, , , , , "Mn. 1“ k t" t OF cADMEL i , 1g. HJN ac.» . fink we... .5- P4. a hunt- an. row.“ '..¢ n... v .‘ .afififl {jaggc Im’ l 3» m‘fim A... a.” 9. .5... an“: H“: ,h. “‘0‘ g- ”n J. m. .1... if . .~: ‘- QM AH“ 5‘. v ' I .‘ C ‘ . :c’“ I» ”r”! Mum‘s.d ”.5“. _ 339.7; .. .u'».r':x;.-‘:x;a.:wm-.,. h-m'nii'fifimgzrr'fi M 31.1" ($9 “P I J . . . -l 'IE.I fllllllHllHHIIHIIIHIUIIIIIIilllllllllHHIIIIIIIIHHIIII 1293 01764 0032 ABSTRACT THE SEARCH FOR THE WEAK (1.14 Mev.) GAMMA RAY 93 CADMIUM115m AND g LITERATURE RESEARCH 95 2396, 22119 AND 23121. by Ricardo S. Pascual, Jr. To furnish an additional verification of the pre- viously reported l.l4-Mev. gamma ray from Cadmiumllsm, the spectrum of Sodium22 (the 1.28-Mev. gamma) and Scandiumg'6 (the 0.88-Mev. gamma) were subtracted from the scintilla- tion spectrum of the Cadmium isotOpe obtained with the 256- Channel Analyzer. The resulting spectral neighborhood show- ed a full-energy peak at 1.14 Mev. In addition, some of the latest information and 96, Tell9 and Te121 in future experiments on these isot0pes. Furthermore, some theoretical predictions on the internal conversion coef- estimates on To were summarized to aid ficients of these isotopes were made for comparison pur- poses with the observations of future experiments on these same isotopes. THE SEARCH FOR THE WEAK (1.14 Mev.) GAMMA RAY 115m 93 CADMIUM AND A LITERATURE RESEARCH 91} 3396, 23119 AND 23121. by Ricardo S. Pascual, Jr. A Thesis Submitted to the College of Science and Arts Michigan State University of Agriculture and Applied Sciences in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Physics 1962 Approved: \lfiflm’t B‘JZLLW ACKNOWLEDGEMENTS I am greatly indebted to Dr. William Kelly who suggested the problem and assisted in the actual investi- gation through his proposal of the subtraction technique; and to Dr. Herbert Bolotin who later assumed a similar task. I am very grateful to Dr. Bolotin for his guidance and help to make the completion of the research possible, and for his painstaking efforts in checking the manuscript. ii TABLE OF CONTENTS I. Introduction . . . . . . . . . II. Interaction of Gamma Radiation with Matter . . . . . . . . . III. The Scintillation Spectrometer IV. The 256-Channel Analyzer . . . V. The Observed Spectra . . . . . VI. The Search for the Gamma Ray . VII. The Literatgre Research: 9 l. Technicium . . . . . . . . . 2. Telluriumllg . . . . . . . . . 5. Telluriuml21 . . . . . . . . . VIII. Internal Conversion Coefficients IX. Appendix . . . . . . . . . . . X. Bibliography . . . . . . . . . - o O o - iii LIST 93 TABLES Table I. Energies, relative intensities, and half-lives of the ’Y'S of Tellg. . . . II. Coincidences in the 4.7d Te isomer . . . . III. Relative intensities of conversion lines of Te121 . . . . . . . . . . . . . . Appendix: (I - Tables of Internal Conversion Coefficients IX) for the Gamma Rays (X - Tables of Internal XIII) for the Gamma Rays (XIV - Tables of Internal XVI) for the Gamma Rays of Mo96 . . . . . . . . Conversion Coefficients of Sb119. Conversion Coefficients of Sblal. . . . . . . . (XVII - Tables of T% for Gamma Transitions XXV) of M096 . . . . . (XXVI- Tables of T% for Gamma Transitions XXIX) of Sb119 . . . . . (XXX- Tables of T% for Gamma Transitions XXXII) of Sb121 iv 50 58 - 65 63 - 65 65 - 66 e7- 71 71- 75 74 Figure LIST 9E FIGURES Energy Distribution Among Beta- Particles of Radium E . . . . . . . 2. The Single-Channel Analyzer . . . . 3. The Scintillator-Photomultiplfier Assembly . . . . . . . . . . . . . . 4. The Preamplifier . . . . . . . . . . 5. The Analyzer Arrangement . . . . . . 6. The Scintillation Spectrum of Cd115m 7. The Scintillation Spectrum of Na22 . 8. The Scintillation Spectrum of Sc46 . 9. The Cd Spectrum (Minus the 0.94- and 1.50-Mev. Peaks) . . . . . . . . . . 10. The Cd Spectrum (Minus the 1.30-Mev. Peak) 11. The Proposed Beta-Gamma Coincidence Arrangement . . . . . . . . . . . . 12. Proposed Decay Scheme of T096 . . . 15. PTOposed Decay Scheme of To96 & Nb l4. Tentative Decay Scheme for Tell9 . . 15. Tentative Decay Scheme for Te121 . . Appendix: 1. Decay Scheme of Cd115m . . . . . . . 2. Decay Scheme of To96 . . . . . . . . 5. Decay Scheme of Tellg. . . . . . . . 4. Decay Scheme of Telzl. . . . . . . . Page 10 13 15 19 26 27 28 29 30 51 57 58 47 53 75 76 77 78 INTRODUCTION RADIOACTIVITY: Radioactivity is the emission of energetiC'parti- cles (alpha or beta particles) or electromagnetic radia- tions (gamma rays) from unstable nuclei. The only means of detecting and measuring these emissions is through the ob- servable effects of their interaction with electromagnetic fields and matter. One of these means is the Scintillation Technique which is based on the effects of interaction of the radioactive emission with special substances known as "phosphors"; this will be explained in necessary detail in the later portions of this paper. For this particular presentation, it is necessary to discuss only two types of radioactive emissions: (1) Beta Particles: A number of experiments in the past have proven that this type of emission is composed of faSt-moving electrons; the only distinction from the earlier-defined electron be- the fact that these energetic particles originate from the nucleus instead of the extranuclear electronic orbits of the atom. There are no electrons existing as such in the nucleus. An electron, however, may be formed and ejected from the nucleus by means of a neutron decay into a proton and an electron (accompanied by a neutrino). The electri- cally neutral neutrino with a negligible rest mass is emitted to conserve the energy and the angular momentum in this neutron decay process. Beta particle emission is an isobaric process, producing a daughter nucleus which 1 has the same mass number (the nucleon number; i.e., the total number of protons and neutrons in the nucleus), but having an atomic number (i.e., the number of protons or the number of atomic electrons) which is one more than that of the parent nucleus. When the transition is from the ground state (state of lowest excitation energy) of the parent nucleus to the ground state of the daughter nucleus, the energy available for the beta decay comes from the differenceiJlmass of the nuclei involved. One method for determining the velocities of these particles (hence their energies) is by the measurement of 'the radii of curvature of their paths in a uniform magnet- ic field of constant intensity (perpendicular to the beta beam). By equating the Lorentz force to the Centrifugal force, the velocities can be obtained as a function of the known magnetic field intensity or the radius of curvature. This then, may result in a velocity or momentum distribu- tion of the beta particles from the radioactive source. The resulting momentum (or energy) spectrum from a beta disintegration is distinct from other types of Spec» tra characteristic of the same atom (viz., optical , char- acteristic X-rays, etc.); in that, it is a continuous one. The other characteristic spectra are ling spectra. The continuous beta Spectrum exhibits a "preferred" energy (the energy possessed by the greatest number) and a maxi- mum energy limit. This maximum limit or "end-point energy" is interpreted as the energy released in this particular radioactive disintegration. A typical beta spectrum is shown in Fig. l. Oftentimes, the continuous beta spectrum is superim- posed on a "sharp line" spectrum which is an indication of the presence of electrons which have been ejected from the extranuclear orbits of the atom. These internal conversion (IC) electrons are emitted as a result of the interaction J I I I I I I I I L 9 GA 0.1 o. 094 0-5' 0-6 .1 0.3 a, no u .4. Enemy; of acts Varficleo (Men) Fig. 1 Ester” Oiotribufion among the Beta-articles of «‘J‘Wfl E . . of the orbital electrons with the electromagnetic field of their own nucleus. The ejection of an orbital electron leaves the extranuclear portion of the atom in an excited state. There are a number of ways by which this instabili- ty could be removed by the atom itself. In one, the remain- ing orbital electrons may rearrange to fill the vacancy created by the IC electron (inner orbit) and in so doing, emit fluorescent X-rays. Each X-ray photon represents the energy released in a particular electronic transition. In this case, the energy of the X-ray photon is the difference between the binding energies of the initial and final states of the particular electron which participated in the rearrangement to fill the vacancy left by the IC electron. Another possibility by which the atom may return to stability is the so-called Auger effect. Here, the photon energy which would have been manifested as a characteris— tic X-ray, is utilized to eject another orbital electron, the Auger electron. This phenomenon is also known as a radiationless transition Since the X-rays which would have resulted after internal conversion, are not emitted and another particle is emitted instead. (2) Gamma Rays: After the emission (Alpha or Beta Decay) or capture (Orbital Capture, Particle Bombardment, etc.) of a parti- cle, the resulting nucleus is left in an excited state. One way by which the energy of excitation of this nucleus may be decreased is through the emission of gamma rays. The allowed nuclear energy levels are discrete and since gamma rays are the result of transitions by the nucleus from one energy level to another, then gamma ray energies too are discrete; and conversely. The energy of a gamma photon then is the difference between the excitation ener- gies of the nuclear energy states involved in the transi- tion which results in this particular photon. Gamma emis- sion alone, does not change the proton-neutron composi- tion of the nucleus but may bring the isotOpe to its ground state (one of lowest energy) through a number of such transition steps; each transition giving rise to a gamma photon emission. The energies of the gamma rays then are indicative of the energy states which the nucleus oc- cupied in its transit to the ground state. Like X-rays, gamma rays are electromagnetic radia- tions, as Shown by some well-known experiments (e.g., crystal diffraction experiments). X-rays, as previously ex- plained, involve only the extranuclear transitions; while gamma rays on the other hand, are the result of nuclear transitions from one energy state to another as the nucleus proceeds to stability. There are instances, however, in which the nucleus undergoes a transition to a state of lower excitation ener- gy without the emission of a gamma photon. Instead of emit— ting the photon, the electromagnetic field of the nucleus interacts with the extranuclear orbits and thereby causes the ejection of one of these electrons. In this case, the energy which would have been emitted in the form of a gam- ma photon is utilized in the ejection of an orbital elec- tron. The kinetic energy of the ejected electron then is the nuclear transition energy less the energy which bound the electron to its former orbit. These energetic elec- trons which are emitted from the atom through this process are called internal conversion electrons. Knowledge of the energies of these IC electrons and the orbital binding energies then will give the total energy of this transi- tion. INTERACTION OE GAMMA RADIATION WITH MATTER As previously introduced, the Scintillation Tech- nique is based on the interaction of nuclear radiations with phosphors, a special class of substances which emit light upon absorption of these radiations. At this point, it is important to classify the interactions into basic types, with the understanding that the total absorption of the gamma ray energy may (as in actual cases) involve com- binations of a number of these basic interactions: (1) The Photoelectric Effect: This is the type of interaction in which the total energy of the gamma ray is utilized in ejecting an orbital electron. The resulting energetic electron is called the photoelectron. A free (unbound) electron cannot absorb the gamma energy and become a photoelectron; another body, the nucleus, is necessary for the conservation of momentum in the process. This requirement (bound electron) added to the fact that gamma energies-are discrete, explains the discrete nature of photoelectron energies. The kinetic energy of the photoelectron is the difference between the incident-gamma energy and the binding energy of this elec- tron before the ejection. ' (2) The Compton Effect: It is quite possible for an electron to be ejected from the atom even if the energy of the incident gamma ray is not tetally utilized in the process. In this type of 6 interaction, called the Compton Effect, the gamma ray un- dergoes a scattering process with an electron (considered free and stationary) of an atom, analogous to a two-parti- cle collision (this was predicted by the wave-particle du- ality of light, or conversely for all electromagnetic ra- diations in general). This process results with an ejected electron, the Compton electron, and a scattered gamma ray. The resulting wavelength of the gamma ray will be longer due to its loss of energy to the Compton electron. The energy of the Compton electron and the wavelength of the scattered gamma ray may be calculated through the applica- tion of the De Broglie Principle and the Conservation Laws of Particle Collisions (relativistic). It is worthwhile to mention at this juncture that since only a partial transfer of gamma ray energy is in- volved, the Compton electron carries less kinetic energy than the photoelectron; for incident gamma rays of the same energy. (5) Pair Production: In the presence of matter, a gamma ray of energy greater than about 1.02 Mev. (the rest energy of two elec- trons) may be totally converted into a positive (positron) and a negative (negatron) electron. These particles created from electromagnetic radiation may lose their kinetic energies (each about half the difference between the inci- dent gamma energy and 1.02 Mev.) through ionization by im- pact on the neighboring atoms, or through their interac- tion (Coublomb type) with the electromagnetic fields of a nucleus or some orbital-electron distribution. A positron which had been stopped in this manner will then combine with a neighboring electron (free and stationary) to pro- duce two oppositely-directed gamma photons of 0.511 Mev. each. This process, in which particles disintegrate and radiant energy appears in their stead, is called annihila- Eigg; as contrasted to the creation of an electron pair (pair production) from a gamma photon. The annihilation gamma photons may further be converted to particle energies by means of one of the basic interaction (or combinations thereof) already explained. THE SCINTILLATION SPECTROMETER From the early scintillation method of counting alpha particle emissions from radioactive substances, has developed a more complicated but more reliable and useful technique. The older method was very inconvenient since visual counting of the number of fluorescences (scintilla- tions) on the Zinc Sulfide target was the only means of getting the disintegration rate. Thus, only weak activi- ties could be investigated. Recently, the field of nuclear decay studies had been greatly expanded due to important developments in electronic counters and in phosphors. These developments served to give rise to a kind of spectrometric set-up in popular use today. It is necessary, at this point, to devote a dis- cussion to the Single-Channel Anal zer, the basis of multi- channel Analyzers. The Single-Channel Analyzer: This prototype of the multi-channel Analyzer used in the experiment, is made up of a scintillator-photomultipli- er assembly (the detector) and some analyzing components (viz., a preamplifier, a linear amplifier, a discriminator and a scaler). A block diagram of this arrangement may be found in Fig. 2. (l) The Scintillator-Photomultiplier Assembly: A number of substances have been found to emit 9 lO nuumfimz< #mcnmxuéfirsmm 2C; N .wE — 510m. L0$~t~§iummp / £3.10) .13: _ Lemma—LEE. — as... a .._.__.....a fi/ __ a KG? .. climactic, \N\ t.+.__3£e0\~\ O“) 11 light upon absorption of nuclear radiations. These sub- stances are called "phosphors"; their means of absorption of nuclear radiations had been explained in the previous sections. Gamma radiation energies that are converted to parti- cle energies (i.e., photoelectrons, Compton electrons or electron pairs) are further converted to fluorescent radia- tion in the phosphor since these particles are easily stopped and their kinetic energies absorbed by the phos— phor. On the other hand, gamma rays and X-rays emitted (produced through the annihilation or the photoelectric and Compton processes) near the phosphor surface, may pass through the phosphor without being absorbed and con- verted to fluorescent radiation. This problem of photon- escape may be remedied to a large extent, by the use of a larger-sized phosphor and the provision for normal inci- dence of the radiations on the phosphor surface, to im- prove the possibility of absorption. Another of a number of requirements for the Scintilla- tion Technique is that as much of the fluorescence (pro- duced by the phosphor) as possible, Should be received by the detector, the Photomultiplier tube. The light that is emitted by the phosphor is randomly-directed and must be conveyed towards the receiving end of the photomultiplier tube, the photocathode. This may be accomplished by the use of reflectors which will internally reflect the light to the preferred direction. In addition, the light from other sources than the phosphor must be prevented from finding its way into the photocathode window. This may be solved by masking off the scintillator unto the photocath- ode window, thus keeping the scintillator-photomultiplier component light-tight from the outside. The glass encasing the photocathode window also pre- sents a problem. The fluorescence coming into the window 12 may be reflected (and possibly internally reflected) by this glass layer and thus find its way back into the phos- phor and thereby be lost through absorption. This light- loss may be minimized by making an optical joint between the glass window and the scintillator. For instance, the Dow Corning Fluid (No. 200), as a joint, will graduate the optical density of the material confronting the light in its passage into the photocathode; thereby diminishing the reflection of light back into the phosphor. In applying this Fluid on the photocathode window, care must be taken so as not to form air bubbles in the layer (these bubbles may themselves cause the reflections we are trying to pre- vent). These precautionary measures may be fully under- stood through Fig. 3. Here the Tl-activated NaI crystal (in the form of a right-circular cylinder 1% inches in diameter and 1% inches thick) is encased in an aluminum can (about 0.01 inch thick and with a glass bottom) lined with MgO (reflector); this type of scintillator is avail- able commercially (Harshaw). The light emitted by the phosphor eventually finds its way to the photocathode, after a series of internal reflections by the scintillator lining. Through the photo- electric process, this light ejects electrons from this photosensitive plate (photosensitivity, in a mild sense, is a measure of the photoelectric response as a function of the luminance). These photoelectrons are then acceler- ated to a nearby plate, the dynode, by a higher electric potential. The photoelectrons hit the surface of the dyn- ode with such a velocity as to cause the ejection of sev- eral electrons, called secondary electrons. The secondary electrons are further attracted to another dynode and their impact gives rise to more secondary emission. These secondary electrons are attracted in a similar manner, by 15 fliuminum Can M30 reflector Dow Cumin? Fluid N31 (T1) Cupid H. / 1“ 57.22%. g ’14 1| Glass E 1 : H ...... 5. ' H ”luminum Rear i ll Focusing Shin/0' ”/Wlhdm F317 ”It‘ll", 73p: Dumorfi: 6292 FIG . 5 THE SC INTILLATOR—PHOTOHULTI PLIER ASSEMBLY . 14 a number of consecutive dynodes which are higher in poten- tial than the preceding ones. The net effect of this re- petitive process then, is a progression of the number of secondary emissions; and the number of secondary electrons received by the last plate of the photomultiplier tube,'the anode, can be made very large. Some photomultiplier tubes can transfer as much as 106 secondary electrons (or even more) to the anode, for every single photoelectron ejected from the photocathode. Thus, a single photoelectron at the start of this progression will register a voltage pulse in the plates of a condenser connected to the anode. In this sense, the photomultiplier component provides pulses which are sufficient in magnitude to be utilized and analyzed by the subsequent electronic components. It is very important to note at this point, that in the scintillator-photomultiplier pairing, the entire spec— trum of the phosphor fluorescent emissions must be within the photosensitivity range of the photocathode. We have so far, explained what is considered the de- tector components of the Analyzer; the following sections will be devoted to a description of the analyzing compo- nents: (2) The Preamplifier: The preamplifier of the photomultiplier serves to amplify the voltage pulses obtained directly from the pho- tomultiplier tube. This is a linear amplifier; the choice of this type of amplification is to preserve the linearity of fluorescence response of the NaI (crystal) phosphor, for instance. Provisions are also made so as to present a low-impedance output to the other portions of the Analyzer, through the use of a Cathode-Follower type (Fig. 4). 15 mm....:.._n_244Janan Mada—.40) 10—1 Fan— 2. l mu....__._n§ i;§o (Minus the .< ..3 z. ...‘x. 5.5. .2: 3 3— K ....TraU M L......:..<32,~._.EL.J. .*_ -- .44-. ;_._. c 140 120 1 80 60 51 ....zm2m624mm4 mozweozao <22J55 C. Radiations in Coincidence: (a). The 0.214-Mev. gamma and electrons from the 82 kev. transition (through a variable field, 1800 focusing beta-ray Spectrometer with a "double-Slit" Spectrograph insert).56 (b). The 0.506-Mev. and the 0.070-Mev. gammas (scintillation Spectrometer).57 D. Relative Intensities of Conversion Lines:58 Table III. MILL: IC Line Area under line Peak height Relative (arbitr. units) (arbitrary I ' Intensity (kev.) units) (ave. of area & peaks) 82-K 5420 i 850 506 i 26 75 82-L 3950 1 980 475 1'26 100 82-M 560 i 140 107 i 52 18 214-K 571 i 57 108 i 7 16 214-L 55 i 5 14 i 5 2.2 54 Bhatki, et al., loc. cit. 55 Ibid. 56 Katz, et al., 100. cit. 57 Bhatki, et al., op. cit., p. 1467. 58 Katz, et al., op. cit., p. 10. 51 E. Nature of the Isomeric Transitions:59 Using the above relative intensity values, IC co- efficients and NK/NL ratios were computed and the values so obtained are between a 24 (mag.*) and a 25 (elec.*) for the 282 kev transition, and between a 21 (mag.**) and a 22 (elec.*) for the 214-kev. transition. Furthermore, the NK/NL ratio so obtained for the 214- kev. transition is between a 21 (mag.+) and a 22 (elec.+). The theoretically obtained half-life x-(1 + Ne/Nqo was found to be 1.0 X 1010 sec. for the 82-kev. transition. F. Angular Correlation Measurementszl+0 Using a thin-lens beta Spectrometer as the fixed detector a scintillation counters for the movable de- tectors, the measured correlation was found to be of the form: 1 + A2Ph(cos 0); in agreement with the the- oretically predicted angular correlation for the known 5/2 1/2). The measured values of A2 (corrected for geome- try) are: -0. 015 + 0.007, -0.007 1 0.007, and -0.10 + 0.04 for the K-, L—, and the K-K cascades respec- tively for Telal. Comparing the first of these coef- ficients with theory, Shows that the second transi- tion is a mixture of (5.6 i 0.50)% E2 and 94.4%IM1. spin sequence in the Te isomers (ll/2 39 ** 40 Katz, et al., 0p. cit., pp. 10-11 Theoretical values for this ratio was obtained from Hebb & Nelson (Phys. Rev. 58:486, 1940) and Drell (Phys. Rem TgéoreticaTAvalues for this ratio was 9fr m the curves by Lowen et a1.(Phys. Rev. 75: 529,149) Theoretical values for this ratio was 9from Rose, et al., "Tables of K-Shell Conversion coefficients" (privately distributed). Goldberg, et al., 0p. cit., p. 1550. 52 Using the Biedenharn and Rose notation, the ratio of reduced matrix elements is plus. The results of the K—K angular correlation is consistent with the K—‘7 correlations and are used to prove that the correla- tions, which are smaller than the M4—Ml correlation, cannot result from reduction of the M4-Ml correlation by the action of extra-nuclear fields. G. Utilizing the data obtained by microwave tech- niques, the electric quadrupole moment for this daugh- ter nucleus was found to be; Q = -1.5 X 10-24cm2. 41 In another investigation, where a hollow-cathode discharge tube was used and a Fabry-Perot etalon for resolving the hfs; the result was, Q = (-O.55 i 0.10) X 10'24 cm? It was further explained why the original value given above is not valid.42 41 42 G. Sprague & D. Tomboulian, Phys. Rev. 92: 105 (1955). K. Murakawa, Phys. Rev. 100: 1569 (1955). 55 H. PTOposed Decay Schemes: (i) Izun1f 9“ d Te m. // 82 ml /2 /1 d3/2 ,/ 2J4 kan / ,/ / / :74 Tel“ 5": ||30 kev. / Ec 8W2 187. . 575 kev. 506.166» / 70k". 0 d5, ESLIZI Fisoléi Tentative Decay Scheme for Telel" (From Bhatki et al.45) 43 Bhatki, et al., op. cit., p. 1468. INTERNAL CONVERSION COEFFICIENTS An excited nucleus with excitation energy less than the binding energy of any nuclear particle may de-ex- cite by either one of two competing processes: (1) by emission of gamma rays; or (2) by internal conversion. The ratio of the transition probability of (l) to that of (2) is defined as the internal conversion coefficient (total). This total conversion coefficient is found to depend very strongly on the transition energy, the atomic number Z of the emitter, the binding energy of the shell (or subshell) from which the IC electron originated, the multipOlarity L or angular momentum of the radiated field (the competing gamma emission) and the character of the nuclear transition (electric or magnetic) which in turn uniquely determines the nuclear parity change once L is fixed. It does not, however, depend on the nuclear wave function, since it is only a measure of the probabilty of one of the competing‘ processes (as compared to the other) and not a measure of the transition probability of the nuclear decay itself. It may, however, give a clue to the nature of the electro- magnetic emission. Comparison of the theoretical (e.g., the independent- particle model) and the experimental (e.g., half-lives of gamma transitions) would allow a deduction of the multi- polarities of the gamma transitions. In addition, this may give information on the angular momenta and the parities of nuclear states by direct measurements through angular cor— relation experiments. To furnish the theoretical side of the comparison, the internal conversion coefficients tabulated by Rose* (for * M. E. Ross, Internal Conversion Coefficients (North- Holland Publ. 00., Amsterdam, 1958). 54 55 the atomic numbers 42 and 51) were plotted as a function of the gamma-ray energy (in units of the electron rest-energy in Mev.). From the resulting curves, the associated inter- nal conversion coefficients for 42111096, 51Te119 and SlTelal (for their respective gamma rays of energies up to about 200 kev.) were interpolated (the results are in Tables I to XVI, Appendix). Using the equations on p.56 (Appendix), the half-lives associated with each gamma transition (for both electric and magnetic; up to L = 5) were calculated and tabulated (See Tables XVII to XXXII, Appendix). These theoretical estimates (Weissk0pf) are to be compared with the results of angular correlation experi- ments in the future. APTENDIX Half-lives of Gamma Transitions: Using the independent—particle model, Blatt and 1 Weisskopf arrived at expression (currently known as the Weissk0pf estimate) for the (partial) half-lives of gamma transitions. These expressions have been tabulated2 in more convenient forms (for different multipolarities) us- ing a nuclear radius constant of 1.2 x 10'15 cm. The Table is partly reproduced here: Half-lives of Gamma Transitions L Tfi (e1) 1 6.75 1'2/5 E‘3 x 10'15 sec. . 2 9.57 1'4/5 3’5 x 10'9 sec. 5 1.98 1'2 E‘7 x 10“2 sec. L T% (magn) 1 2.24 A0 E.3 x 10'14 sec. 2 5.12 1'2/5 E‘5 x 10"8 sec. 5 6.60 A-4/3 E'7 x 10"2 sec. 1 J. M. Blatt and V. F. Weisskopf, Theoretical Nuclear Physics (Wiley & Sons, N. Y.,Il952) p.627. 2 A. H. Wapstra, G. J. Nij h and R. Van Lieshout, Nuclear Spectroscopy Tables North—Holland Publ. 00., Amsterdam, 1959) p. 71. 56 57 Appendix: (Continued) The tabulated expressions refer to the transition probability associated with the emission of multipole radiation. In order to get the actual lifetimes of the associated gamma transitions it is necessary to correct for the transition probability associated with the in- ternal conversion process: e1 magn (1 + OCT) T 91 (1) agn T75 (v) where “:T is the total conversion coefficient, given by: OCT = OCK + 1.28 (OCLI + OCLII + OCLIII). The .dC-subscripts refer to the particular shell (or sub- shell). 58 Appendix: (Continued) Tables of Internal Conversion Coefficients*: I. For Gamma Rays of M096: ]:,For the 0.216-Mev. Gamma Ray (k = 0.4227) C21 C12 C23 /5L zég .433 K" 5'16“ My (.13 6,37 c-z) 2.9.51.4) 2,74 {-2) /.5‘2 [-0 7'37 ['0 LI-Subshe“ A22 [—3) 6.50 («3) 2.3%- (—2) 3.27 {—3) 45/0 {—2.} 220 {—2. LI—Sutshcll .5100 {—r) 1.x: («3) A75! {-2) /.27 {—y) /.27 /-3) /.,7 (‘2. L Ln I SubsI-uc" Z7! f—S’) /.25'/-3) ”7(4) 4.20 [—5) [.20 (4) Mi: {-2.} 21" /.35‘(—-3) fiflK-J) 6.17/4.) 3.41% {-3) 2.0/f—2) /.26 {-0 K/ 2L £74 7. /5' 4!. 7f 50.: 7:37 5775'" L1 / / I / / / (#1,, o.°¢lo 0. I715 (1.6/05 0.03” o-o7aL oJ/Iz. L / / / / / K m- 0. 0‘3! 04723 05374 0.012! 0.0.156 04° "° * Interpolated from curves constructed with the values given by Rose (CZ'S for electric, A3's for magnetic; numbers in parenthesis are the powers of the factor,, 10). Subscripts of the coefficients stand for the multi- polarity, 1. The R value stands for the gamma energy in units of the electron rest energy (in Mev.). Appendix: 59 (Continued) II.For the 0.258-Mev. Gamma Ray (k = 0.466) C11 2 C1: .AZ /55 /45 K-Shell 7.;0 (~3) 41.50 {-2 2.0/ (4) Z./6 {-2) /./3 [-1) 51m {—4) H-Suhskcil 9.40 («4] 4.63 {—3) A94 {—2) 2.57/15) /.30 {—2) 6.5314) LfiI-Subshell 3.60 {—5) 7. 5'0 {—7) /.03 {—2) 7.4! (4} 7.7514) 7. 757-: L111: -Subsh¢ll 5260 {—5) 7.00 [—7) 9./0 {—3) 3.34 {-5) 5130(4) £70 {-3) 21‘ A03 {-3) é./i'/-3) 3196-2) 2.67/4) AWN-2) raw—.2) K/ZL 2m 7.5/4! mi two 738/ 6.2:” L1 / / / / ~/ / 1/ / / / / / / //L 00333 07420 0.5307 0.0376 0.068! 0-//37 L / / / / / / I 0.05% 0.1723 0747/ 0-0/3/ 0.0.10: 04344! Appendix: III,For the 0.512-Mev. Gamma Ray =: 60 (Continued) (k = 00611) 01 02 0: fli fl: fls K "SheH 4.37 {—3) /.P2 {—2) 4.70 {-2) LOPEZ) éééof-J /.77(—/) LI—Subshcll 4,5054) L176 (’3) 5.70 (,3) /.2¢{—3) 53/0 {—3) 2./7[*Z) LI ..Subshell A42 {—5) gas—r45) 2.517(4) 7/77—55 3.33 {—7) 2.x; {-3) Ln; - Subshc“ 2.2/ {-5) 2.21 {—4) ”WK—3) A4745) /.6/ {—90 2./o/-3) ZL 74/1 {—40 2.3/ {—3) /./2 {—23 A3043) 5.7063) 2.4042) K/ZL flfl/é 721’? 5.07 £33 7.70 5-7/ IV.For the 0.451-Mev. Gamma Ray (k = 0.885) a, a, a, A”, A A K-She“ /.47(-:) 516363) ALI/#2) 44375-5) /.¢?[-2) 445362) LI-SUBSMH /.7{/[—-{l) {Jo/.7) ma (.3) goo/«40 /.7.2/-3) 51706:) LII-5‘49“" 7.27/4) 7.73M) 3.90M) 734 x-r) 24177-0 4427M) LI-Subshefl 4.77/1) 4.204;) 2.4414} 51077—4) 3.3.51.5) 2.77/49 21.: /. 187—4!) Lad—4!) 2.39 {—3) .57/7/—¢j AF¢é3J 4J2 f—3) K/ 2L £0.25“ [ti/A? 29¢ £5425“ r.” 714/2 Appendix: 61 (Continued) VLFbr the 0.560-Mev. Gamma Ray (k = 1.096) r___ _ Cir1 a, (23 fl, fl, fl; K- Shell 9.9967) 2.97f—3) 727.763) 2.6343) 7.7763) 2.5442) L: 5055“" /.06 {—4) 3.): {—7) Mezzo 3.0/7.7) 9.00440 .25: (.3) LI ..Subshell 2./7(—6) 2.0/ {-5') 734/ fl7) 7.20 («6) 3.7765) /. 70 (~70 Lm—Subshcll 3.53M) 470(4) 7. 751-5) 271(4) Aarfir) 2 7.7/10 21' /-/-Z {—50 3.53/40 A06 (“3) 3.///—¢J Raf-40 2.173(4) K/ 2L 1’. 7.3% 550/ 2369’! 145157 1.37% 7.54 V]. For the 0.725-Mev. Gamma Ray (1: = 1.418) fl fl fl 01 92 a: 1 2 3 K’Sl’m" 550(4) /,y;{..3) 3451-3) A5614) 3.70653) z/Of-J) LI—Substcu 577.515) “7(4) 3. 74%;!) “7(4) {1.4/rfl-flA/0f-3) Ln—Subshcll 400(4) zai/K—c) mafia 3.51M) xii/J) 571/Ar) Lm-Subsh¢|| We.) 4.0.4.) 2.0/4) 7375-.) won) 2.57m) 2L 4.” (4) /.72 [-40 5436(4) A72 [-7) 4.41/4) /./7 [—.:] K/ :1. am? I. M: 7.7% 873/ nafl’ 7.7.2/ 62 Appendix: (Continued) VILFor the 0.770-Mev. Gamma Ray (1: = 1.507) a a a fl fl fl 1 2 3 1 2 3 K’She“ {7 726.41) 727 (.3) :7. 705-3) /.26 (‘3) 33306-3) ZFD/“3J LI —Suhshe|| 5125' {—5) 7. 357.4) 3. 73 Q7) 7. 4/3 [—7) 3.77M!) K 77/4 Ln: “S“bShe" 7.30M) 51737-7) 3.7365) 2751—4) 72:77.5) 7473(4) Ln-Subslaell 7376-0) 4.77fi7) 7.57 6.5-) 7,776.7) 3.7.36.0) 10665") 21' 1747/45") 7. 7’6 [—7’) 3.57450 74/7670 3.77/40 257/41) K/ZL £7774! 7.7.7.7 [4067 £523 [ca/’3 307,2 VII/.For the 0.804-Mev. Gamma Ray (k = 1.575) C2, C22 a: 51 fl: 4: K-Slaell 571/[67) 7741—3) 2.5243) 7.73 {—3) 2.73/-:) 6.77(-:) LIISub‘he" firs-(d) A2365!) 2.77%;1) /. 37 [—51] 3.3.9140 7.7757) Ln ..Sulnshcll Z3of-7) 44751-4) 2.6/ [-59 2.62 64) 7.70(—-:) 3.701;) Lm-SUBSHCH [,7/_4) 7407/4) /.3,2/-$’) /.&7/—6) 3.3? {-6) /.6f(-59 214 5707/45) 7.3.: («40 3./i6¢) 7.35'{-y) 3.577(7) {4.73440 K/ 2L 7. £45? I. 777 7: 04/3 )7. 370 P. 3Y6 7. 933 Appendix: 65 (Continued) lX.For the 0.840-Mev. Gamma Ray (k = 1.644) C71 02 03 fl: fl: fl: K—Shell .70.- “) 703 7.3) 2.27 7—3) 7.0.2 {-3) 2.07 70) £77 {-3) LI-SUBSM" 77.77- 7.5-) 72/ (~40 2.77 {-7) 7.77 {—7) 277 M} 7.77 67) LI-SUbSHe“ 7.7/2 {—7) 7.2.2 (*6) .7./£ Ad 2.32 [—6) 7.442 6-6) 2.77 fig LM‘SUbshen /. 04 [-5) 3.77/2) 7.07 (J) 9.5:: [-7) 2.1"? (1)/.377 fl!) 2L 7.6.2 {—5) 7.77 41/] 2.27 {-7) 7.22 {-7) 3.07 [—7] 7.73 {—71} K/ 21- 57957 E 4717/ £02/9’ KJ/Ja £3735 £37ZI II. For the Gamma Rays of Sbllg: X.Fbr*the 0.155-Mev. Gamma Ray (k = 0.299) CZ; C12 as fit ”2 fl: K—Shell 075’ [—2) 2.90 {—7) /.7/7 0) 7.6? [-7) 7.77 (0) 4.30 (0) LI-Subshe" 510;— 74) 2.00 [—2) 727(4) /.£’2 (.2) /.r2 {-7) 7.77 {a} LI”SUb$h¢” £30 [4!) 7. 70 [-2] 3.527(4) /.07 {—3) 7.?0 £2) Ah {—7) Lm—Subshell 6.0: [-6 717/4.) 235(4) 3.3 75:/[0) 54f7fl/J ZL 1.0/£3) (./7/«2) 709/4) 7.76 {-2) 7.7! ('7) /.P/ (a) K/ 2L 7,970 47.700 7.777 2577/ 0.3” 3.77.? 1;; / / 0.363% / / / ’1’: / / / / / / / 0.0!)? 0.473! / 0. 05,7 0.77/94 0.7.436 1L]! .JZEJT- «03;;2 <;;;:; 1:07;; 2:;72 ;:;;;0 Appendix: (Continued) XI.For the 0.270-Mev. Gamma Ray k = 0.528 = E (— — j. C21 02 as ”1 fl: p3 K’sl13” A03 (_2) 51.3,? fig) 743 [—4) 3.60K—2) A66 {4.) 6.650 [-4) LI ‘5u5"‘¢” 7.07 {.3} 7.512 (a) 7;; Fe) 377/0) 2.70 (4) 7751—2) 1.1;" 5055“” 7.57 7.53 7357—3) 7.72 {-2) 2.0.2 {—7) 7. 77 (3) 7.30 {—2) Lm’sub’h‘" 7.77053 7.77 7.3) 7. 777—2) 5170 (~59 7.0700 7.7/7.2) 2L 7.22 (~3) 7.0514) 7357—2) 44-23(6) 2-4/0/'3) AZVK-U K/ZL 7735' 4.2/3 3.75/7 5575' 6.73/ 522/1 LI / / oil/r / / / / J, 0.06/3 0.2977 / 0.0.6' 009/0 0.7374 L / / / /,_., / / II 0.0790 0.247/ 0-7037 0071,47 00¢?! 0-7735 xu.For the 0.645-Mev. Gamma Ray (k = 1.262) C11 C12 C13 /61 K3: /eb K’SHQH 7.77 (-3) 3,77 (3) 7251—3) 7.03 [—3) 7.27 7,2) 27:” 6.2) LI-SUbs‘W" 7.27/40 3.77 {—7) 7.77/4) 4477(7) 7.37 6:) 3.47/4) LI-Subflvell 3. 77/4) 3.72 («5) 2.37 [-7) 7. 7/ ('5) (JOY-5') 1.2/(7 Lm-Subshe" 577/2) 2.717(4) 7.72 [—7) 5200/2) 2.73/4) (72 fif’] 2L 737(7) 2277—7) 727(3) 777(7) 7777—3) 777 («7 K/ZL £722 7.74/7 6.646 77.273 7.7.27 7,074 65 Appendix: (Continued) XFor the 0.950-Mev. Gamma Ray (k = 1.819) a1 a2 03 fit flz fl; K-‘Shell 5.70 {-4) 7.37/4) 2.9r7f-3) 7.77 {-3) 7.2763) 701-3) LI-Subshell 0.23 {—s') 7.52 {—4) 3.24 {-40 7. 77/47) 5207(4) 7.77/4) Ln" Subsheu /.6/6 [—4) 710 (4) 411/ {—5) 5170 [-6] 015/{'65) Ziof-f LI-Subbhefl 1,074,) 7.7, [.7] 74777-5) 7.7.2 {—7) 07751—4) 2.73/4") 21' 6-5'7Z—5) 7.67/4!) 3. 90(4) 7. 77/40 073/ A77) 7. :22 («3 “/2L 7.7367 7.760 7. 737 57.957 £067 7'57” III. For the Gamma Rays of Sblal: XIV. For the 0.070-Mev. Gamma Ray (k = 0.136) a1 a: as fli flz ”3 K-Shell 574/514) 3. 0'0 (0) 2.7517) 7. 0'0 {0) 7.70 [7) 7.4112) LI’Subd‘d' 54705-2) 3.00 {4) /.4/5'/o) /-65'[-—/) 3.75' [0) 44520) Ln-Subskcll 6.7043) 410(4) 3.70 {7) 7257-2) arr/a7) 7. 4/0 {0) LL-Subshcll 0, 007.3) 7207.7) 7. 0077) 0.30 -—3) 7.7047) 7.27/7) 2L 0'. 77f-2) 7. 70 70) 7.24477) 7. 707 {-7) 7775' 70) 9.07 (7) K/ ZL 7.77.2 /. {/2 2.97? {-7) [12% «flfflo 7.73.5” L1 / 0.326! 00342 / / / 1:” / / / / / / /L 0.7773 0737/ 077:0 0. 070': 0-7727 0.77.“! I 0. 2370 7 7 0. 0200 0. 2757 07/99 Appendix: (Continued) 66 XVCFor the 0.506-Mev. Gamma Ray (k = 0.99) C21 (ii C23 .K% /32 /65 K“Sh€u 2737-3) 7457—3) 7701—2) 7770 73) 2.37 {—2) 7.70/4) LI—Subshcll 2.27 (~47) 6157—4!) 7.7773) 7. 70 [—41] 2.77/4) 7.7063) LI‘S‘A’SMN 7.70 {—7) 9757—5) 7.20/4) 3.57 (—5') 7. 97 (~60 1’. 75(4) I‘m" 5""553" 7. 77 (‘5) 7.00759 0.70640 arr/7) 0077-0) 0777—7) 21. 2.4/7 {-7) 7.52 HQ 2.77/4) 30-0-77) 3.73 [—3] 7.07/4) K/ZL 7.77/7 7.570 0:72;! 7.757 7.5177 7.57% XVLFor the 0.575-Mev. Gamma Ray (k = 1.125) a1 a: as fl; flz fls K- Shell Air/«3) 44737-3) 7.77/4) 0730 {—3) 7.77 /—2J 44351—2] L1 ..Subshell 7. 77 [—7) 7.77/4) 7.27/5) 7.07/47) 7. 77/3) 5700/4) L1-Subshel! 51777—7) {.77 {—r) 3.70/4) 2.7.770) 7.27/7) star/.7) LII-3055M” 7777—7) 77.22 7.0) 7. 707—7) 7.75/7) 3.77/4”) 3.02 {—7) 2L 7.7067] sin/(4) 7.77/3) 7.37. {—7) 2.///—3) 7.37/—3) K/ZL 7.723 7.777 7.777 7.375 7.777 7.777 6’7 Appendix: (Continued) Tables of .HaIf-lives of Gamma Transitions for Different multipolarities: 1. For M096 XVII. E = 0.216 Mev. 1.28 (0C, 1..) ‘CT T72 ($60.) T’ih) (sec) E1 /. 725' {-3) /. 352 {—2) 3.74/54 {—717) 3. /i’7 [-750 E2 7770 /-2) 7. 570 («2) 4!. .275“ /—9) 7.732 {—7) E3 Z f7?/— 2) J. 7410/ —/) 7. 7.27 {—7) 7. 777/ (. 7 ) Ml {77702 (.3) 3.200(4) 2. 757 [—72)‘ 2.223 (—— AZ) M3 7.7/3 [-7) 7. 770 [—7) 3.707! (0) 6. 741.2 (a) XVIII. E = 0°g?§_nEY1__ “pm“ ,_u -M_- __ 1.28(0CL) OCT T’L (sen) 132(7) (SEC.) BI 7. 32763) 70/72 {-2) .2. 372 (-77) 2.357 {—74) E2 7.77043) 5339/ L2) «$770 [—3) 2.76/7 [—F) E3 7.777(4) 2.5'07/-7) %777(—/) 3.977 {—7) M1 3.775(4) 2.507 {—2) 7. 772 {—72) 7.727 f 41) M2 7. 7751.2) 7777/7) 7777 /- 5) 7.723 {—7) M3 page/4) {./4/7 (’7) 3.4/70 [0) .2./4/.7 ( 0) 68 Appendix: (Continued) XIX. E = 00312 “ev. 1.28 («(1') OCT TY; (SEC.) T3 (7) (sec) E1 7. z 25 {-4) 4. 77.2 {-3) /. 0.522 (47) /. 057 [—740 E2 2.952 /. 3) 2.”; [-2) Z 07/ /- 9] 7.2/0 (— 9) E23 A42? (.2) 0.2.2? [—.2) 7.777 [#3) 7.475” («3) M1 745-073) 7.24/7 [-2) 7.27; {—3) 7.375" {—3) M2" 7. 575/71) 5.357 72) 7.777 (27) 5033 7- 7) M3 3.323 {—2) /. 903 (4) 9’43” [—0 5.2/7 {-x) XX. E = 0.451 Mev. 1.28 («L 1.) 0C '1‘ Tyz (556-) TyggY) (sec) El .7. 377 (as!) 7707 7— 3) 3. 49.2 {—5) 3.4/77 {—Is') E2 73527 («4) 7. 41777—3) /. /35' 7— 7) 7/4/2 '7— 7) E 3 3' 053 {—3) /. 7757—2) 5355/ [—4) 5. 77/, (~40 M1 7. 737 (— 5‘) 52 034/ (’3) .2. 7130 {—759 .2. 776/2 (.45) M2 2.353 {—3) 7725 {—2) 73%” {—7) 72775” [—7) M3 7.737 (.3) 53/74 {—2) 3. 757 [#2) 3.717 {—2) 69 Appendix: (Continued) XXI. E = 0.560 Mev. 1.2807.) 0C1: ’ Ty2 (sea) Tyzh') (5m) E1 74/30 (.0) /./4/(-3) 772? (.45) 7.727 («6) E2 44520 (...) 3.723 (.3) 3. 757 7x0) 3.0]. (-—/0_) E3 7352 {-3) 7032 {-3) 723.; (~41) 7:47 {—7) M1 3. 97/ {—4) 3.020 {—3) 7.272 (~43) /. 2.74 [—0) M2 7220 {-3) 7. /20 {—3) .2. 77 {-7) .2. 702 {—7) M3 3.722 {-3) 2.502 {-2) £477 (—/) (5674/ {-0 XXII. E = 0.725 Mev. 1.28 (0C I.) OCT T72 (SEC.) 135(1) (55c) E1 Z722 {-5‘) 7.3.6261) 7.7/7 (~46) £7.23 (4‘) E2 2.207(4) /.7// [—3) 7072 {—/0) /.07I/ 740) E3 5:572 67) 44007 {—3) 2.03.2 {—5) @0510 [—5) M1 2.20/ (.4) 7770 {—3) 5:”? {-77} 5:777 [-40 M2 5:70 7+0 7770 {—3) 7.377 («7) 77.2? [-7) M3 7577 (.3) 70727-2) 77/0 {—0 77.27 [—0 7O Appendix: (Continued) XXIII. E = 0.770 Mev. _—_¥__——— l.28 (oCL) .CT Ty.(sec) Tyz (’7) (sec; El 7.777 {—5) 5.470 {-7) 7.027 (47) 7.0.3/ 777) E2 7777 (.7) 77.77 7:) 7.777(4)) 7.77.7 (—//) E3 .7, gm (.7) 3.370 (.3) 7377—!) /.337 f- 6') MI 7773 44’) 7777 73) 77777 (47) 7. 777 (77/) M2 5037(4) 3.7077— 3) 02777 /-7) £77.? £7) M3 /. .237 7.3) 7. 037 (.32 7. 272 L7) 7.357 77) XXIV. E = 0.804 Mev. |.28(0CL) 0(1- T yz ($20.) Tyzh) (530.) El 7. 7577-5) 5:77 {—7) 7477 (47) 7./73 {-M) EZ 7770 [—7) 73/7 [—3) 7.375" {—7) 7.337 [-7) E3 4407777) 27777:) 7.773 M) 7. 777 {—7) MI /. 72¢ 77) /. 372 {-3) 74 3/0 {—70 7.307 (77) M2 4.7172 [—7) 3.377 («3) 7.7/30 («7) 644/76“ (*7) M3 /. 072 {—3) 7. m {—3) 7. 7/7 (~47) 7.700 [-7) 7l Appendix: (Continued) XXV. E = 0.840 Mev. J11 1.28 (ea!) OCT T7. (550.) Tysz) (550.) E1 .2 7/47 7.5-) 7. 77/ 77) 0777.7 {~/7) 53 W7 (47) E2 7579 /_ ,7) /./7’.2 [—5) 507/ [—//) 5:077 /—//) E3 3.703 L7) 2.7.20€3) 7327/ {—7) 7.270 (*4) M1 7575‘ {—7) /. /77 [—3) 3. 770‘ {—40 3. 777 [—40 M2 3‘. 7577-7) 2. 7f7f-3) 3:544" /-7] 3.507 {-7) M3 9. /.23 (.51) 71$? [—3) 5:05.? {—3) 5:07? [—3) 2. For Sbllg: XXVI. E = 0.15} Mev. 1.2802(1) °CT TX? (520) TVZC'Y ) (550.) E1 7777 {—5) 7:727 [-2) 7.3.73 (47) 7.777 {—00 E2 7. 77742) 0.770(4) 4375' [-7) 7709 {-7) E 3 /, 04/77.) 2.737(0) .2. 0/3 (v) 7. /2(/ 7— /) M1 2.5'0ff—2) /. 73/ {-9 52.272 (—/.2J 7.257 (42.) M2 2.37360 7707 [0) 6. 370 fit) /. 573” [—5) M3 2.3/7 (0) 37/7 [0) 5:77! (0) 5274/5” 67) 72 Appendix: (Cnntinued) XXVII. E = 0.270 Mev. [28(0CL) aCT Tyz (St-Le.) Tyzh) (sec) El 7573 {—3) 7x27 {—2) 7397 {—7) 74/3 747) E2 7. 027(7) 527.2 [—2) 7077 [—7) /.//7 {-7) EB 557772) 2.777 fix) 7777 [—2) 73.37 {—2) MI 527/273) 77/77 #2) 7773 («72] /./3f/ /—/2) M2 3. 777 {—2) 77/7 («4) 7.570 7— 7) ' 74977 (4) M3 7.5% [-4) 7.077 M) r. 770 [—0 707? {7) XXVIII. E = 0.645 M33; |,23( oCL) °CT T}; (sum) Tyzh) (sea) El /. 752 {—7) 73537—3) 7035’ [47“) /. 7737 (4;) E2 5717/ (.7) 3. 759 {—3) 772.? [40) 76/37! {—M) E 3 7777 L3) 7.77/0 {—3) :20 7W [- 5) 3. a// [-73 MI 7.2356 4) 7475363) 7' 307 {—450 17:37? (45/) M2 A707 {—3) 7717/ (.2) /./37 [-7) /,/5-7' {—7) M3 5327 (.3) 3.7173 {—2) 2.37/7 {—5) 2.4/27 [—3) '73 Appendix: (Continued) :5 XXIX. g: 0.950 Mev. |.28(OCL) OCT T22 (553-) Tyz(’7) (sec) El 7430 {—7) 7.773 {—7) 3.777 747) 3.777 {—7) E2 2.777 {-7) 7777- 7-3) 2.277 {-7) 2.50/ (.7) E3 4!. 777 f— 7!) 3. 770 («3) 2.327 [—7) 2. 334/ {—7 ) Ml 2.5/7/41) 2.0/2{-3) 2. 777 £77) 2.7.77 (47/) M2 7. 700 {—7) 7.970 {—3) 774/7“ {—7) 7.7717 67) M3 A537 43) 7.077 {—2) A757 [—7) 5777/ {-40 5. For Sblalz m. E = 0.070 Mev. l-23(°CL) °CT Tyz (sen) T12”) (sen) El ’7. 376 (’2) .53/Y9 (—/) 57270 {43) £020 /—/3) E2 .2. 432 (o) 5". 732 (0) /. 37/7! {—7) 7.3/7- {—7) E 3 7. 2737 (w) x. 71237 (+2) /. 7.25- 7—2) /. 77/2 [0) MI 2.3/4! {—0 /. 73/ '(0) 2.37/ {—7) 7.73/ {—7) ML 5.3777 [0) 2.7357767) 2. 773 (— 5') 7.777 {—7) M3 72/727772) 2.777276%) 41.757 (,0 7.337 [42) 74- Appendix: ‘ (Continued) XXXI. E = 00506 Mev. [28(oCL) aC-T Tyz (sec) T337) (sat) El 32/541 {-7) 2. 7757-3) 2.///’ £45“) 2.723 [.ny E2 7 090 73) 7.770 [-3) 77757—70) 4. 720 {—xo) E3 3.702 [—3) 2.070 («2) 7570 {-71} /. 5'72 («7) MI 7097/73) 7777/ {-3) 7 7/5/ [43) 77.27 {-7) M2 71.007 (.3) 7.77/ {—2) 3.77/ A?) 3.747 {—7) M3 72777-2) 72777 7.2) 7277 {—2) 7.277 («2) XXXII. E a 0.575 Mev. |.28(0CL) OCT Ty. (SECo) 13/207) (SEC.) El 2.30/ 77) 7 770 (.3) 7 777 {—7) 747/7 77:) 52 7.777 {—7) 72277 £3) 7.777 [—M) 2.7/7/ [—xo) E3 .2. 37:73) 7377 {-2) 7.7/7 flfj 7,707 {—5) MI 70737—7) . 7./07 {—3) 7/7/ [—0) M77 {-8) M2 7.773 {-3) 7737 7—2) 7770 (,7) 2.027 {—7) M3 7.773 («3) 5777(4) 520767 {—3) 5.307 {—3) '75 . mnnd ..m + moud mde «mud mnmd .3... On... «...... $¢£H2~ N: O- X 0 +3... _ IN mmeum racon— ...§.3 mo H ......L age... .-33 .4. «1.3 .... .ol . 4 I'll! «uuxn.-~\3 «K ohmé amuéu or... ox... ob ac .o Chungm/ as {3.3 23.8 to cs 0..» u... fi‘z :6 900.0 ~+N\~.v .rae / .5... K to... .( on; «+25 Um? 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IMIJ nucmEEou u.m - .umxmnn 33 W A\6.6v > I Axufiv m oz: .13 . 1 .3 .32 ..II I. a... no... ...: r... i. ... n.— 3: .... 1 Wu 9. av . ... 3 m L a: F. + . :2: m L m: no .0 . Q: n 1 E r - 3 do? ....n m .... . :1: m z . . u no? I ...-n ~ m I m I. mv " to m a: m : .m r - E E ......c. r. r... ............. .... “an..." : 2 ....u 32.8 .. ... g ...: n5 Q. n.— 9N ad Qn o— N— 78 ullral'J ON 5 9n :xoo. nan... am mEEw . UHF: I HUI .lfi E on a“. u 22. .0 , «S c . m :6 swoo. 2.8 a. —,.lrl.l. /[_N_ w shN 3H”... n 0 n... a a ...: we no xmA 3? .ME. .3: 32. .... :3 .... .... - m m ( u .1 o.— lm. :3 . Q m we . m m w 85 .32 E u.» 1 3 .H 2: .33.» .232. 2; _ :.~ .32: : 9.8 w m _ HQHoN ‘.M-.(§ _ . .1 Q». AT . 23 T UM . — On . .. fl. wsusum m a ¢ a u + . . :2: .Na 1 3 ...m CE 3.“ .32 «3: ... E nufi m? «.5 =1. ”22.. . u I. \32... :3... . lllllL .3 3 3.2: .N.OX go o... . n oh .9!" udwn._....n.: .............. .. ”4”.le 0 HI ~52... ........ .mmm... ....... .. 1.2.5 p.20Av VI .. 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