (4.5) R(3.3) R(5.3) (1(6.3) CD'VII'V'IUOW) (6.3) 9P(46)+l5393.5 MHz 9 P(321- 25.8 = Pumping 9 P(50)+l5354.2 9 P(46)-9466.| 9P(34)+l30l2.2 9 P(30)-IZ9549 9 P( 40)- 9860.7 Energy level diagrams for the waveguide CO2 laser and infrared-microwave sideband laser system used 13 for infrared-infrared double resonance in C83F in this work. 194 double resonances that were apparently the result of cascading collisional processes(67) or of vibration- vibration energy transfer(60). Ne concluded from these preliminary experiments that a waveguide CO2 laser and infrared-microwave sideband laser system is a very useful combination for infrared-infrared double resonance, at least for the pumping of a single transition and the observation of a variety of double resonances. Nith the experimental diagram shown in Fig. 6, in which the pumping and probing beams travel in opposite directions, the sum of two laser frequencies at resonance in a three-level experiment should be equal to the sum of the frequencies of the two molecular transitions, irrespective of the molecular velocity components; that is, _ pump + 0probe pulp + "probe "o o = constant . (24) Figure 9 shows the variation in frequency of the pumped molecular velocity group with pumping frequency for a three- level double resonance (combination of B and A). The spectra shown were obtained by probing transition A with the positive sideband generated by combination of the 9P(46)CO2 laser line and P-band microwave radiation. Each time the pumping frequency is changed, the laser pumps a different velocity group. The saturation effect of one particular 196 ....... O O .............. ...................... ........................... are e .... ......egeooee. ee ...".- eeeeeeee C eeeee eeeee eeeeeeee eeeee e ....... eeeeeee eee e .......................... eeeeeeeeeeeeeeeeeeeee eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee ....... ........ ................................. .0” e. .00 e0“ eeeeee Ttansmittance . eeeeeeeee .......... ................................. eee““°. ...“. . . .07...” .............. eeeee ..... eeeeeeeeeeeeeeeeeeee I... set. eeeeeeeeeeeeeeeeeeeeeee .. ...- ........ s .0 ................. ...... 02" ....... ...... ...°'0'ee00se‘e 09”.... 0 .. 1‘ 1 L l5.30 I533 IS.36 I5.39 l5.42 I5145 FREQ. (GHz) Figure 9. Variation of the position of the pumped molecular velocity group with pumping frequency. The transition 1. °a(5,3) of the 2V3 ~ 03 band of 1308 r. The °n(4,3) transition of the 03 hand 3 was pumped at a different frequency for each the spectra A-F. 196 velocity group in the upper state was monitored by a weak probe field. The increased population for a small range of velocity is shown in the spectra. From this kind of variation, the tunability of the waveguide CO2 laser could be determined to be greater than 110 M82, which is a reasonable value considering the CO2 pressure broadening. One of the advantages of infrared pumping is to transfer only the molecular velocity group which is in resonance with the laser frequency. Since the waveguide CO2 laser was frequency modulated for stabilisation purposes, actually a range of velocity groups was pumped. By increasing the modulation amplitude the range of velocities pumped could be increased. Figure 10 shows the variation of the width of the molecular velocity group pumped with modulation amplitude. For this spectrum, the positive sideband generated from the 9P(46)CO2 laser line and P-band microwave radiation was used at ~108 mTorr of sample pressure. The oR(4,3) transition in the v3 band was pumped and the QR(6,3) transition in the 203 v 93 band was probed. From these spectra, the need for a highly stable pumping laser was comfirmed to study the velocity preserving collisional process. Th ee-Leve Do b eso a c 197 ........... (A) ................ (8) .................................................... ‘(C) ......................... (o) 8 .............. g ........................ ...(E) .é ..................................... a) ....... C ......... (a ............... p. "cw= 2134- V, °R(5.3) IS. 35 IS. 37 I5. 39 I5. 4| IS. 43 IS. 45 FREQ. (GHz) Figure 10. Variation of the range of the molecular velocity group pumped with the modulation amplitude of the pumping laser. The modulation amplitude was increased in steps from (A) to (E). The QR(4,3) transition of the 93 hand was pumped. 198 For the three-level double resonance (combination of B and C) which has the upper state of the transitions in common, the oR(4,3) and oP(6,3) transitions of the v3 band were pumped and monitored, respectively. Since one component of the molecular velocity groups was transferred into the upper state by pumping, the upper state was overpopulated at a particular velocity. Therefore, as shown in Fig. 11, the °P(6,3) transition shows a saturation-dip at a frequency corresponding to the pumped velocity group. By tuning the laser frequency, the saturation-dip was shifted to another position, as shown in Fig. 12. In this experiment, the positive sideband generated from the 9P(60)CO2 laser line and P-band microwave radiation was used and the sample pressure was ~20 mTorr. The 9P(60)CO2 laser. line is very weak in our system and many commercial CO2 lasers cannot generate this radiation. However, by adjusting the laser gas mixture to the optimum condition for the 9P(50)COz laser line, approximately 100 mN of laser power could be obtained. Even with this low power for the sideband generator, excellent spectra were obtained (Figs. 11 and 12). This fact demonstrates the usefulness of the infrared-microwave sideband system for both linear and nonlinear spectroscopy. By using isotopic CO2 lasers, we can get almost continuously tunable sideband radiation throughout the 9 - 11 pm region. 199 0) L) c: .9 E U) 3 13 ,:_- CH3F V3 °P(6.3) I5. 25 l5.30 l5.35 I5.4O l5.45 FREQ. (GHz) Figure 11. Observation of a saturation-dip in the QP(6,3) transition in the 93 band from three-level double resonance with a common level in the upper state. The QR(4,3) transition in the 93 band was pumped. 200 Q) (J c d” E ..... E U) 5 p: ‘3CH3F 123 °P(s.3) l5.25 I530 l5.35 Is.40 l5.45 FREQ.(GHz) Figure 12. Observation of a saturation-dip in the QP(6,3) transition in the 93 band from three-level double resonance with a common upper level. The pumping frequency in this figure has been shifted slightly from that in Figure 11. 201 As a result of the depletion in population of the J = 13 4. I = 3 level in the ground state of OH I achieved by 3 pumping the oR(4,3) transition. the oP(4.3) transition also shows a saturation-dip at a particular velocity group; this is shown in Fig. 13. The probing transition was monitored -by scanning the negative sideband generated from the 9P(46)002 laser line and x-band microwave radiation at ~46 mTorr of sample pressure. This is a three-level double resonance (combination of I and D) with a common level at the lower state. One of the advantages of infrared-infrared double resonance is to be able to observe the population difference between vibrational states compared to other types of double resonance. With the overpopulation at one velocity group achieved by pumping the oR(4,3) transition of the v3 band, the QR(5,3) transition of the 293 ~ 93 hand shows the pumping effect very clearly with a sharp saturation spike. figure 14 shows this double resonance effect resulting from three-level double resonance with a common level between two transitions (combination of B and A). In this spectrum a sharp saturation-spike is seen. in which the position and the width of the spike depend on the pumping freouency and the modulation amplitude of a pumping laser, respectively. for the observation. the positive sideband generated from the 9P(46)CO2 laser line and P-band microwave radiation was Transmittance 9. 36 Figure 13. 202 L A _J 9.40 9.44 9.48 9.52 9.56 FREQ. (GHz) Observation of a saturation-dip in the QP(4.3) transition in the v3 band from three-level double resonance with a common level in the lower state. The QR(4.3) transition in the v3 band was pumped. Transmittance ISJS Figure 14. 203 = 3 ------- Without pumping — With pumping '3CH3F 2V3<—V3 °R(5.K) A I A l5.2$ I535 |5.45 l5.55 I565 FREO.(GH2) Observation of the increased intensity of the oR(b,3) transition in the 2v3 v 93 band that results from three-level double resonance with a common level that is the upper state for the pumping transition and the lower state for the probing transition. Also shown is the increased intensity of the remaining °R(5,l) transitions that result from increased population of the v3 = 1 state caused by pumping the QR(4.3) transition in the fundamental band. 204 used and the sample pressure was ~96 mTorr. Usually the rotational relaxation rate (~l usec) is much faster than that of the vibrational relaxational rate (~l msec). Both rates increase linearly with pressure. Under the conditions of our experiment, the rotational rate is so fast that a Boltzmann distribution is established among the populations of the rotational levels in both states and this saturation is not changed by variation in sample pressure up to ~l Torr. However, the vibrational populations do not follow a Boltzmann distribution and are strongly affected by sample pressure. figure lb shows the variation of the double resonance effect at the peak frequency of the direct pumping with sample pressure. This is a comparison of the peak height of the transferred spike in the 0“6.3) transition in the 2v3 . v3 band with pumping and without pumping. As the sample pressure increases. the double resonance effect (saturation effect) decreases because of the increase in the vibrational relaxation rate with the sample pressure. -Leve Do e According to the selection rule for collisional process (oJ = 0, :1. A! = 0), the possible candidates of four-level double resonance are the combinations of B and B [pump / Iunpump Figure 15. 20 . l5 - IO - 5 _ . O *—-('. ‘ . . 60 IOO I40 I80 PRESS.( mTorr) Variation of the double resonance effect on the intensity of the QR(5,3) transition in the 2V3 v v3 band with sample pressure. The lower level of this transition is directly pumped by pumping the QR(4,3) transition in the v3 band. The solid line is a smooth curve drawn through the points. 206 and B and F in Fig. 8. No significant double resonance effects were observed for these combinations. He believe that this is because 3 and F are transitions in the fundamental band with high intensity and the collisional effect is small. For this experiment, the amplitude modulation of the probing radiation at 33.3 kHz was used. However, if we modulate the pumping radiation, it may be possible to observe the pumping effect from four-level double resonance on a fundamental band transition. For the evidence for indirect pumping to all rotational levels in the excited state (v3 = l), the transitions QP(22,!) of 293 . v3 band were chosen because they are within the range of tunability of the sideband system and their energy levels and quantum numbers are much higher that of the direct pumping level. Comparison of peak heights with pumping and without pumping shows that the intensity of all the transitions was increased by a factor of 2 - 4. Figure 16 shows the spectrum obtained from this case of four-level double resonance, in which the negative sideband generated from the lOR(14)CO2 laser line and P-band microwave radiation was used with ~112 mTorr of sample pressure. . The QP(l7,3) transition of the 2v3 . 93 band was chosen for observation of the variation of the effect of indirect pumping with pressure, because its frequency is within the tunable range of a sideband system and its peak 207 =3 K=I.o m e g ------- wIthout pumping g -- With pumping E cg ‘3CH3F p. . 21135-323 °P(22.K) I3.Io I126 l3.42 I158 I174 I330 FREQ.(GHz) Figure 16. Observation of the indirect pumping effect to all rotational energy levels in the first excited vibrational state (v3 = l) by pumping the QR(4,3) transition in the 93 hand. The intensity of all transitions in the 2v3 . v3 band appears to increase with pumping. 208 is completely isolated from other transitions. From Fig. 17 it can be seen that the indirect pumping effect decreases with increasing sample pressure. As in the previous case of direct pumping, this phenomenon can be explained from the increasing vibrational relaxation rate with sample pressure. In Fig. 17, the ratio 1.0 means that there is no effect of indirect pumping on the intensity of the transition. The lOR(30)CO2 laser line and microwave radiation at a frequency of 15452 “Hz were used to generate the negative sideband for this experiment. The diagram in Fig. 18 may be used to explain indirect pumping phenomena. Without pumping. all vibration-rotation energy levels are subjected to the Boltzmann distribution. The population of the first excited state (v3 = l) is approximately 1* of that of the ground state and the population of the second excited state (v3 = 2) is only 18 of that of the first excited state. We therefore write the relative populations as 99, l, and 0.01. The effect of pumping causes a non-Boltzmann distribution in the ground state and first excited state. The population of (4,3) energy level in the ground state and of the (5.3) level in the first excited state are equalized by strong pumping of the QR(4.3) transition. They therefore become 60 and 50. The overpopulation at the upper state decays to the ground vibrational state by vibrational relaxation and into other rotational levels in the first excited vibrational state by 209 2.0L 1...... Am... LO" 1 l l 1 1 Figure 17. ICC 200 300 400 500 600~ PRESS. ( mTorr) Variation of the effect of indirect pumping on the intensity of the °P(l7,3) transition of the 293 ~ v3 band with sample pressure. The oR(4,3) transition in the v3 band was pumped. The solid line is a smooth curve drawn through the points. 210 ~.Ol% ~.0I% Va=2 w W ~I‘/o V5: ‘H% (5.3) “'99./e v3=o W— . (4.3) \____——\,______J Unpumped Figure 18. Schematic diagram of the molecular population changes caused by pumping the QR(4,3) transition in the v3 band. The numbers above each level are relative populations. 211 either rotational relaxation. (Joxsvagl) + (J’.l'.v3=1) " (J".K”.v3=1) + (JM ,3" 0V3=1)s or by vibration-vibration energy transfer, (J.l,v3=l) + (J’,K',v3=0) 4 (J",K”,v3=0) + (J"',K"'.v3=1). In either case we imagine that collisions cause a small net loss in population of a connected level in the ground state and a corresponding gain in population of an excited state level. At the steady state, the population difference between the ground vibrational state and the first excited vibrational state does not change very much by pumping (99 - 1 = 98 . 97 - 3 = 94), while the population difference between the first excited state and the second excited state increases by a factor of 3 (~l 4 ~3). This explanation seems to agree with the experimental results. In order to confirm the above explanation explicitly. a frequency region was chosen in which a fundamental and a hot band transitions coexist. The region selected is the negative sideband tunable range generated from the lOR(20)CO2 laser line and X-band microwave radiation from 9.4 to 9.8 GHz. The evidence for indirect pumping to all rotational levels in the first excited vibrational state can 212 .Oo oo~I an mafia-an «nonuuz ADV was .ehsusquIOu loch as cash a: 0:3 ca noqauansu» Am.vvma on» no mean-5a new: any .euauequIO» moon as mafia-an unoAuwI A