ENGINEERING RESEARCH INSTITUTE THE UNIVERSITY OF MICHIGAN ANN ARBOR TECHNICAL REPORT TO JANUARY 1, 1958 INVESTIGATION OF NUCLEAR-ENERGY LEVELS M. L. Wiedenbeck Professor of Physics ERI Project 2375 OFFICE OF NAVAL RESEARCH, U. S. NAVY DEPARTMENT CONTRACT NO. Nonr 1224(13) SPONSORING AGENCY PROJECT NO. NR024-015 January 1958

FOREWORD Of the following seven articles, five are reprints of papers published in The Physical Review and the Bulletin of the American Physical Society during 1957 and 1958, and one has been accepted for publication by The Physical Review, and will probably appear in Volume 109 of that journal. The entire group of papers is submitted as a technical report for the year 1957. The study of nuclear-energy levels is being continued both in the Physics Department of the University and at the Argonne National Laboratory, under their Participating University Program. /^e A)Ng^<^ M. L. Wiedenbeck

I TRANSITION ENERGIES AND NUCLEAR LEVELS IN Sm152, Sml54, Gd152, AND Gd154 AS DERIVED FROM THE SEPARATED ISOTOPES OF EUROPIUM

Reprinted from THE PHYSICAL REVIEW, Vol. 107, No. 6, 1621-1625, September 15, 1957 Printed in U. S. A. Transition Energies and Nuclear Levels in Sm152, Sm154, Gdl52, and Gd154 as Derived from the Separated Isotopes of Europium* J. M. CORK, M. K. BRICE, R. G. HELMER, AND D. E. SARASON Harrison M. Randall Laboratory of Physics, University of Michigan, Ann Arbor, Michigan (Received April 8, 1957) Specimens of highly enriched Eu151 and Eu153 were irradiated in the Argonne CP-5 reactor and the product isotopes studied in both magnetic and scintillation spectrometers. Eul52 decays by electron emission to Gd152 and by K capture to Sm'52. Eul4 emits beta particles leading to Gd154 but no evidence appeared for positron emission or K capture leading to Sm'54. The many conversion-electron lines together with coincidence data allowed the evaluation of the gamma transitions and their arrangement in plausible nuclear level schemes. The beta spectra were resolved by the use of the double-focusing spectrometer. Each of the daughter nuclei is even-even in structure. A comparison is made of the observed lower energy transitions and the prediction from the "collective" model for rotational states. NORMAL europium consists of two stable isotopes whose masses are 151 (47.8%) and 153 (52.2%). On neutron capture two long-lived radioactive isotopes of europium are produced. Many studies1 have been made of these activities. Mass spectrometer analyses2 of the active europium emitter showed it to be composed of two activities of nearly the same half-life. Spectrometer observations of the combined activity could not, except for a fortunate guess, lead to the correct assignment of the many gamma energies. With the availability of the separated isotopes of europium the possibility of a proper interpretation of all observed conversion electron lines and gamma energies exists. A report3 on the gamma energies derived from Eu512 as observed in a scintillation spectrometer has been presented. Eu152 can decay either by K capture to Sm152 or by beta emission to Gd152. By using a scintillation crystal alone, the energies cannot be precisely evaluated nor is it possible with certainty to conclude in which of the final nuclei the transition occurs, except as this can be deduced from coincidence measurements. In the present investigation enriched Eu15l (92%) and Eu153 (95%) were irradiated in the maximum flux of the Argonne reactor for one month. The resulting strong sources were studied in both magnetic photographic and scintillation spectrometers. Some thirty well-defined electron lines whose energies are presented in Table I are observed for Eu152. In addition, the energies of eight Auger electron lines have been evaluated, yielding values between 31.7 and 39.9 kev. It is apparent that certain groups of electron lines * This investigation received the joint support of the Office of Naval Research and the U. S. Atomic Energy Commission. 1 S. Ruben and M. Kamen, Phys. Rev. 57, 489 (1940); Cork, Shreffler, and Fowler, Phys. Rev. 72, 1209 (1947); see also Hollander, Perlman, and Seaborg, Revs. Modern Phys. 25, 469 (1953); 0. Nathan and M. Waggoner, Nuclear Phys. 2, 548 (1957); F. S. Stephens, Jr., thesis, University of California, 1955 (unpublished). 2 Karraker, Hayden, and Inghram, Phys. Rev. 87, 901 (1952). 3L. Grodzins, Bull. Am. Phys. Soc. Ser. II, 1, 163 (1956); H. Kendall and L. Grodzins, Bull. Am. Phys. Soc. Ser. II, 1, 164 (1956). have energy differences characteristic of the electronic binding energies of samarium while other lines are better satisfied by the corresponding differences in gadolinium. The K-L difference for gadolinium is about 3 kev greater than for samarium, and since the energy of each electron line is good to about 0.2% a fairly certain conclusion can be made of the element in which each gamma transition occurs. When only a single electron line occurs, as is sometimes the case, the proper placement may be aided by coincidence observations with the scintillation spectrometer. Similarly, the approximately twenty electron lines obtained with Eu154 are shown in Table II. Since the mass separation was not complete, there was some trace of each of the strong electron lines due to Eu'52 when Eu154 was studied. These contamination lines are not recorded in the tables. The remarkable similarity between the spectra from the Eu152 and Eu154 sources for the energy band from 100 to 700 kev is shown in the reproduction of a composite spectrogram in Fig. 1. Many of the electron lines for the two sources seem to have not only nearly the same energy but also TABLE I. Conversion electron energies in kev and their interpretation for Eu'52 (long-lived). Electron Interpre- Energy Electron Interpre- Energy energy tation sum energy tation sum 75.4 K Sm 122.3 567 K Sm 614 114.8 L2 Sm 122.1 or K Gd 617 115.3 L3 Sm 122.1 578.0 L Sni 585.7 120.5 M Sm 122.1 612.3 K Sm 659 122.0 N Sm 122.1 or K Gd 662 198:5 K Sm 245.3 645.0 K Sm 691.9 237.7 L Sm 245.4 684.2 L Sm 691.9 243.8 M Sm 245.4 731.8 K Gd 782.0 294.7 K Gd 345.1 773.8 L Gd 782.1 337.0 L Gd 345.1 825 K Sm 872 343.5 M Gd 345.2 or K Gd 875 362.2 K Gd 412.2 922 K Sm 969 398.3 K Sm 445.2 961 L Sm 969 or K Gd 448.5 1045 K Sm 1092 404.3 L Gd 412.2 1071 K Sm 1118 456.9 K Gd 507.1 1111 L Sm 1119 498.1 L Gd 506.5 1369 K Sm 1416 539.0 K Sm 585.9 1408 L Sm 1416 1621

1622 CORK, BRICE, HELMER, AND SARASON TABLE II. Conversion electron energies in kev and their interpretation for Eu'54. Electron Interpre- Energy Electron Interpre- Energy energy tation sum energy tation sum 73.0 K Gd 123.2 675 K Gd 725 115.0 L Gd 123.1 686 L Gd 694 115.6 L3 Gd 123.1 709 K Gd 759 121.2 M Gd 123.1 825 K Gd 875 122.5 N Gd 123.0 or K Sm 872 198.1 K Gd 248.3 949 K Gd 999 239.8 L Gd 248.2 or K Sm 996 246.5 M Gd 248.5 958 K Gd 1008 484.9 K Gd 535 1000 L Gd 1008 or K Sm 532 1231 K Gd 1281 542.0 K Gd 592 1273 L Gd 1281 or K Sm 589 643.7 K Gd 694 TABLE III. Summary of gamma-ray energies in kev as derived from electron conversion lines. Eu162 Eul64 62Sms9012 e4Gdss682 62Sm92154 64Gd9064 122.2 345.1 123.1 245.3 412.2 248.3 585.8 507.0 694.0 691.9 782.0 1008 969 1281 1118 1416 Other energies (Single conversion line, coincidence data) 445.2 535 614 or 617 592 659 or 662 725 872 1100 759 1092 875 1170 999 similar intensities. This shows the futility of attempting a solution by using unseparated isotopes. An estimate of the contamination of Eu162 in the Eu154 is shown by observing the relative intensity of the line at 75.4 kev which is a K line for a Sm'12 gamma ray at 122.2 kev. Similarly the conversion lines for the 345.1-kev gamma in Gd152 appears on the Eu154 photographic plates. No trace of the Eu154 lines was noticeable on the Eu152 plates. This is due to the relatively small capture cross section for neutrons in Eu153 compared with their capture in Eu151. The gamma rays in Gd and Sm as derived from the electron energies are listed in Table III. Certain of these are expressed with confidende where both K and L lines are observed. When only single lines are observed, the assignment to the correct daughter isotope and hence the correct energy is dependent upon coincidence observations. In a very few cases this information is not certain and alternate values are given for the gamma-ray energy. The scintillation spectrometer was used to obtain three types of data. With the specimen of Eu'52 near the crystal a "singles" curve showing peaks as presented in Curve A, Fig. 2, is obtained. Now by inserting the source in a cylindrical hole in the top of the crystal, a "sum" curve is obtained. This shows the additive effect of combining certain energies that are in immediate sequence such as the x-ray at 41 kev and the gamma ray at 122 kev to give a new peak at 163 kev, as shown in Curve B. Coincidence data are observed between beta energies and the complete gamma spectrum and between individual gamma peaks and the remaining gamma energies. Those gamma transitions that are in coincidence with betas must occur in gadolinium, since no positron emission could be found from either source and K capture yields only x-ray conversion electrons. By interposing various thicknesses of aluminum between the source and detector, the approximate energy of the coincident betas was established. For example, in the Eu'52 source the 345-kev gamma ray shows strong coincidence with beta rays of energy greater than 400 kev. The 781-kev peak is in strong coincidence with beta energies less than 400 kev and in weak coincidence with higher energy betas. Those gamma transitions FIG. 1. Electron spectra for sources of Eu'52 and Eu'54 for energies from 100 to 700 kev. FIG. 2. Scintillation spectrometer data for Eu'52. (a) Singles distribution; (b) summation peaks; (c) coincidence peaks with the 122-kev gamma ray.

TRANSITION ENERGIES AND NUCLEAR LEVELS 1623 not in coincidence with betas are assumed to be in samarium. Gamma-gamma coincidences are observed for each source. Curve C in Fig. 2 shows the coincidences between the 122-kev gamma ray and gamma rays of other energies. A resolution of the curves shows coincidences at 245, 872, 969, 1118, and 1416 kev. This leads to the placement of the 872-kev gamma ray in samarium even though only a single conversion line was measured for it. The 245-kev gamma ray was in coincidence with peaks at 122, 872, and 1170 kev. No coincidence could be observed between it and the 969-, 1118-, and 1416-kev gammas. The 1170-kev gamma ray was not observed by electron conversion but the coincidence peak is strong evidence that it exists. The 445- and 969-kev gamma rays were definitely in coincidence. Eu152 FERMI PLOT ~ '"*,.. 1.46 "."~...-. 1 fi:\ -\ 0.15 4 0.55\ 08.8 1. " ' 1......8.7 0.2.4.6. 1.0 1 4 1.6 1.8 2.0 ENERGY IN Mev FIG. 4. Fermi plot and analysis of the beta spectrum of Eu14. energy in Eu152 (Emax= 1459 kev) has the unique firstforbidden shape, while the 680-kev component has the allowed shape. Allowed forms are assumed for the three weaker branches. In Eul64 no forbidden shapes are evident. In both isotopes the successive subtraction involved in analyses of the Fermi plots lead to relatively large uncertainties in the endpoint energies of lower components. A summary of the energies, branching ratios, and logft values is presented in Table IV. The relative intensities of a number of the internal conversion lines in both isotopes were measured, both by means of microphotometer traces of the photographic plates and with the double-focusing spectrometer. In Sm'52 the K/L ratios for the 122- and 245 -kev gamma rays are found to be 1.5 and 3.3, respectively, and that for the 345-kev gamma in Gd152 is 4.6, indicating that all three transitions are electric quadrupole. In Gd154 the 123- and 248-kev gammas have K/L ratios of 1.2 and 4.6, respectively, which are again consistent with E2 transitions. For the higher energy gamma rays the L lines were, in general, too weak to permit reliable intensity measurements. The decay of Eu'52 and Eu154 in every case leads to an even-even nucleus, for which the spin of the ground state is zero. The energies of the first excited states of TABLE IV. Summary of beta transitions in Eu152 and Eu54. 0,2.4.6.8 1.0 1.2 1.4 ENERGY IN Mev FIG. 3. Fermi plot and analysis of the beta spectrum of Eu'62. In Gd152 the 345-kev gamma ray was found to be in coincidence with peaks at 412, 782, and 1100 kev. The 412- and 782-kev gamma rays were not in coincidence. The entire Eu154 gamma spectrum was in coincidence with betas, thus indicating that all of the transitions occurred in Gd154 and none in Sm164. The gamma ray at 123 kev was in coincidence with others at 248, 592, 694, 875, 1281, and possibly 700 and 1000 kev. The 248-kev peak was in coincidence only with energies of 123 and 759 kev. A peak in the region of 700 kev was in coincidence with another at 875 and possibly 1000 kev. The beta spectra of Eu152 and Eu154 were observed with the double-focusing spectrometer. In each case the spectrum was found to be complex, as shown by the Fermi plots in Figs. 3 and 4. The component of highest Rel. abundance Isotope Energy (kev) % logft Eu152 1459~15 21 11.6 1050=420 6 11.7 680~20 51 10.1 360~440 13 9.7 220~40 9 9.1 Eu154 18424-20 7 12.4 16004-20 3 12.1 833-30 20 10.9 554~30 30 9.9 246~430 28 8.9 150-40 12 8.7

1624 CORK, BRICE, HELMER, AND SARASON 600 500 ) 40C 300 S 20C CD w z w lc I 0 - *60 *80 '80.82.80 '78 464.62.78 '.\~~~~~~~~~ *'76~~~78 *60 - */.76.74:: *76 * 64. *68 * *72-. *72 *6.2.. *64, 66 * 62 o80 '78 FIG. 5. The energy of first excited states for eveneven nuclei as a function of neutron number. L * RESULTS OF PRESENT INVESTIGATION I I I 1 I I J I I. I I I Il I I I I. I I I I I. I -. - - - - - - -. - - - - 86 88 90 92 94 96 98 100 102 104 106 108 110 12 114 116 118 120 NEUTRON NUMBER even-even nuclei in this region depend critically upon the neutron number. The data currently available are shown in Fig. 5. The points indicated by asterisks are the results of the present investigation. The strong Eu52 63 89 spectral similarity shown in Fig. 1 is really due largely to the like structures Sm'52 and Gd154, both of which have 90 neutrons. Level schemes for the daughter isotopes Sm152, Gd152 and Gd54 are presented in Figs. 6, 7, and 8. These level schemes are consistent with the available coincidence data, and include all but three of the observed gamma transitions. The first two excited states of Sm152 and Gd'54 have nearly the same energies, which is not unexpected considering that the two nuclei differ only by a pair of protons. In this region the collective model of the nucleus is expected to apply, predicting a series of rotational excited levels with even spin and parity (0+, 2+, 4+,.* ) and with energies proportional to 1(1+1). The expected ratio of second to first excited state energies, according to the collective model, is then 10:3, and this ratio is generally observed in the region indicated by the flat part of the curve in Fig. 5, well away from the shell closures at magic numbers. In Sm152 and Gdl54, each with 90 neutrons, the E2 character of the two strong low-energy gamma rays is as expected for transitions between rotational levels, and suggests that the first and second excited states have spins 2+ and 4+, respectively. The spin assignment of 4 to the second excited state is confirmed, in the case of Gd164, by the absence of a beta transition to the ground state, and the 0-2-4 spin sequence has also been established by angular correlation measurements FIG. 6. Level scheme for the Sm152 nucleus. (Position of dotted transitions not well established.)

TRANSITION ENERGIES AND NUCLEAR LEVELS 1625 in both isotopes.4 In both cases the ratio of second to first excited state energies is found to be 3:1. The small deviation from the predicted value is attributed to the fact that these isotopes lie just at the lower edge of the band of neutron numbers where the collective model is expected to hold. In the Sm'52 energy level scheme, K-capture branches are indicated where the estimated intensities of the gamma transitions seem to warrant them. That Kcapture occurs directly to the 122-kev level is indicated by the fact that the 122-kev gamma forms a strong summation peak with the x-ray alone, as well as with other gamma rays (Curve B, Fig. 2). A comparison of the relative intensities of the 122-kev gamma ray in Sm152 and the 345-kev gamma ray in Gd152 indicates that roughly 80% of the Eu'52 decays are by electron capture. 152 64G 88 FIG. 8. Level scheme for the Gd'64 nucleus. 1.100 1.100.3451 _,0 FIG. 7. Level scheme for the Gd152 nucleus. In Gd152 no beta transition to the ground state is observed. The unique first forbidden (AI=2, yes) shape of the highest energy transition, leading to the 345-kev excited state, suggests that the ground state spin of Eu152 may be 4, with odd parity. The unusually high logft values of the high-energy beta transitions are probably due to their K forbiddenness, since they go from a state with I=K=4 to states with K=0 (K being the projection of the total angular momentum on the nuclear axis of symmetry). The lowest energy beta transition (-220 kev) does not lead to an energy level from which we have observed any deexciting 4 L. Grodzins (private communication). gamma radiation and has, therefore, not been shown in the level scheme. No beta transition to the ground state is observed in Gd164. The transitions to the first two excited levels are interpreted as ordinary first-forbidden, suggesting a spin of 3, odd parity, for the Eu164 ground state. The high logft values for the beta transitions are again attributed to K forbiddenness. Coulomb excitation of Sm154 5 has led to the observation of a gamma ray at 82 kev. In the present investigation no evidence for this transition appears, nor is there conclusive evidence for other transitions in Sm154. Since this isotope is stable, electron capture in Eu164 should be energetically possible; but it may be concluded that either the branching ratio for this process is small, or most such transitions lead directly to the ground state. The level schemes proposed here for Sm152 and Gd152 are somewhat similar to those proposed3 by Dr. Grodzins. Certain additional gamma rays are observed while some others are not found as reported. The values of the gamma-ray energies in some cases differ, but at lower values the results from the magnetic spectrometer are undoubtedly more reliable. The level scheme proposed here for Gd154 is almost the same as that suggested by Stephens, again with some revision of the gamma-ray energies. 5 N. P. Heydenburg and G. M. Temmer, Phys. Rev. 100, 150 (1955).

II DIRECTIONAL CORRELATION OF THE GAMMA RAYS OF Se76

Reprinted from the Bulletin of the American Physical Society, Series II, Vol. 2, No. 7, 341, November 29, 1957 Directional Correlation of the Gamma Rays of SeO6.* E. G. FUNK, JR., AND M. L. WIEDENBECK, University of Michigan.-Directional correlation 'measurements have been made on the 0.65 Mev-0.55 Mev, 1.40 Mev-1.20 Mev, and 2.05 Mev-0.55 Mev gamma-ray cascades in Se76..Previous investigations of the 0.65-0.55 correlation12 had indicated an assignment of 2+ to the first two excited states (assuming 0+ for ground state), with a large quadrupole content (>85%) in the 2-2 transition. The present investigation of this correlation confirms these spin assignments and shows the 0.65 transition to be almost pure E2 (<1% Ml). The 1.40-1.20 and 2.05-0.55 correlations are consistent with a spin value of 3+ for the 2.60-Mev level, with the 1.40-Mev gamma ray being pure Ml and the 2.05-Mev transition being a mixture of 95% E2 and 5% Ml. * Supported in part by the Michigan Memorial Phoenix Project and in part by the Office of Naval Research. J. J. Kraushaar and M. Goldhaber, Phys. Rev. 89, 1081 (1953). F. R. Metzger and W. B. Todd, J. Franklin Inst. 256, 277 (1953).

III DECAY OF Gdl6l

Reprinted from the Bulletin of the American Physical Society, Series II, Vol. 2, No. 7, 341, November 29, 1957 Decay of Gd'6l.* L. C. SCHMID, S. B. BURSON, Argonne National Laboratory, AND J. M. CORK, University of Michigan. — 64Gd61 (3.73-min) was produced by neutron irradiation of enriched gadolinium oxide (95.4% Gd160) in the Argonne reactor (CP5). This decay is characterized by femission to several excited states in 65Tb161. From a study of the radiations, the existence of five excited states is deduced. These have energies of 56.8, 315.5, 417.5, 481.7, and 582.8 kev. There is also evidence for a level at about 135 kev. Eleven transitions were observed. Internal-conversion-electron groups representing eight of these were measured using magnetic spectrographs. These transitions have energies of 56.8=0.2, 102.0+0.4, 166.24~0.6, 180.8~0.3, 267.3 ~0.8, 283.9=0.4, 315.5=t0.5, and 360.8~0.5 kev. These eight, as well as transitions of 78~2, 482~=5, and 526~t5 kev, were detected by scintillation methods. The transitions are fitted into a consistent decay scheme by means of coincidence measurements using the Argonne 256-channel scintillation spectrometer. * Work performed under the auspices of the U. S. Atomic Energy Commission.

IV DIRECTIONAL CORRELATION OF THE GAMMA RAYS OF Gd154

Reprinted from the Bulletin of the American Physical Society, Series II, Vol. 2, No. 8, 395, December 19, 1957 Directional Correlation of the Gamma Rays of Gd164.* G. D. HICKMANt AND M. L. WIEDENBECK, University of Michigan.-Direction correlation measurements have been made on the gamma radiation from the excited states of Gd14. The results of these measurements indicate a spin sequence of 4(Q)2 (Q)0 for the 0.248 Mev -0.123 Mev correlation. Preliminary measurements on the higher excited states indicate a spin of 2 for the 0.998-Mev level, and a spin of 3 for the 1.130-Mev level. These results are in agreement with values proposed by J. O. Juliano1 on the basis of conversion coefficients measurements. A spin of either 2 or 3 can be assigned to the 1.404 level, with a probable value of 5 for the 1.723 level. Other possible spin assignments for some of the higher excited states will be discussed. * Supported in part by the Michigan Memorial Phoenix Project and Office of Naval Research. t Eastman Kodak Fellow. I J. 0. Juliano, UCRL-3733 (1956).

V DIRECTIONAL CORRELATION OF THE GAMMA RAYS OF Se76

Accepted for publication in The Physical Review, Volo 109 DIRECTIONAL CORRELATION OF THE GAMMA RAYS OF Se76* Eo Go Funk, Jr., and Mo Lo Wiedenbeck Department of Physics, University of Michigan, Ann Arbor, Michigan (Received October 4, 1957) Directional correlation measurements have been made on the 0.65 Mev-055 Mev, 2.05 Mev-0o55 Mev, and lo40 Mev-1020 Mev gammaray cascades in Se76 following the beta decay of 26.8-hr As76 The energy levels of Se76 were found to have spins 0+, 2+, 2+, and 3+ in order of increasing energy. The 0.55- and 1.20-Mev gamma rays are pure electric quadrupole; the 0.65-Mev gamma ray almost pure electric quadrupole (<1% dipole); the 1,40-Mev gamma ray pure magnetic dipole; and the 2.05-Mev gamma ray a mixture of 95% electric quadrupole and 5% magnetic dipole. A possible explanation of the decay scheme in terms of vibrational levels is presented, Io INTRODUCTION The decay of 26.8-hr As76 has been investigated by many authors.5 The presently accepted scheme which was proposed by Kraushaar and Goldhaber4 and confirmed by Kurbatov, Murray and Sakai5 is shown in Fig. lo Directional correlation measurements have been made previously on the o0.65 Mev-0055 Mev cascade. On the basis of results which were obtained without energy selection, Kraushaar and Goldhaber4 assigned spin 2+ to both the O055-Mev and 1.20-Mev levels with the 0.65-Mev gamma ray consisting of 20-66% dipole and 6 r e t 80o 34 quadrupole radiation. Metzger and Todd repeated this correlation using pulse-height selection and confirmed the 2-2-0 assignment. Their results indicated that the 0,65-Mev gamma ray is almost pure quadrupole (Q>85%). *Supported in part by the Michigan Memorial Phoenix Project and in part by the Office of Naval Research. 1Ko Siegbahn, Arkiv. Mat. Astrono Fysik 34A, No. 7, 1 (1947). 2p Hubert, Jo physo et radium 12, 823 (1951)o 3P, Hubert, Ann. phys 8, 662 (1953). 4J. J. Kraushaar and Mo Goldhaber, Physo Rev. 89 1081 (19535) 5Kurbatov, Murray, and Sakai, Phys. Rev 98, 674 (1955)o 6Fo R. Metzger and W. Bo Todd, J. Franklin Insto 256, 277 (1953)o

A 76 2 -0.36 76 2.5% SE 1.76 16% 1.40 2.05 (0.02) (0.04) \ 2.41 2.96S\ ' - 2+ 50.5\ \ 0.65 1.20 (0.20) (0.21) - 2+ 0.55 (1.00) 0+ Fig. 1. Decay scheme of As76 proposed by Kurbatov et al.5 (The numbers in parentheses are the relative intensities.) Assuming the ground state of As76 to be 2- on the basis of Nordheim's rules7 and considering beta-decay data and relative intensities, Kurbatov et al.5 made a probable assignment of 3+ to the 2.60-Mev level. (The ground state spin of As76 has since been measured to be 2 by an atomic-beam method.8'9) It was decided to investigate the 2.05-0.55 and 1.40-1.20 correlations to make a definite spin assignment to the 2.60-Mev level and to reinvestigate the 0.65-0.55 correlation. The observed gamma-ray spectrum (Fig. 2) and summing spectrum are in agreement with the decay scheme reported by Kurbatov et al. II. EXPERIMENTAL PROCEDURE A conventional fast-slow coincidence circuit was used for the measurements. It has an effective resolving time of 1 x 10-8 second. The instrument has been described in a previous paper.10 The scintillation counters consisted of 2-in. x 2-in. NaI(Tl) crystals mounted on RCA type 6342 photomultipliers. The counters were shielded frontally by 3/16 in. of aluminum. 7L. Nordheim, Revs. Modern Phys..2, 322 (1951). 8F. M. Pipkin and J. W. Culvahouse, Phys. Rev. 106, 1102 (1957). 9Christensen, Bennewitz, Hamilton, Reynolds, and Stroke, Phys. Rev. 107, 633 (1957). l'tewart, Scharenberg, and Wiedenbeck, Phys. Rev. 99, 691 (1955).

300 400 PULSE HEIGHT Fig. 2. Scintillation spectrum of gamma rays following the decay of As76. Although differential discrimination was used to provide energy selection, lateral lead shielding was also employed in some measurements to eliminate coincidences due to scattering. The source material was obtained from Oak Ridge. It was in the form of As dissolved in dilute HC1. Small amounts of Sb122 and Sb124 were present in the source material. The decay was carefully studied, and it was found that the effect of the contamination on the correlations was negligible. The liquid source was contained in a cylindrically shaped Lucite holder 1/8 inch in diameter and 3/8 inch in length. All correlations were done with the source centrally mounted, a distance of 10 cm from the front face of each crystal. The half-life of the O.550-Mev excited state has been measured to be (2.3 ~ 1.5) x 10-11 sec,ll and the half-life of the 1.20-Mev state is expected to be short. Because of this and the fact that the source was in a dilute solution, the measured correlation functions should not be attenuated due to extranuclear fields. 11C. F. Coleman, Phil. Mag. 46, 1135 (1955).

The data were taken in the sequence 90~ + (90~ + G) + (270~ - G) + 2700, running 5 nmin at each angle. Measurements of the accidental coincidence rate 'were taken periodically. The real *to accidental ratio was greater than 5 to 1 for all the correlations. The real coincidence rate was normalized by dividing by the two single counting rates N1 and N2 and multiplying by N1(180~) N2(180~). This method provided sufficient correction for source lifetime effects, source alignment, and any slight drift in the singles rates. A least-squares fit of the data was made to the function W(G) = 1 + A: P2(cos 9)+ A4 P4 (cos 9), where Pk is the Legendre polynomial. of order k. Annihilation radiation was used to correct for the effect of finite angular resolutiono12 This correction was applied to the normalized expansion coefficients A. and A, giving the corrected coefficients A2 and A4. IIIo RESULTS 0.o65-Mev-0.55-Mev Correlation Both differential discriminators were set at position A as shown in Fig. 2 so as to include both the 550-kev and 650-kev photopeaks. Lateral lead shielding was used for this correlation. The data are shown in Figo 35 The solid curve is the least-squares curve corrected for finite geometry and the error flags indicate the root-mean-square statistical errors of the experimental points. The broken curve is a plot of the theoretical correlation function for a 2(Q)2(Q)0 cascade. The experimental values of the expansion coefficients corrected for finite geometry are A2 = -0.042 ~ 0.015 and A4 = 0.319 + 0.023. The errors quoted are those defined by Rose in Eq. (30).13 If one assumes a spin of 0+ for the ground state of Se76 (eveneven nucleus), the experimental coefficients are not compatible with any combination of spins considering pure dipole or quadrupole radiation. If a mixture in the 650-kev transition is considered, only the 2(D,Q)2(Q)0 sequence will fit the data. The mixing parameter 6 is defined as the ratio of the reduced matrix elements P and a for quadrupole and dipole radiation respectively,14 If 6 = P/a, then 82 is equal to the ratio of the intensities of quadrupole and dipole radiation. Q, the quadrupole content, will be equal to 52/(1+82), and the dipole content will be 1 - Q. In Fig. 4 the values of A2 and A4 are plotted vs Q for a 2(D,Q)2(Q)0 sequence. The error flags represent the experimental values of A2 and A4. From Fig. 4 it is seen that the data are consistent with a value of Q equal to 0.997 ~ 0.002. This is in agreement with the value of Q> 0.85 found by Metzger and Todd.6 12Eo L..Church and J. J. Kraushaar, Phys. Rev. 88, 419 (1952). 13M. E. Rose, Phys. Rev. 91, 610 (1953). 14L C. Biedenharn and Mo E. Rose, Revs. Modern Phys. 25, 729 (1953).

1.15 Q Fig. 3. Directional correlation of 0.65-0.55 Mev cascade. The solid curve is the leastsquares curve corrected for finite geometry and the broken curve the theoretical correlation function for a 2(Q)2(Q)0 sequence. Fig. 4. A2 and A4 versus Q, the quadrupole intensity, for a 2(D,Q)2(Q)0 seauence. The shaded regions show the values of Q corresponding to the experimental values of A2 and A4.

It can thus be concluded t;ht the.first and second excited st.,es hay.:? spins of 2+ and that the 0.650-Mev gamma ray is a mixture of 99.7 ~ 0.2% electric quadrupole and 0.3 $ 0.2%0 magnetic dipole radiation. 2.05-Mev- 0. 55-Mev Correlati.on. For the 2.05-Mev-0.55-Mev correlation, one discriminator was set integrally at C and the other differentially at D as shown in Fig. 2. Lateral lead shielding was used for this correlation. Because of the low coincidence rate, data were taken at only four angl&s.. The experimental data and leastsquares curve corrected for finite geometry are shown in Fig. 5. The corrected coefficients are A2 = -0.027 -.+0.022 and A4 = -0.075 + 0.033. The negative value for A4 rules out the-c.ombainations 4(Q)2(Q)0 and 2(D,Q)2(Q)0 since both require a positive A4. Thie data can best be explained by the sequence 3(D,Q)2(Q)0. In Fig. 6 the- the:oretical values of A2 and A4 are plotted vs Q, the quadrupole content of the 3-2 transition. It is seen that the experimental values of A2 andiA4 are compatible with a value of Q 0.948 + 0.014. Since an E1-M2 mixture of this magnitude is very unlikely, it is reasonable to conclude that the 2.05-Mev gamma ray consists of 94.8 + 1.4% E2 and 5.2 T 1.4% Ml radiation. On the basis of this and the selection rules for gamma transitions, a value of 3+ can be assigned to the 2.60-Mev level. 'This assignment agrees with that of Kurbatov et al.,5 which was made on the basis of log ft values and relative intensities. w0 20l.R 160' 180~ 0 0.2 0.4 Q 0.6 0o 1 Fig. 5. Directional correlatifon of Fig. 6. A2 and A4 versus Q for a 2.05-Mev-0.55-Mev cascade. 3(D,Q)2(Q)0 sequence. The shaded areas indicate the values of Q corresponding to the experimental values of A2 and A4.

The data can almost be explained by a l(D,Q)2(Q)0 sequence. However, a spin of 1 for the upper level is very unlikely because of the absence of the 2.60-Mev crossover transition, 1.40-Mev-1.20-Mev Correlation For this correlation the discriminators were both set integrally at position B (Fig. 2) so as to include everything above the 1.20-Mev photopeak. No lateral lead shielding was needed. The data are shown in Fig. 7, the solid curve being the least-squares curve corrected for finite geometry and the dotted curve the theoretical curve for a 3(D)2(Q)0 combination. The corrected experimental coefficients are Ag = -0.076 ~ 0.022 and A4 = -0.003 + 0.032. It is seen that the error in A4 is ten times larger than the coefficient itself. Thus the existence of any A4 is questionable. When only A2 is considered, a value of A2 = -0.077 ~ 0.019 is obtained. This is in good agreement with the theoretical value of A2 = -0.0714 for a 3(D)2(Q)0 cascade. Considering this sequence, the maximum amount of quadrupole admixture in the 3-2 transition consistent with the data is 0.05%. The data can also be explained by the sequence I(D,Q)2(Q)O. Iowever, the possibility of spin l for the 2.60 level has already been ruled out. Fig. 7. Directional correlation of 1.40-Mev- 1.20-Mev cascade. The solid curve is the least-squares curve corrected for finite geometry and the broken curve the theoretical correlation function for a 3(D)2(Q)0 combination.

Thus a spin of 5+ can be assigned to the 2060-Mev level with the 1.40 -Mev gamma ray being almost pure Mio IVo SUMMARY AND DISCUSSION The results of the correlations confirm the assignment of 0+, 2+, 2+, 3+ to the energy levels of Se76 in order of increasing energyo The 0055 -Mev and 1o20-Mev gamma rays are found to be pure E2 radiation, the 0o65-Mev gamma ray 99.7 ~ 0.2% E2 and 0.3 + 0.2% Ml1 the 2o05-Mev gamma ray 94.8 ~ 1.4% E2 and 502 T 1o4% Ml, and the 1.40-Mev gamma ray almost pure Mlo In the intermediate regions between closed-shell nuclei and those nuclei with many particles in unfilled shells, excited states corresponding to quadrupole vibrations about a spherical equilibrium shape are expectedo An enhancement of E2 transition probabilities is usually associated with these vibrational stateso A review of the theory of vibrational excitations and a summary of experimental data on nuclei in these regions has been presented in the review article on Coulomb excitation by Alder et al 15 Se76 is one of the nuclei which exhibits vibrational stateso The first excited state in Se76 has been reached by Coulomb excitation, and the cross section for this process was found to be much larger than the cross section expected for a single-particle excitation,16 This is strong evidence that the excitation is due mainly to a cooperative vibrational motion involving many nucleons. Thus the first excited state is mainly the result of a onephonon vibrational excitation The ratio of the energies of the second and first excited states and the fact that the 0.65-Mev gamma ray is almost pure E2 indicate that the second excited state is also mainly vibrational in character, probably a two-phonon vibrational excitationo If there were no coupling between the vibrational motion and the individual particle motion of the outer nucleons, the two-phonon vibrational state would be three-fold degenerate with spins 0, 2, 4 and even parity However, this coupling, which can be very complex, usually splits the three levels. The very different nature of the two transitions originating from the third excited state is difficult to understando One possibility is that the third excited state is due to a two-phonon vibrational excitation coupled with a single-particle excitation of the ground state configuration. If this is true, then the 1.40-Mev gamma ray occurs between two states with the same number of phonons and is primarily a single-particle transition, This could account for the fact 15Alder, Bohr, Huus, Mottelson, and Winther, Revs. Modern Physo 28, 432 (1956). 16Go M. Temmer and N. Po Heydenburg, Phys. Rev. 104, 967 (1956).

that the 1.40-Mev gamma ray is almost pure dipole radiation. However, the 2.05-Mev transition would require both a change in phonon number and particle excitation. This could give an enhanced E2 transition probability and might account for the large E2 component in the 2.05-Mev transition. ACKNOWLEDGMENTS The authors wish to acknowledge the help of F. C. Chang and R. Arns in recording some of the data.

VI A RE-EVALUATION OF THE BETA AND GAMA ENERGIES FROM Ho166, Nd147, AND Sm153

Reprinted from the Bulletin of the American Physical Society, Series II, Vol. 3, No. 1, 64, January 29, 1958 A Re-Evaluation of the Beta and Gamma Energies from Ho166, Ndl47, and Sm163. J. M. CORK, M. K. BRICE, R. G. HELMER, AND R. M. WOODS, JR., University of Michigan.*Using enriched sources of Ho165, Nd'46, and Sm162 strbng specimens of Ho166, Nd147, and Sm'63 were made by neutron capture. Studies of the strong sources by both magnetic and scintillation spectrometers showed the existence of some gamma rays not previously reported, more exact values for the low-energy gamma rays, and better resolution of the components of the beta spectra. In Ho166 gamma rays occur at 80.25, 970, 1377, 1540, and 1620 kev, and the maximum beta energies are 1839, 1758, 869, 380, and 220 kev. Nd147 yields gamma rays at 91.3, 120.6, 198.2, 277.0, 321, 400, 441, 533, 597, and 688 kev, with beta components at 812, 380, and 230 kev. In Sm163 gamma rays are found at 69.8, 103.5, and 173.6 kev and beta components at 813, 710, and 640 kev. A level scheme is presented for each nucleus that is in complete agreement with observed data.

VII INTERPRETATION OF GAMMA-GAMMA DIRECTIONAL CORRELATIONS INVOLVING DIPOLE-QUADRUPOLE MIXTURES

INTERPRETATION OF GAMMA-GAMMA DIRECTIONAL CORRELATIONS INVOLVING DIPOLE-QUADRUPOLE MIXTURES* Ro Go Arns * and M. Lo Wiedenbeck Department of Physics, University of Michigan, Ann Arbor, Michigan A collection of curves is presented which is intended to provide a quick method for interpreting -7y directional correlations when one or both gamma rays involve a mixture of dipole and quadrupole radiation. The present work is based on the previous calculation of F-coefficients by Ferentz and Rosenzweig1l The range of spins included is expected to cover most cases of practical interest. I. TRANSITIONS OF MIXED MULTIPOLARITY IN y-y CORRELATION Denote jl, j, and j2 as the initial, intermediate, and final momenta of a cascade in the gamma decay of a nucleus. Let the transition between ji and j be a mixture of 2L1 and 2Ll+l poles. Similarly describe the second (LL,+ transition as a mixture of 2L2 and 'r.Y 2L2+l poles. The theoretical angular.J correlation function will then be of 2 (L,2+ J2 the form: W(G.) ' A1) A2) K (cos G) (1) K even in which the constant A;V) for the vth transition is dependent only upon the spins and multipolarities involved in that transition. The A1 Y are of the form: *Supported in part by the Michigan Memorial Phoenix Project and by the Office of Naval Research. **Dow Chemical Company Fellow. 1M. Ferentz and N. Rosenzweig, ANL-5324 (1955)o

A )' = FK(LV,LvJvj) 2VFK(LVLV + 2F(LLl ) + FK(Lv+l,Lv+l,jvlj) (2) The summation over K in (1) runs from zero to the least of 2j, 2(L1+l), or 2(L2+1)o The FK(L,L',jl,j) are the F-coefficients as defined and tabulated by Ferentz and Rosenzweig1 62 is the ratio of the intensity of the Lv + 1 radiation to the Lv radiation in the vth transition of the cascade. The least-squares fit of experimental points in an angular correlation experiment2 is normally made to the function: W(G) = 1 + G2A2P2(cos G) + G4A4P4(cos g) (3) where the GK are attenuation factors dependent upon the geometry of the experiment, etc., and: AK 4 (4) Due to the special properties of the F-coefficient, viz: Fo (L,L,j',j) = 1 (5) Fo (L,L+l,jj) = 0, (6) equation (4) becomes: AK = (1) A2) - y l+ (7) Define Qv as the fraction of the Lv + 1 multipole in the vth (mixed) transition. Qv bears the following relation to 6v: 2 qv = -. (8) V Then 1 - Qv is the fraction of the Lv multipole in the same transition and, upon substitution, equation (7) becomes: 2M. E. Rose, Phys. Rev. 91, 610 (1953).

AK = A.^) Ai2) = [FK(Ll,Ll,Jl,j)(l-Ql) + 2FK(Ll,Ll+l,jl,j) iQl(l-Ql) + FK(Ll+l,Ll+l,jl,j)Q1] [FK(L2,L2,j2,j)(1-Q2) + 2FK(L2,L2+1,j2,j) JQ2(1-Q2) + FK(L2+1,L2+1,j2,j)Q2] (9) II APPLICATION TO CASCADES WITH MIXTURE IN ONE TRANSITION Equation (9) takes on an especially simple form when one transition is a mixture of dipole and quadrupole radiation and the other is unmixed. If, for example, the mixture is in the first transition: A2 = A(1) A 2) = [a(l-Q) + bQ(-Q) + cQ] F2(L2,L2,j2,j) (10) A4 = A) A(2) = [dQ] F4(L2,L2,j2,j) (11) where: a = F2 (lljlj) b = 2F2 (1,2,jl,j) c = F2 (2,2,ji,j) d = F4 (2,2,jl,j) (12) In terms of the first transition only: A( = [a(1-Q) + b \/Q(1Q) + cQ] (13) Adl) = dQ (14) A plot of A2 vs Q for equation (135) is an ellipse. Equation (14) is a straight line in the variables A41) and Q. The curves tabulated in this report are plots of A1v) vs Q and A4v) vs Q for single transitions between states of various spins~ The least-squares fit will yield values of A(EXP) + and AEXP) ~ e4 where the EK are the R.MoSo statistical errors. In order to determine the quadrupole content of the mixed transition, the AEXP) + e2 and AEXP) ~ E4 must be divided by the corresponding F-coefficients from the unmixed transition [cf. equations (10) and (11)]. The resultant numbers are then compared with the graph in order to find the range of Q consistent with the experiment.

A() and A ) are plotted to the same scale vs Q in the following graphs. The absence of an Aiv) line indicates Ajv) = 0 III. APPLICATION TO CASCADES WITH MIXTURES IN BOTH TRANSITIONS If both steps of a cascade are mixtures of dipole and quadrupole radiation, equation (9) assumes the form: A2 = Al1) A42) = [al(l-Qj) + bli Q(l-Q1) + clQ1] [a2(l-Q2) + b2 JQ2(-Q2) + c2Q2] (15) (1) (2) A.4 A() A(2) = [dQj1] [d2Q2] (16) where al, a2, etc., are defined as in (12) and Q1 and Q a re again to be found by graphical analysis. In this case a value of AkV cannot be assumed for either transition. However, the set of values of A4v) satisfying: (1) (2) (EXP) A.2 A2) = A )+ ~2 (17) A(1) A(2) - (EXP) + (18) can be calculated. The values of Ail) and A;2) satisfying (17) can be plotted against one another to the same scale as the single transition mixture curves of this report. (Any graph paper with 20 lines to the inch will suffice.) Various single transition mixture curves can be placed with scales to coincide with the AkV) axes of the experimental graph [i.e., graph of equation (17)]. Then a value of Q1 consistent with the first transition will correspond to a range of values of Q2 for the second tran.sition required by the experimental graph and vice versa. The same procedure can also be applied to equation (18). IV. NOTATION Each curve is identified by the spins of the two states involved in the transition. They are listed in the form: j(D,Q)j, where in all cases j is the spin of the intermediate state. j j is the spin of the initial or

final state of the cascade depending on whether the graph is used to describe the first or second transitiono A list of the coefficients a, b, c, and d used in computing the graphs is appended in Table Io Often it is desirable to know the mixing in terms of 6, the mixing parameter In each case where b [as defined in (14) and listed in Table I] is positive, the upper portion of the ellipse corresponds to 6 positive, If b is negative, the opposite is trueo TABLE I COEFFICIENTS a, b, c, AND d USED IN COMPUTATION OF THE SINGLE TRANSITION MIXTURE CURVES j j' a b c d 1 1 -03536 -2o1213 -0o3536 0 i 3 +0 0707 +0 9487 +0o3536 0 2 1 +0o4183 -1.8708 -0.2988 +0.7127 2 2 -0o4183 -1.2247 +0o1281 -0.3054 2 3 +0.1195 +153093 +0,3415 +0.0764 3 2 +0o3464 -1.8974 -.o1237 +0.6701 3 3 -0 4330 -0.8660 +0.2268 -0.4467 3 4 +0o1443 +104434 +0o3093 +0.1489 4 3 +0.3134 -1.8804 -0o0448 +0o6088 4 4 -0o4388 -0.6708 +0.2646 -0.4981 4 5 +0o1595 +1o5136 +0o2849 +0o1937 5 4 +0.2944 -1.8619 000000 +o05666 5 5 -0.4416 -0o5477 +0.2831 -0.5230 5 6 +0.1698 +1.5566 +0.2669 +0.2241 6 5 +0.2820 -1.8464 +0.0288 +0.5370 6 6 -0.4432 -0.4629 +0.2936 -0.5370 3/2 1/2 +0.5000 -1.7321 -0.5000 0 3/2 3/2 -0.40 -15492 0.0000 0 3/2 5/2 +0.1000 +1.1832 +0.3571 0 5/2 3/2 +0~3742 -1.8974 -0.1909 +0,7054 5/2 5/2 -0.4276 -1.0142 +0.1909 -0 3968 5/2 7/2 +001336 +1.3887 +0 3245 +0,1176 7/2 5/2 +0 3273 -1.8898 -0o0779 +0.6367 7/2 7/2 -0.4364 -0.7559 +0.2494 -0.4775 7/2 9/2 +0.1528 +1.4832 +0.2962 +0.1737 9/2 7/2 +0 3028 -1.8708 -0o0197 +0.5857 9/2 9/2 -0o4404 -0o6030 +0.2752 -0.5125 9/2 11/2 +0o1651 +1.5374 +062752 +0.2102

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