HI | l l \ \l‘ll‘Hlll! HI I \ HI m éxmmémm mmwmmée ox 13545 £236.41? mate? G? 3533? ms: $52.52? 339393 for She Bagraa a? M 3. .RRICHIGMé SWJE fiNE‘fiERSE‘E‘Y §§aai饧 A” fia‘fi'eé: 963 an“ (BAN SSSSSS mumulmuifix'lwnflififljflmmmfjw 3129 LIBRARY Michigan State University ABSTRACT AN EXPERIMENTAL DETERMINATION OF THE DECAY ENERGY OF BA131 AND TE121 The energy for the decay by electron capture of Ba131 and Te121 was measured. For BalEl, the ground state energy difference between Ba131 and Cs131 was found to be ll60i8 Kev. This was determined by finding the decay ener- gy to the 1046.5 Kev state by measuring the L to K-capture ratio for the transition to that state. Log ft values are given for the different transitions. A value of 0.221.03 was measured for theaLK/ (1+wkT) conversion coefficient for the 125.7 Kev transition. The decay energy for the decay to the 575 Kev state of Te121 was found to be greater than approximately 400 Kev. Evidence is presented to show that the 1130 Kev transition is in coincidence with a low energy gamma-ray. It is also postulated that the 506 Kev transition is to the ground state. AN EXPERIMENTAL DETERMINATION OF THE DECAY ENERGY OF 131 BA AND TElQl By Daniel A. Gollnick A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Physics and Astronomy 1963 ACKNOWLEDGMENTS The author wishes to thank Dr. William H. Kelly for suggesting this problem and for his invaluable assistance throughout the course of its execution. Appreciation is also expressed to the National Science Foundation for the financial support of the work. *éééi'éf-‘Etéi-fi-Iiflfl-Wr'fi-Béié ii I. II. III. IV. TABLE OF CONTENTS IITPRODUCTIODIOOO0.0.0.0000...OOOOOOOOOOOOOOOC;O A. STATEMENT OF PROBLEM ...................... B. THEORY OF ELECTRON CAPTURE ................ 1. GENERAL....................... ..... ..... 2. ELECTRON CAPTURE ENERGY................. a. NAss DIFFERENCE...................... b. POSITRON ENDPOINT ENERGY............. c. INTERNAL BRENBSTRARLUNC.............. d. L/K ELECTRON CAPTURE RATIO........... EXPERIMENTAL SETUP............................ EXPERIMENTAL RESULTS......... ............. .... A. BA131 RESULTS.............................. 1. INTERNAL BRENSSTRARLUNC ENPERINEITS..... 2. L/K CAPTURE RATIO EXPERIMENTS........... 3. CONVERSION COEFFICIENT NEASURENENTS..... B. TE121 RESULTS....... ..... . ...... ........... CONCLUSIONS................................... BIBLIOGWHYOOOOOOOOOOOO0......OOOOOOOOOOOOOOO 111 O\ O\ '4} 4* KN KN R) [U l--' f—‘CI IO N) to F4 +4 e1 F4 :4 ox -b s: u) -b a— 4r .E (D LIST OF FIGURES Figure 1; Ratio of the number of bremsstrahlung pho- tons to the number of K-captures vs. the endpoint energy of the photon. Transition energy vs. LI to K-capture ratio. Block diagram of experimental arrangement for measuring internal bremsstrahlung spectrum. Simplified decay scheme for Bal3l. Ba131 gamma-ray spectrum in coincidence with cesium x-ray. Ba131 singles gamma-ray spectrum. Te121 singles and coincidence gamma-ray spectra. Tentative decay scheme for Tel2l. Proposed decay scheme for Tel2l. iv Page 10 ll l6 17 22 23 I. INTRODUCTION A. STATLJERT CF PROBLEM According to nuclear sy stematics, the ground state energy difference between the two nuclei Ba131 and 05121 is about 1.7 Kev. However, on the basis of recent log ft measurements, it is thought that the value for this energy difference is too larre (l). The present work has attempted to measure the transition energy for the decay by electron capture of Bal31 to Csl3l. It was also observed that no experimental determination of the decay energy of Te121 had been made. Since the methods used for the BalBl measurements could be easily adapted to Te121 the establishment of the 119121 to Sbi21 transition energy Tas also made a part of this work. The decay energies determine the forbiddenness of the transitions. Let the comparitive or reduced half-life be defined as f( E,A)t Ifiiere AE is the transition energy, Z is the atomic number, and t is the half-life. The function f 1 takes into account the effects of transition energy, and nuclear charge on the half-life. The ft product should be roughly constant for all transitions of the same degree of forbidden- ness. For electron capture the function is {(AE,‘Z) .-= 1'; TT'("K ‘1“ AEkz + ”L: ‘1in AELr‘ * N) where n is the number of electrons in the shell, 2 is the Dirac L/ radial wave function, and AEK is the transition energy minus the bind_ing energy of the K electron (2). If capture of LII and higher shell electrons is neglected, f becomes {(46.1) =‘--;_‘|T(9k A‘EK *9“ AELI) For Z<60, the function may be further simplified by assum- ing that (AELI -4AEK)<6 AJ=O,l;A1=2 no first forbidden 711 AJ=0,1 yes second forbidden 13 AJ=2,3 no third forbidden 18 AJ=3,4 yes Thus by measuring the log ft for an electron capture decay, it will be possible to assign a degree of forbiddenness to its transition, which may in turn give information about the spins and parities of the nuclear states involved. B. THEORY OF ELECTRON CAPTURE l . GENERAL In general, in nuclear reactions it is possible to ig- nore the electrons existing outside of the nucleus. How- ever, in the process of electron capture, these electrons play a major role. Here a nucleus decays by capturing an atomic electron. This type of nuclear reaction can be char— acteriaed by P A1- €°——%’ .DA'fl/ 7. -I 2" where P and D are the parent and daughter nuclei, is a neutrino, and Z and A are the atomic mass and number. In the specific case in which the captured electron is from the K shell, the process is called K—capture. Electron capture competes with "ositron eaission I when the mass of the parent atom is greater than the mass of the daughter plus two electron rest masses. For light nuclei, the energy separation between states of neighboring isobars is usually so large that positron and electron capture decay are almost assured. On the other hand, for heavy nuclides smaller mass differences tend to prohibit positron decay. For very heavy isotOpes, alpha decay is sometimes seen to compete with electron capture. In some nuclei, K—capture is energetically impossible. These nuclei can still exhibit L-capture, however. The capture produces a hole in the electron shell. This is soon filled by higier shell electrons dropping down to fill the vacancy. X-rays are emitted which are characteristic of the isotOpe. They can be used to show that an electron capture has taken place. 2. ELECTRON CAPTURE ELERGY a. MASS DIFFTRENCE 4 It is possible to measure the ground state energy dif- ference between the the parent and daughter (ie., the tran- sition energy) in several different ways. Probably the most direct method would be to measure the atomic mass dif- ference in a mass spectrometer. In this method, the transi- tion energy is given by AP: MRI- W1") where NIZ) and M(Z - l) are the atomic masses in units of moc2, of the parent and daughter, and.AE is the transition energy. b. POSITRON END POINT ENERGY A second method involves the measurement of the end point of the positron spectrum for transitions between known initial and final nuclear states. In this case, the transition energy is given by (2) A5: WP+E1 +1 where W? is the end point energy of the positron spectrmm in units of moc2, and E1 is the binding energy of the ato- mic electron that is ejected with the positron. c. INTERNAL BRENSSTRAHLUNG The capture process also results in an abrupt change in the charge of the nucleus, decreasing it by one posi- tive unit. This forces the nucleus to adjust its charge distribution. When the atom thus alters its dipOle moment it can emit an x-ray photon which is called an internal 5 bremsstrahlung photon. This radiation differs from the radiation produced when a charged particle is accelerated, the latter being known as external bremsstrahlung. The reaction energy in electron capture is shared between a bremsstrahlung photon and a neutrino. Thus the internal bremsstrahlung radiation produces a continuous Spectrum of energies. The upper energy limit, in units of moc2, is given by (4) Wb= AE +U‘EK) where wb is the upper limit of the bremsstrahlung,.AE is the transition energy, and (1 - EK) is the energy gained in capturing a K electron (the rest mass energy minus the binding energy of the electron). If the upper limit of the bremsstrahlung can be determined, then it is possible to calculate the transition energy from the above relation. The energy distribution of the bremsstrahlung is (4) NWT/MW = C(W) a? fin. (WPIWFO‘W where N(W)dw is the number of photons in the energy inter- val between w and wa-dw, wp is the upper energy limit of the photons,d-is the fine structure constant, and C(W) is a complicated function of w which,for small values of N, can be considered a constant C. Thus wp can be found by making a Kurie type plot of (N/WC)% vs. w and locat- ing the intersection of the plot with the w axis. The ratio of the total number of bremsstrahlung pho- tons to the numberRof K-captures is (4) [ NM/N. JW = Vim “’91 O O\ 3 where NC is the number of K-captures. A graph of this function vs. the photon end point ene gy is given in Fig 1. Since the ratio is proportional to ng, it will be easier to measure experimentally the transition energies for K-captures of high WA. .8 d. L/K ELECTRON CAPTURE RATIO In general, it is also possible for a given nucleus to capture electrons from one of the L sub-shells instead of from the K shell. It can be shown that the ratio of the number of LI-captures to the number of K-captures can be used to determine the decay energy of an electron capture reaction. According to Rose (5), the ratio of the probabilities of L1 to K-capture is given by 2 ‘L PLI .— (£611) 1“,) PK %M BR where qi is the energy of the i neutrino, a is the exchange correction, and g1 is the Dirac radial wave function of the i shell, whose value can be determined from the literature (3). The neutrino energy is given by qfsAE — E1 where E1 is the i shell binding energy. The above relations yieldAE as k AE‘ ELI—M. E“ where M2: Egg 2i)"- I-LL Pg flu: A graph of this relation vs. the LI to K-capture ratio is given in Fig. 2. The variable u is determined from the eXperiment. -' -1 II. EKPERIKEITTL SETUP The first attempt to obtain the transition energy of Figure 1. Ratio of the number of bremsstrahlung photons to the number of K-captures vs. the endpoint energy of the photon A NFL K>" Inm+0hs per K~¢qpiure O. m l I O , - 1 1 l l 10 so 100 $00 1000 Energy of Bremsstrahlung (Kev) 7 Figure 2. Transition energy vs. L1 to K-oapture ratio 40‘F—“ O 40 1 l wa SUD-d "—"" o «,7 ‘SH 155 ' 0 Transition Energy (Kev) 9 Ba131 involved the measurement of the endpoint of the bremsstrahlung spectrum. The spectrum in coincidence with a ground state gamma-ray transition was desired. Fig. 3 is a block diagram of the experimental arrangement used, and Fig. 4 is a simplified decay scheme of Ba131 (1); Sodium iodide crystals, three inch by three inch diameter were employed as detectors. The two crystals were mounted on Dumont type 6363 photomultipliers. The pulses from the phototubes were fed to cathode followers which drove coaxial cables connected to the amplifiers. A multichannel pulse height analyzer recorded the results of the eXperi- ment. As seen in Fig. 3, the pulses from each detector were also used in a coincidence circuit. The cathode fol- lower outputs were sent to Cosmic Radiation Lab linear am- plifiers. One of the signals was then passed through a sin- gle channel analyzer to a Cosmic Lab Multiple Coincidence Unit. The other signal went directly to the coincidence unit. The single channel analyzer was adjusted so that it allowed only the desired gamma-ray pulses to pass. Thus the coincidence circuit would gate the multichannel analyzer so that it would record pulses only when a gamma- ray of the desired energy was present. By introducing an artificial delay in one branch of the circuit, it was possible to record the accidental coincidences. If the counting rates in the two detectors are denoted by N1 and N2, the accidental coincidence rate is given by 2TN1N2 where T is the resolving time of the coincidence circuit (7). The individual counting rates Figure 3. Block diagram of eXperimental arrangement for measuring internal bremsstrahlung spectrum lPreamp Detector Linear ”Cathode AmplifierHFollower Single Channel Analyzer F Fast‘ Slow ‘ Coinc.’ Gate. -Inverter 'RIDL ' Amplifier Source 'fl<' I Multia ' Analyzer channel ,% I Detector Preamp Cathode Linear Follower Amplifier S Inverter RIDL . Pulse Amplifier Shaper ‘lO. Figure 4. Simplified decay scheme for Ba13l. Iowa; I0%.5' Q11}? 83011 \ (£65 6115 6W5 u46.5 371.3 3718 215.8, 115.8 03.7 113.7 ll 12 N1 are given by N1==Neps where N is the actual singles count rate, e is the efficiency of the detector for the radiation of interest, p is the peak to total ratio, and s is the solid angle subtended by the detector. By subtracting the spectrum of accidentals from the coin- cidence spectrum, it is possible to obtain the spectrum of true coincidences. This corrected spectrum should con- tain the internal bremsstrahlung spectrum. The results of these experiments are presented in the next section. The second attempt to measure the transition energy involved the determination of the K to L capture ratio. Essentially the same experimental setup was used as in Fig. 3, which was explained above. Since the spectrum in coincidence with an.x-ray was desired, a 6 millimeter sodium iodide crystal with a thin beryllium window was used for the x-ray detector. This thin window was con- siderably more efficient in transmitting the low energy x-rays than the aluminum window of the three inch crys- tal employed in the bremsstrahlung measurements. The results of the K to L ratio measurements were recorded by a Nuclear Data Transistorized Multichannel Analyzer, which proved to be highly stable with respect to gain and zero level shifts. This prOperty was used to advantage on the long runs necessary to obtain reasonable statis- tics in the coincidence spectrum. 131 The Ba was obtained in the form of Ba(NO3)2 from Oak Ridge National Laboratory. It was reactor produced 13 from a sample of 23% enriched Baljo. By standard radio- chemical procedures, the Ba131 was separated from Cesium contaminants. The separated material was made into a disk source of diameter 0.6 cm., which was mounted in the center of an aluminum holder of dimentions 6.5 by 9.0 cm. The TelBl was obtained from Brookhaven National Lab- oratory where it was cyclotron produced. It was also pUr- ified by radiochemical procedures. The Te121 was deposited on a 3.6 cm. long strip of gold foil, which was then mount- ed on an aluminum holder as described above. This source was allowed to age for about 12 half-lives to reduce the amount of the 17 day activity which was initially present. III 0 Ellii‘t‘ELRIIAEA‘LALJJ EKIJ. SULTS 171 L A. BA ’) I‘FSULTS l. IATERLAB SthooidnhLUI” ELPER KEY?“ 7 The first attempt to measure the decay energy of BalJl involved the determination of the endpoint of the internal snectrun in coincidence with a ground state A: bremss trahlung transition. with reference to the decay scheme in Fig. 4, it was possible to use the 1046.5, 619.5, or the 372.8 Kev ground state transitions. If the transition energy to the 1046.5 Kev state is assumed to be of the order of 200 Kev, then the graph in Fig. 1 shows that the ratio of the number of bremsstrahlung photons to the number of K-captures is of the order of 10?; fbr'this transition. For the other transi- tions of interest the ratio is of the order of 10—4. This extremely low production rate, coupled with the fact that tide photons would have an ener:y distribution, made the deter- mination of the endpoint impossible. Data were taken for each of the ground state transitions mentioned above, but the low energy portion of the bremsstrahlung spectrum was complete— ly masked by second order effects such as gamma-ray summing in the detectors. Absence of any high energy bremsstrahlung would tend to support the assumption of a decay energy consi- derably less than the 1.7 Nev postulated by systematics. 2. L/K CAPTURE RATIOS An attempt was made to obtain the decay enerc Uy by finding the K to L capture ratio. If PK is the fraction of electron captures that proceed by K-capture, wK is the 14 15 K fluorescence yield, SK is the detector solid angle, eK is the detector efficiency for K x—rays, Ng-K is the num- ber of gamma-ray x-ray coincidences, and N8; is the num- ber of gamma-rays detected, then Ng—K N3 where PK is defined by the relation P ( —N_E+N“LN”+LL‘—=l+ A_‘_:.£_ PK " NR PK Here N1 is the number of captures to the i shell, a is the PK wk ngK = exchange effect correction (8), and the factor A is to account for capture by LII and higher shells. Solving for FLT/PK in terms of experimentally measurable quantities PLI_ N9€KWK_S_K_-)' . “pg-4 T _¥ Ng-K According to Brysk and Rose (6) PLI. _ EEK-)1 15;); “‘5: ‘ (‘kk (9:: where gLI and 8K are the Dirac radial wave functions, and qi is the energy of the neutrino (A.E - E1), where E1 is the i shell binding energy. Thus the transition energy can be obtained in terms of tabulated constants and exper- imentally determined numbers. The results for Ba131 follow. Fig. 5 is the spectrum in coincidence with the Cesium 31.64 Kev K x-ray (with accidental coincidences removed) and Fig. 6 is a singles spectrum (with background removed) corrected to the same time as the coincidence run. Both spectra were analyzed by using standard "stripping" tech- niques, beginning at the high energy end. The following eXperimental numbers were obtained. NK_1045.5 := 6079:: 90 Nlo46.5 = 360056 I: Goo eKsK : 0.0261300» wK z 0.8761.005' Figure 5. Ba131 coincidence spectrum with cesium x-ray A 496.1 I . ‘ 1 lo _. 372.8 10" ~ 619.5 i \ 10“ -‘ 830.9 10'1 __ l i 4‘ ‘ I (o’- “Iwfitv'fihwa-‘hdv' “-m— ~_"»_.-._ ‘1” __ r.5-AA.'--~\ qm. — Wo,_..__. 131 Figure 6. Ba singles gamma-ray spectrum (1. 496.1 18 The constant a is given by the relation* a: l+ H/z A value of 1.07 was used. The decay energy to the 1046.5 Kev level by this method was found to be 97i25 Kev. Thus the ground state energy difference between Ba131 and Cs131 was found to be 1143125 Kev. It is apparent that certain errors will be introduced because of the uncertainty in the fluorescence yield,de— tector efficiency, and solid angle measurements. In many cases these errors can be eliminated. If the isotOpe has two or more levels which decay to the ground state, it may be possible to find PLI/PK ratios for both transitions. According to Fig. 2, valid results may be obtained for levels to which the transition energy is of the order of 500 Kev or less. By taking the ratio of these ratios, the efficiencies, solid angle, and fluorescence yield cancel, giving a more accurate experimental result. In this case .EEL __1Vk-! IEL Psi .— NK-l NJ where PKl is the probability of K-capture to the first state, and PK2 is the K-capture probability to the second state. This can be solved to give (617.5.) 1 __ I + OLA (qLI/fix)1([5”/‘€k£ _J l 1 451‘ a _ PKl/PKL “Mom/5K) from which the decay energy can be found by the relation (qu) ‘ AE-Etr l it): XE ”El: *This relation is, strictly, only for z<2o. The val- ue used was obtained by extrapolation. 19 where the shell binding energies are tabulated (3). The 1046.5 Kev state was used as state 1 and the 619. Kev state was used as state 2. The experimental numbers for the 619.5 state are EK_619.5=>21488i150 N61945==ll4878911050 The value of (qLI/qK)2 for capture to the 619.5 Kev state was found to be 1.060 by successive approximations. This gave a value of 1.390 for (qu/QK)1 for capture to the 1046.5 Kev state. The decay energy to the 1046.5 level by this method was found to be 113:8’ Kev. Thus the ground 131 131 state energy difference between Ba and Cs was found to be 115918 Kev. 3. CONVERSION COEFFICIENT MEASUREMENTS It is possible for an excited nucleus to decay by not emitting a gamma-ray photon. One such process is known as internal conversion. Here, the energy of the excited nucleus is transferred internally to an atomic electron, which is ejected with the transferred energy minus the elec- tron binding energy. The fraction of K electrons which are converted,to the number of emitted gamma-rays is called the K conversion coefficient and is designatedatK. The fraction of total transitions going by K conversion is d‘K/ (l+$T) whereuLT is the total conversion coefficient GT=¢th+~). Following the emiSsion of a K conversion electron, a K x-ray may be emitted. These x-rays can pro- duce coincidences with those gamma-rays which are in cas- cade with the transition which is internally converted. 20 Thus certain gamma-ray peaks may be enhanced in the coin- cidence spectrum. The number of coincidences will now be d . va : (NY eKSKWK PK ) ,+(I‘L+¢T)(NYQKSKWK) , where the second term arises as a result of the conversion x-rays. The above relation can be solved to yield 35.5.. _. NK‘L._. ... PK H’d‘r NTQKSKWK The data taken in the previous section can be used to give (*K/ (1+oLT) for the 123.7 Kev transition by finding the enhancement of the 922.9 Kev gamma-ray peak which is in coincidence with the 123.7 Kev transition. Thus (0M: ) _ Nan/13K l+°‘T 113.? N41... ekskwl The following experimental data were used. ‘ Pumas) NEG—922.9: 2827155 N922-7 :1286751-360 eKsK = 0.0211o001 Pk(1046.5) = 0.74:0.15 From these data, the fraction of K conversion electrons is 0.29 for the 123.7 Kev transition. The number of 1046.5 coincidences is given by ' Nkwoqss : [VIM/9,5 QKWK 5K PKUWLJ) By taking the quotient of this expression and the expres- sion for the number of 922.9 Kev coincidences, the rela- tion for the 123.7 Kev transition becomes it: ._ NK‘411J1 NIOVAS’ (P ) _ P (Ii-film? - mamas Nan?) KUNM) KUDW’J) Thus the uncertainties in the efficiencies, solid angle and fluorescence yield have been eliminated. The result for this method gives the fraction of K conversion elec- trons for the 123.7 Kev transition as 0.22:.03. This value is in good agreement with the value of 0.18i.04 which was found by Kelly and Horen (1) another way. B. TElglRESULTS The method of capture ratios to determine the energy of decay by electron capture was applied to Tel2l. The cor- rected singles and coincidence spectra are given in Fig. 7, and a tentative decay scheme in Fig. 8 (9). According to this decay scheme, the 575 and 1130 Kev transitions are to the ground state. Measurements were made using both of these transitions. These data were obtained fot the 575 transition. NK—575 = 1691011500 I'C575 == 426915012100 eKsK-z 0.053 From these data, a value of 0.121.02 was obtained for PLI/PK. As can be seen in Fig. 2, this value falls on the flat por- tion of the decay energy curve, hence the uncertainty in the decay energy to the 575 Kev level is very large. At best, a lower limit (corresponding to PLI/FK;0.14) can be established at about 400 Kev. Examination of the spectra in Fig. 7 indicated certain discrepancies in the tentative decay scheme. It can be seen that the 506 Kev transition was not enhanced in K x-ray-gamma- ray coincidences relative to the 575 Kev transition, as would be expected from the tentative decay scheme. Since the 70 Kev transition would be expected to be highly converted, it can be concluded that the 506 Kev transition is to the ground state. Measurements with the 1130 Kev transition showed that it is enhanced in coincidence. Thus it must be in coincidence with a low energy (>30.5 Kev) highly converted transition. All these conclusions are incorporated in the proposed de— cay scheme, Fig. ,. 21 singles and coincidence gamma spectra T6121 Figure 7. 'Ifiull.lfln 4| 5 7 5 Singles Coincidence-r-—- 1130 ’l‘ Figure 8. Tentative decay scheme for To ”30 575' 506 ________jr 70 23 121 192 S 1!“! i d 0 Te '1’ 51 4.9 Figure 9. Proposed decay scheme for Te121. 1% f F 1H “g“ 0 Ill _ __________ €115.04, TE 52 6 9 O m I S 575» ,e 5051/ m ~O {3 S. _ - _ _ _ - - "229-5 1 o 24 IV. CONCLUSIONS For BalBl, two values were obtained for the electron capture decay energy to the 1046.5 Kev state by slightly different methods. The results were 97:25 Kev and 113:8' Kev. These results agree quite well with the value of 117310 Kev which was recently reported for this transi- tion by Robinson (10). Using my value of 113 Kev, the following results were calculated for transitions to the other states, and their respective log ft values. Ener- gies are in Kev. LEVEL DECAY ENERGY LOG ft 1046.5 113 6.1 696.5 463 7.7 619.5 540 6.3 372.8 787 6.9 215.8 944 7.2 On the basis of systematics, no parity change is expected for these transitions. Thus the log ft values found show that all these transitions axezq forbidden. This is in agreement with what would be predicted on the basis of available shell model states. Measurement of theotK/ (1+:1T) conversion coefficient for the 123.7 Kev transition gave 0.221.03. This result agrees closely with the result of Kelly and Horen (1) who obtained a value of 0.181.04 from conversion electron measurements. This tends to support the results of the decay energy measurements of the pre- 25' 26 sent work. The decay energy for the decay by electron capture of Te121 to the 575 Kev state was shown to be greater than approximately 400 Kev. It was concluded that the 1130 Kev transition is in coincidence with a highly converted low energy gamma-ray of energy greater than 30.5 Kev. It was also concluded that, since the 506 Kev transition was not enhanced in coincidence relative to the 575 Kev transition, the 506 Kev transition is to the ground state. The 70 Kev transition is then from the 575 Kev level. These conclu- sions are presented in a modified decay scheme. V. BIBLIOGRAPHY (l) W.H. Kelly and D.J. Horen, To be published, 1963. (2) J.K. Major and L.C. Biedenharn, Rev. Mod. Phys. _2__6_. 321. (1954)- (3) WapStPa: Nijgh, and Van Lieshout, Nuclear Spectros- copy Tables (Interscience Publishers Inc., New York, ‘39). (4) 0.8. Wu, Beta and Gamma Ray Spectroscopy, edited by Kai Siegbahn (Interscience Publishers Inc., New York, 1955). (5) M.E. Rose, Beta and Gamma Ray Spectrosc0py, edited by Kai Siegbahn (Interscience Publishers Inc., New York, 1955). (6) H. Brysk and M.E. Rose, Theoretical Results 9p Orbital Capture, (AEC Research Report ORNL 1830, 1955). (7) R.E. Bell, Beta and Gamma Rav Spectroscopy, edited by Kai Siegbahn (Interscience Publishers Inc., New York, 1955). (8) J.N. Bahcall, Phys. Rev. Letters 9, 500 (1962). (9) Nuclear Data Sheets, National Academy of Sciences, National Research Council, (1960). (10) B.L. Robinson, Bull. Amer. Phys. Soc., 1, 541 (1962). (11) Y. Beers, Theory pf Error, (Addison Wesley Publish- ing Company, Cambridge, hass., 1953). 27 APPENDIX: ERROR ANALYSIS A summary of the formulae used in evaluating the errors of the various quantities measured in this work is included in this section. The numerical values of these errors are also included. By standard rules for combining independent errors in products and quotients (11), the error in PLI/PK is found to be Pt; 1 1 ‘44 AK. ( > T where L 1 1 1 AP A~v ‘ ANN . fish + 9.21: ffi) (P )1: NY) + Ny—K) Got-5k (”K A The error in the efficiency included error in measurement as well as quoted error in the tabulated efficiencies for NaI crystals. Errors in wk and A are as listed in the literature (3). The error in the singles and coin cidence totals include statistical counti lzg error, background subtraction error and a correction for uncertainty in the peak sums (area under the curves). By alternating true and Wool ental coincidence runs of equal length, errors due to the uncertainty of the half-life were H1 “1 sized. The error in the decay energv is obtained from 1 ME ‘ PU: A AE— Ed" K ,1, usJ z ‘-=—— -—‘_“ WILGI‘G FK 9‘. |’ M The errors in the numerator aLd denominator of AE are not independent (11) A EI-‘(AEK 4M A(AE)= (L}“ ) + U-MJ‘ -, g. as 444 ‘ here LA(EL1~MEU]= (Min) +£M‘w‘93 ”M" [131.1] T( K (7:) 2B 29 I and 1 1 It Emma _L Ewe/p.31 A (|‘M)~ - "AM - "4/L( flflig‘l] + 1" PLI/PK In the second method of determining the decay energy, is given by the relation AE 2 Eu. ~ (Ga/(fa EK l— (Ga/4:} hence the error in A.E is (MAE) = A [ELI ‘ (TI/MFG Awu/m, where @(%‘)‘]= (Afi) +( (A?) +(A 7) " 1. 2. {LI’LQ 1 a A 3‘ _ AU’Ea) l 1. Pi f M ( 3 ) - |<.//