The ωp = ωn = 12 excitations in the odd nucleus 172Tm

Nuclear Physics

71 (1965) 481--496; ( ~

North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

r i l E ~"~p= ~'~n = I EXCITATIONS IN T H E O D D N U C L E U S l~2Tm P. G. HANSEN, H. L. NIELSEN, E. T. WILLIAMS and K. WILSKY

Research Establishment Risi~, Roskilde, Denmark Received 20 April 1965 A b s t r a c t : The decay of 50 h 17~Er has been investigated by electron and gamma-ray spectrometry

and coincidence techniques. Excited levels, characterized by the quantum numbers (K, In), have been established at the following energies in keV: 61(2, 3-), 407(1, 1-), 446(1,2-), 475(0, 0-), 535(0, 1-) and 610(1, 1+). The levels can be interpreted in terms of the Nilsson orbitals expected in this region. Thus the four states from 407 to 535 keV are taken to belong to the configuration p ½+[411 ] -¢- n ½- [521 ], which gives rise to bands with K = 0 and K = 1. These two bands have an anomalous structure, partly because of the even-odd splitting in the K = 0 band, partly because o f the Coriolis coupling between the two bands. By an analysis of the beta-transition probabilities in the decay of XTSEr and o f iV°Tin it is shown that the Coriolis coupling vanishes in the odd-spin states in agreement with expectations. However, an analysis based on the level spacings in X~°Tm and tT~l'm indicates that the appreciable rotational perturbations of the even-spin states deviate from the theoretical value.

E [ RADIOACTIVITY tTSEr [from lT°Er(2n, y)]; measured Ey, Ir, Eee, I~e, 7-ce'coin, cc. I 17~Tm deduced levels, J, z~. Enriched source.

1. Introduction The levels observed in strongly deformed odd-mass nuclei are very well accounted for ~) by the Nilsson model, according to which the nucleons move independently in a spheroidal potential, so that each orbital has a projection ~ of total angular momentum upon the nuclear symmetry axis. In the extension of this scheme to the twoquasi-particle states in even-mass nuclei one assumes that the nuclear properties are largely determined by the presence of two unpaired nucleons giving rise to intrinsic states with K = If21 - f221. In this way it has been possible to explain spins and parities for the low-lying states (mainly the ground states) of many odd 2-4) nuclei and to explain a number of excited states above the energy gap in even 4) nuclei. The applicability of this scheme seems well justified by the available data, and the pertinent question must now be what its limitations are. Particular interest is focussed on the phenomena caused by the residual interactions such as the singlet-triplet splitting 5, 6) and the odd-even shift in K = 0 bands 6, 7). Also it is not yet clear how pure the twoquasi-particle states are. In order to answer these questions, more experimental information is desirable, and, although odd nuclei are experimentally rather inaccessible, the study of these nuclei seems the best starting point because the situation is here somewhat less complex than above the energy gap in even nuclei. 481 September 1965

482 -

p.G. HANSENe t

al.

The present paper deals with the decay of 50 h 172Er to levels in 172Tm. Previous studies s-11) of this decay had been based largely on scintillation counters and remained inconclusive because of the presence of highly converted transitions, while the work reported in the following depends primarily on conversion electron spectra and e--~, coincidence experiments. After the publication of a preliminary report 22) on this work some additional experiments have been carried out, and although the level scheme shown in fig. 8 is essentially unchanged from that of ref. 12), the new evidence provides further support for the correctness of all its main features. The level scheme of 172Tm is of special interest because the four levels at 407, 446, 475 and 535 keV excitation energy seem 22) to belong to a family of states in which both the neutron and the proton have ~2 = ½, so that intrinsic states with K = 0 and K = 1 occur. In analogy with the anomalous K = ½ bands in odd-mass nuclei, a configuration such as that encountered here is expected to have a special behaviour, which is discussed in the final section of this paper.

2. Experimental Techniques and Results 2.1. SOURCE PREPARATION The isotope 172Er was produced by irradiation o f 10-15 mg samples of enriched (96 ~o) 17°Er2 O3 in the 1.8 x 1014 n" cm 2 • s- 1 flux of the DR3 reactor through the reactions 17°Er(n, 7,)171Er (7.5 h) (n, ~) 172Er (50 h). From the yields of activity we estimate the (reactor) neutron-capture cross section of 171Er to be 250 b, the uncertainty being within a factor of two of this figure. After the main part of the 171Er activity had decayed, the sample was purified by hydroxide and fluoride precipitations, and erbium was isolated from other rare-earth activities (mainly 171Tm (1.9 y ) a n d 172Tm (63.5 h)) by cation-exchange chromatography with lactic acid as the eluant. Sources of approximately 400 #Cur 172Er were obtained together with comparable amounts of 169Er, a beta emitter (0.34 MeV) the radiation of which did not interfere in the gamma spectroscopy. For the experiments with the beta-ray spectrometer a thin source of 1-2 pCur mounted on a 200/~g • cm -2 aluminium backing was prepared by means of the electromagnetic isotope separator at the Institute for Theoretical Physics in Copenhagen. 2.2. GAMMA-RAY SPECTROMETRY The low-energy gamma rays were measured with a K X-ray escape spectrometer 13) based on a xenon-filled proportional counter. The resulting spectrum (table 1 and fig. 1) clearly showed the presence of a 68 keV gamma-ray in addition to Tm K~ and Ka X-rays. The remaining part of the ~ spectrum was studied with a 2.7 mm thick lithium-drifted germanium semi-conductor counter 14). The line width for this detector was about 5 keV in the low-energy region and thus permitted the observation of a number of new transitions (fig. 2). The detection efficiency as a function of the ? energy was determined by means of standard sources to a relative accuracy of

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Fig. l. Low-energy y-ray spectrum of ZY=Errecorded during 40 min with a xenon-filled proportional counter operated in coincidence with escaping Xe K X-rays. The peaks labelled with the y energy in keV are the Xe-K~ escape peaks. The line shape is complex with a less intense Xe--K# escape peak on the low-energy side of each line; thus the peak in channel 26 is the Xe-Kp escape peak corresponding to the Tm-K= lines. 1:~1Er'~)112128 I

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Fig. 2. High-energy y-ray spectrum of ZY=Errecorded during 60 min with a 2.7 mm thick Li-drifted germanium counter. The photopeak energies are given in keV. Lines from the 7.5 h Z~ZEr impurity are present, and the growth of the a72Tm daughter activity shows up in the 181 keV peak.

17=Tin NUCLEUS

485

-t-20 ~o, so that the intensity values given in table 1 could be obtained. Finally, rather accurate intensities for some of the more intense lines were available from NaI(T1) spectroscopy 9,11). The growth of t72Tm activity in a purified 172Er sample made it possible to bring the transition intensities for the latter decay to an absolute scale. For the 7 intensities this was done most accurately by Gunnink zt), who found (40+ 1 ~o) for the 610 keV ray. The ? intensities in table 1 have been normalized to this value. 2.3. E L E C T R O N

SPECTROMETRY

The electron spectrum of 172Er was scanned from 6 to 600 keV with a six-gap spectrometer 15) at momentum-resolution settings from 0.6 ~o to 1.1 Yo, but source thickness and the dimensions of the isotope-separated source made the effective resolution inferior to these values (figs. 3-5). The gamma spectrum indicated that no lines L~59.6

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Fig. 4. Internal-conversion-line spectrum of l~2Er for the region 45-70 keV m e a s u r e d with 0.9 % resolution (three gaps).

the "orange" spectrometer. could be expected above 600 keV. Typical parts of the internal-conversion-line spectrum are shown in figs. 3-5, and a summary of energies and intensities for all the main lines is given in table 1. Accurate energy values for the 172Er lines were obtained by means of well-known lines from 171Er and 172Tm present in the sample as well as by means of standard sources. The conversion-line intensities were brought to an absolute scale by comparison with the Ln-~H lines of the 78.7 keV transition (fig. 4) from the decay of the daughter activity 172Tm. It was assumed that these lines have an absolute intensity (in the 172Tm decay lo)) of 36 ~o. As the absolute electron and gamma intensities in table 1 were obtained from two

486

P.G.

HANSEN e t al.

independent normalizations, a check on their consistency was felt desirable. For this purpose we determined the internal-conversion coefficient for the 610 keV transition by comparison with a a37cs source, assuming ~K = 0.095 for the 662 keV transition in 137Ba. The result ~K = 0.0032 is in good agreement with the value 0.0033 obtained from the absolute electron and ? intensities given in table 1. i

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3.6 ' 38 ' 4.0 ' 42 i 4.4 ' 4.6 MAGNETCURRENT(A) Fig. 5. Internal-conversion-line spectrum of XT=Erfor the region 300-570 keV measured with 1.1% resolution (six gaps). A special search was made for a 900 keV beta group corresponding to a transition from ~72Er to the X72Tm ground state. The beta singles spectrum from a chemically separated (but not isotope-separated) ~72Er source was recorded with an anthracene crystal and compared with the corresponding spectra from 172Tm (1860 keV) and 19SAu (960 keV). The presence of the intense 340 keV beta spectrum from Z69Er and of 172Tm activity only allows us to place an upper limit of 10 ~ on the absolute intensity of the expected 900 keV beta group. This agrees with the value (10+8) given by Helmer and Burson 9). 2.4. COINCIDENCE EXPERIMENTS For the coincidence experiments with the electron spectrometer a 7.6 cm × 7.6 cm NaI(Tl) crystal was placed 2.6 cm above the source, and coincidences with a resolving time of 0.2 #s were taken with the/~ spectrometer set on and, for correction, beside the electron line. Characteristic e--y coincidence spectra are shown in figs. 6 and 7, which correspond to the spectrometer settings indicated in fig. 3 and fig. 4 respectively. The absolute 7-detection efficiency as a function of energy was determined by coincidence measurements on sources with known e-7 (or e - K X ) coincidence relationships such as ~37Cs, 57C0, 2°3Hg, 2°7Bi and 6°C0. The intensities of the coincident

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lines could therefore be expressed quantitatively in terms of the coincidence frequency defined 14) as r/ = N, oi.c(1 +~tot)/epNp, where N, oino is the number of coincidence I

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counts recorded in the photopeak of interest (if necessary corrected for summing in the crystal), :Ztot is the total internal conversion coefficient, ep is the photopeak effi-

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ciency, and Np is the number of counts recorded in the electron counter. The coincidence relationships are summarized in table 2. The beta spectrum was measured in coincidence with the 407 and 610 keV gamma rays in order to eliminate contributions from 169Er and 172Tm. A few gammagamma coincidence experiments were performed with two NaI counters placed at right angles and separated by a copper- and cadmium-lined anti-scattering shield. The result of these experiments are included in table 2.

3. Decay Scheme and Multipole Orders The 172Tin level scheme shown in fig. 8 can in principle be constructed from energy sums alone, the order of emission of the gamma rays being determined from intensity considerations. With the multipole orders indicated, the scheme quantitatively exEr172 0+

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plains all coincidence relationships, as can be seen if the calculated coincidence frequencies given in column 3 of table 2 are compared with the experimental values. This way of presentation, however, does not demonstrate that most details of the scheme are logically necessitated by the coincidence experiments, and that some of the multipole-order assignments that are not evident from table 1 in fact follow directly from these experiments. In this section we shall therefore show the details of the arguments leading with great certainty to the 172Er decay given scheme here.

490

P . G . HANSON et aL

The 610 keV transition, coincident only with 292 keV betas, is clearly of E1 multipole order and must be placed as a ground-state transition fed directly by beta decay, so that the energy available is 902+ 15 keV. The high intensity of K X-rays (63 ~o) is not accounted for by the K conversion lines listed in table 1. As the ratio of K~ to Ka is normal (fig. 1), there is nothing to suggest the presence of appreciable amounts of gamma rays in the K X-ray peak, and it must be assumed to have its origin in an unobserved, low-energy K line. The coincidence data (table 2) show that the K X-rays are predominantly in coincidence with the 407 keV transition, and that the lines Lt 59.6 and L~ 67.9 are each strongly in coincidence with the 407 keV gamma ray and with K X-rays. This as well as the presence of (407 + KX) sum lines in the latter two experiments (see e.g. fig. 7) can only be explained if one assumes a triple cascade 59.6-67.9--407 where both low-energy transitions convert strongly in the K shell. The presence of such a cascade with a total energy of 534.5 keV is substantiated by the observation of a 535keV gamma ray and by the coincident beta group of 381 keV, which gives a Q value of 916__+8 keV in agreement with the value obtained above. The relative order of the three transitions is determined by the observation of two cross-over transitions, a 128 keV transition in coincidence with the 407 and a 476 keV transition which connects t across the 67.9 and 407 keV transitions. Both the relative and the absolute order of emission in the triple cascade are fixed by the 203 keV gamma ray, which is in coincidence with the 407 keV gamma, and which, from energy considerations, almost certainly comes from the 610 keV level. This shows the existence of excited states at 407, 475 and 535 keV. The internal-conversion coefficient for the 407 keV transition shows that its multipole order is M1. Likewise the 59.6 and 67.8 keV transitions, which are known from the K X-ray coincidence to have K/L ratios about 5-6, and which convert strongly in the Lt subshell, can only be of M1 multipole order. The K line intensities for the two transitions, when calculated from the L conversion-line intensities and the (extrapolated) theoretical K/L ratios 17), are about 30 ~o higher than accounted for by the total K X-ray strength. This deviation is hardly outside the expected uncertainty in such calculations. On the basis of the coincidence data we deduce 30 ~ and 32 ~ for the absolute intensities of the two K lines'respectively. The 128 keV transition is presumably M1 as for the L conversion coefficient we find 0.17 (theory 0.18 (MI); 0.50(E2); 0.023(E1)). The Lni line of the 29.2 keV transition is in coincidence with K X-rays and with the 384 and 446 keV gamma rays. The observation of a (446 + KX) sum peak (see fig. 6) and energy considerations suggest a triple cascade 59.6-29.2-446. The 164 keV gamma ray, which is coincident with K 446 (table 2), must connect to the 610 keV level and proves that the order is as shown. The level at 446 keV thus defined must also decay via the 384 keV ray in order to account for the depopulation of this state (t/384+ t A n alternative placement, not excluded by o u r experiments, is between the 535 and ~ 61 keV levels.

l¢~Tm NUCLEUS

491

7446 = 104~o). Furthermore the K 384 is so strongly in coincidence with K X-rays that we are compelled to assume the existence of another, strongly K-converted ~ 61 keV M1 transition in 172Tm. Such a transition would remain unresolved from the L~ 59.6. If we let this ~-, 61 keV transition define a level at 61 keV in 172Tm, the 346 keV ray can now be placed between the latter and the level at 407 keV. For the ~ 61 keV transition this requires an intensity of only 3 ~o as compared with the total observed intensity of 42 ~o for the 59.6 keV transition. For the 29.2 keV transition, E2 multipole order is indicated by the L subshell ratio ((l.q + l.qt)/Lal = 0.82; theoretical values 0.83(E2), 1.70(El), 76(M1)). Multipole orders for a number of the other transitions discussed above can be inferred (in some cases tentatively) from the K conversion coefficients given in table I. The arguments given above place all observed transitions, and even an unobserved one, in a decay scheme that is in all its main features unambiguously proved by experiment. The multipole orders given above and in table 1 provide a consistent set of relative parities for the 172Tm levels, and the decay scheme presented in fig. 8 satisfactorily accounts for the intensity flow through the levels. It is worth pointing out that as the electron and gamma intensities have been brought to an absolute scale without any reference to the XV2Er decay scheme, the intensity sum of all transitions to the 172Tm ground state is a test of the completeness of our investigation. In agreement with the ideal sum of 100 ~o, we find for the sum of all observed transitions 92 ~ with an upper limit of 102 ~ if the unobserved ground-state beta transition has the maximum strength of 10 ~ permitted by the experiments. It is possible to estimate theoretically the strength of this beta group by assuming that the intrinsic matrix element is the same as that of the transition between 172Tm and the 172yb ground state 10, 1a). In this way one calculates an intensity o f 1.7 ~o. 4. Assignments In this section, spins and parities for the 172Tm levels are deduced. The levels are assigned as members of rotational bands, each band being in turn characterized by the orbitals of the odd proton and of the odd neutron. The single-particle states are denoted by the quantum numbers 1) f2,~[NnzA]. The quantum numbers of the proton state are given before those of the neutron state, and the sign + separating the two sets is used to distinguish between the states with respectively K = f2p+ f2nand K = If~p- S~nl. The ground state of ~72Tm decays so, 28) by unique, first-forbidden transitions to the 0 +, 2 + and 4 + members of the ground-state rotational band in 172yb and must therefore have spin 2 and odd parity corresponding to the configuration ½+ [411 ] ~ - [512]. These orbitals occur systematically as ground-state configurations for nuclei with respectively 69 protons and 103 neutrons, and the coupling agrees with the empirical coupling rules 5). We further interpret the ~ 61 keV level as the 3- member o f the rotational band built on the ~72Tm ground state. The level at 610 keV is uniquely determined as 1 + since it is fed from the 0 + ground

492

P . G . HANSEN et aL

state of 172Er by a relatively fast beta transition and since it decays to the 2 - ground state of 172Tin via a g a m m a ray of E1 multipole order. The level can be explained as due to the excitation of the odd proton to the -]- [523] orbital, which in 17~Tm is encountered at 425 keV. The l o g f t value of 5.7 observed here for the transition 3 - [523] ~r- [512] is consistent with the assignment ah demanded by the selection rules in the asymptotic quantum numbers and with the log f l value of 6.3 observed for the same transition in the Er 171 beta decay. The four levels at 407, 446, 475 and 535 keV have odd parity, as can be seen from the characters of the transitions connecting these levels to the 2 - and 1 ÷ states. The spins of the four levels, however, cannot be determined uniquely, but the following arguments point strongly to the assignments given in fig. 8. The 407 keV level decays by a strong M1 transition to the 2 - ground state and by a much weaker transition of M1 or E2 multipole order to the 3- state at 61 keV. Therefore the level at 407 keV can best be characterized by the assignment 1-. By the same line of reasoning, the two M1 transitions of almost equal strength leading from the 446 keV level to the 2 - and 3- states suggest the assignment 2 - , whereas 3 - is excluded by the 164 keV E1 transition f r o m the 1 + state at 610 keV. Spin 0 is indicated for the level at 475 keV by the E2 transition to the 2 - state, by the M1 transition to the 1- state, and by the direct beta feed from the 0 + ground state of 172Er. Finally, for the 535 keV level, spin 1 remains the only possible assignment. We have interpreted 22) the four levels as members of two rotational bands with K = 0 and K -- 1, both bands arising from a ½-[521] neutron excitation, which in the isotonic nucleus ~TaYb is encountered 19) 399 keV above the { - [512] state. The coupling of a ½+[-411] proton to a ½-[521] neutron leads to intrinsic states with K = 0 and K = 1, the latter of which is expected 5) to lie lowest. We take the 2 state at 446 keV to be a rotational state built on the 1, 1- band head. The 0 - and 1states at 475 keV and 535 keV must then belong to the band with K = 0. Further support for the interpretation given here can be drawn from a detailed consideration of the beta transition probabilities observed in this work, and f r o m studies of the related nucleus 17°Tm. This information has been included in the discussion (sect. 5) dealing with the properties of the I2p = f2, = ½ bands. 5. D i s c u s s i o n

5.1. BETA-DECAY SELECTION RULES For odd nuclei the selection rules in the asymptotic quantum numbers are the same as for odd-mass nuclei. Only one-particle transitions are allowed, but there is an additional selection rule 20, 21) stating that an operator of multipolarity L can only change the coupling between the particles if L exceeds the total change in projected orbital angular m o m e n t u m t i- Configuration mixing between the two-quasi-particle configurations may relax these selection rules. For example, according to the assignments of fig. 8, the 164 and 203 keV E1 transitions from the 610 keV state are two-particle transitions, and likewise the 128 keV MI transition is A-forbidden.

493

17gTm NUCLEUS

We consider the beta transition ½- [521 ] --* ½+ [411 ], classified as lu in g o o d agreem e n t with the experimental l o g f t values between 6.1 and 6.8 observed in the neighb o u r i n g odd-mass nuclei. I n the decay 172Er ~ t72Tm the initial nucleus is in a paired configuration, and the decay via non-unique, first-forbidden transitions can only take place to the 0 - and 1 - members o f the K = 0 band, whereas the transition to the 1state o f the K = 1 b a n d is A-forbidden. I n agreement with these rules and with the systematics for odd-mass nuclei one observes l o g f t values o f ~ 6.8 and 6.0 for the transitions to the 0 - and 1 - states t o f the K = 0 band, but no detectable feed to the 1 - state at 407 keV. The retardation o f the A-forbidden transition is b r o u g h t out more clearly in the fl decay o f 17°Tm discussed below in subsects. 5.3 and 5.4. 5.2. THE LEVEL STRUCTURE OF THE K = 0 AND K = 1 BANDS F o r a two-quasi-particle state with K = l o p - t 2 n l = 0 the n e u t r o n - p r o t o n residual interaction can couple the two parts o f the collective wave function so that the internal energy becomes spin-dependent 6, 7). The rotational b a n d built on such a K = 0 state will then be split into an even-spin b a n d ( I = 0, 2, 4 , . . . ) and an odd-spin b a n d (I--- 1, 3, 5 . . . . ). Such a n o m a l o u s rotational bands have been observed in the nuclei 22) 156Eu ' 166H0 ' 170Lu ' 176Lu ' 176Ta ' 234pa and 242Am. In the special case considered here, where t2p and f2n b o t h equal ½, additional terms occur, and a rather unusual level structure is to be expected 4) in the general case. The Coriolis force will couple the K = 0 and K = 1 bands with a coupling matrix element that can be expressed 12,1 s, 2a)

(I,g=

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(1)

w h e r e ap and an are the decoupling parameters for the two odd particles. A new term

also enters 7, 24) the expression for the diagonal matrix element for the K = 0 b a n d :

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where B is the even-odd splitting parameter used by N e w b y 7) and by Varshalovich 24) and where the last term is due to a patricle-particle coupling term 7) in the rotational energy. We can estimate the magnitude o f the off-diagonal matrix element (1) f r o m the values for the decoupling parameters ap = - 0 . 8 7 and an = 0.85 f o u n d in the neighbouring odd-mass nuclei. Clearly one m a y expect a cancellation of the coupling term in all states with odd spin, whereas the coupling between the K = 0 and K = 1 ? Since the beta transitions to the two states are respectively pure L = 0 and pure L = 1 because of the I selection rules, and since the intrinsic structure should be the same for both states, the experiment provides an indirect determination of the strengths of the L = 0 and L = 1 rnultipole components in the ½- [521] ~ ½+[411 ] transition.

494

P.G.

HANSEN e t

aL

bands should be appreciable in all even-spin states. The numbers of levels observed in the present investigation is too small to permit a complete analysis of the level spacings, and it is therefore fortunate that the data, combined with data for the neighbouring odd isttope 17°Tm, allow a check on these expectations. 5.3. THE NUCLEUS 17°Tm The beta decay of this isotope (1 - ) populates the ground state and the 84 keV 2 + state of the even isotope 17°Yb with l o g f t values of 9.0 and 9.3, respectively. The ratio of the reduced transition probabilities is 25) 0.53 +_0.05 in agreement with the theoretical value of 0.50 for K = 1 (K = 0 would correspond to a branching ratio of 2.0). The 17°Tm ground state almost certainly corresponds to the configuration ½+ [411]+½-[521] and thus to the 407 keY state in 172Tm. The beta transitions to the tT°Yb ground-state band are seen to be retarded by a factor of ~ 300 as compared with the non-A forbidden transitions to the K = 0 band in 172Tin. The excited states in 17°Tm have been studied through the 169Tm(d, p) reaction 26) and through the investigation of conversion electrons and gamma rays following neutron capture 27) in 169Tm.These experiments establish levels at 38.7•3 and 114.543 keV that can best be explained as the 2 - and 3 - members of a rotational band built on the 17°Tm ground state. It is interesting to note that the 1 - - 2 - spacing of 38.713 keV is very close to the corresponding level spacing in 172Tm (38.7 keV). A level at 149.721 keV has been classified as a 0 - state because it decays by a strong M1 transition to the ground state, but by a much weaker transition (multipole order unknown) to the 2 - state at 38.713 keV. 5.4. THE ROTATIONAL PERTURBATIONS As pointed out in subsect. 5.2, the Coriolis coupling term (l) should be expected to have little influence in the odd-spin states. From a consideration of the decay schemes for 172Er and 17°Tm one can now show with very good accuracy that this is true provided that one makes two assumptions: (a) that a 1- level with K = 0 (½+ [411]-½-[521]), exists in l~°Tm, and (b) that the intrinsic matrix element for a beta transition connecting this state to the ground state of 17°Yb is the same as that for the beta transition connecting the ground state of 172Erto the analogous 535 keV state in 172Tm. The term (l) now implies a mixing of the two 1- states that would, if the effect were appreciable, cause the decay of the 17°Tin ground state by fast transitions having a branching ratio corresponding to K = 0, which is in disagreement with the experimental finding that the transitions are retarded and show a branching ratio corresponding to K = 1. The analysis given in fig. 9 places an upper limit of 0.3 keV on the magnitude of the term (1) or, equivalently, a limit of 0.02 on lap+anl. This is in accord with the values ap = - 0 . 8 7 , an = 0.85 obtained from the neighbouring odd-mass nuclei, and confirms that a strong cancellation occurs in the coupling term for the odd-spin states.

495

Z72Trn NUCLEUS

I n the even-spin states the c o u p l i n g t e r m (1) s h o u l d be o f considerable i m p o r t a n c e . This is b o r n e o u t b y the a n o m a l o u s spacings in the ~7°Tm g r o u n d - s t a t e r o t a t i o n a l b a n d 26, 2v). A n estimate o f this effect can be o b t a i n e d in the following way. A s the 1 - a n d 3 - states in ~72Tm s h o u l d r e m a i n u n p e r t u r b e d , one finds f r o m the spacing o f 114.543 k e V the value t 11.5 k e V for the inertial p a r a m e t e r h2/2,.f. C o n s e q u e n t l y the u n p e r t u r b e d 1 - - 2 - spacing w o u l d be 46.0 k e V as c o m p a r e d with the e x p e r i m e n t a l

.12~..O....f.. jr;)= 1-~E'Jl-,¢=0>.-eN2K-I>. = 150 keY

B(Xq,~-O)

yb.o O* -~

-~

t K=O

o /~oo E

Fig. 9. Analysis of the beta decay of the 1- (K = I) ground state of iT°Tin to the 0 + and 2+ states in Yb a~° on the assumption of mixing of the initial state with a hypothetical 1- (K = 0) level at 150 keV, as indicated to the right in the figure. The theoretical ratio of the reduced beta transition probabilities is given as a function of the parameter x, which depends on the admixed amplitude e and on the intrinsic matrix elements. The experimental result for the branching ratio agrees well with a pure K = I assignment and provides an upper limit of 0.03 for the absolute value of x if one neglects the accidental solution x = --2.1. The limit on x gives lel ~ 2 x 10-8 and, from formula (1) and on the assumption of the 150 keV spacing shown here, an upper limit on lap+anl of 0.02.

value o f 38.7 k e V f o u n d in b o t h 17°Tm a n d 172Tm, so t h a t the depression o f the 2 state e m p i r i c a l l y a m o u n t s to 7.3 keV. U s i n g the values f o r ap, an a n d hZ/2,.f given a b o v e a n d the value 90.9 k e V for the u n p e r t u r b e d spacing between the 2 - states (this value is b a s e d on the 1 - - 0 - spacing o f 67.9 keV), one calculates a value o f 21.0 k e V f o r the energy depression, in disagreement with the empirical result. It w o u l d therefore seem t h a t the i n t e r p r e t a t i o n given here o f the a72Tm levels does n o t c o m p l e t e l y account for the e x p e r i m e n t a l findings, at least n o t if the d e c o u p l i n g p a r a m e t e r s observed in the n e i g h b o u r i n g o d d - m a s s nuclei are used. T h e a u t h o r s are i n d e b t e d to Mr. G. Sidenius for p e r f o r m i n g the e l e c t r o m a g n e t i c s e p a r a t i o n o f lV2Er a n d to Mr. J. L i p p e r t for m a k i n g the G e ( L i ) c o u n t e r used in this t This value agrees well with the value 11.1 keV obtained from the empirical rule ,foda

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r e s e a r c h . W e a r e g r a t e f u l t o D r s . O. W . B. S c h u l t a n d R . K . S h e l i n e f o r i n f o r m i n g us of their 17°Tm results prior to publication, and to Drs. H. Ryde and Z. Szymanski for pointing out a computational

error in the manuscript for this paper.

References 1) B. R. Mottelson and S. G. Nilsson, Mat. Fys. Skr. Dan. Vial. Selsk. 1, No. 8 (1959) 2) O. Nathan and S. G. Nilsson, in Alpha-, beta- and gamma-ray spectroscopy, ed. by K. Sieghahn (North-Holland Publ. Co., Amsterdam, 1965) p. 601 3) C.J. Gallagher, in Selected topics in nuclear spectroscopy, ed. by B. J. Verhaar (North-Holland Publ. Co., Amsterdam, 1964) p. 133 4) C. J. Gallagher and V. G. Soloviev, Mat. Fys. Skr. Dan. Vid. Selsk. 2, No. 2 (1962) 5) C. J. Gallagher and S. A. Moszkowski, Phys. Rev. U l (1958) 1282 6) N. I. Pyatov, Bull. Acad. Sci. USSR (phys. ser.) 27 (1963) 1409 7) N. D. Newby, Jr., Phys. Rev. 125 (1962) 2063 8) C. J. Orth and B. J. Dropesky, Phys. Rev. 122 (1961) 1295 9) R. G. Helmer and S. B. Burson, Phys. Rev. 123 (1961) 123 10) P. G. Hansen, O. J. Jensen and K. Wilsky, Nuclear Physics 27 (1961) 516 11) R. Gunnink and A. W. Stoner, Phys. Rev. 126 (1962) 642 12) P. G. Hansen et al., Compt. rend. congrrs international de physique nuclraire, Vol. II (Editions du Centre National de la Recherche Scientifique, Paris, 1964) p. 538 13) P. G. Hansen, H. L. Nielsen, E. T. Williams and K. Wilsky, Nucl. Instr. 32 (1965) 197 14) A. J. Tavendale and G. T. Ewan, Nucl. Instr. 25 (1963) 185 15) O. B. Nielsen and O. Kofoed-Hansen, Mat. Fys. Medd. Dan. Vid. Selsk. 29, No. 6 (1955); K. M. Bisg~trd, Nucl. Instr. 22 (1963) 221; P. G. Hansen, H. L. Nielsen and K. Wilsky, Ris6 Report No. 68 (1963) 16) P. G. Hansen, O. B. Nielsen and R. K. Sheline, Nuclear Physics 12 (1959) 389 17) NL E. Rose, Internal conversion coefficients (North-Holland Publ. Co., Amsterdam, 1958) 18) P. G. Hansen, Pals6 Report No. 92 (1964) 19) C. J. Orth, M. E. Bunker and J. W. Starner, Phys. Rev. 132 (1963) 355 20) M. E. Voikhanskii and L. K. Peker, Bull. Acad. Sci. USSR (phys. ser.) 25 (1961) 284 21) C. J. Gallagher, Nuclear Physics 16 (1960) 215 22) E. T. Williams et al., Phys. Lett. 15 (1965) 145; J. S. Geiger, R. L. Graham and G. T. Ewan, Proc. Int. Conf. on nuclear structure, Kingston, 1960, ed. by P. A. Bromley and E. W. Vogt (North-Holland Publ. Co., Amsterdam, 1960) p. 610; J. Trrherne, J. Valentin and J.-M. van Horenbeck, Compt. Rend. 258 (1964) 5203; J. Valentin, D. J. Horen and J. M. Hollander, Nuclear Physics 31 (1962) 373; I. Rezanka, J. Frana, J. Adam and L. K. Peker, Izv. Akad. Nauk SSSR (ser. fiz.) 26 (1962) 127; J. Valentin and A. Santoni, Nuclear Physics 47 (1963) 303; R. Foucher, J. Merinis, A. de Pinho and M. Valadarrs, J. Phys. 24 (1963) 203; F. Asaro, I. Perlman, J. O. Rasmussen and S. G. Thompson, Phys. Rev. 120 (1960) 934 23) S. M. Harris and C. J. Gallagher, Phys. Rev. 135 (1964) B875 24) D. A. Varshalovich and L. K. Peker, Bull. Acad. Sci. USSR 25 (1961) 274 25) R. L. Graham, J. L. Wolfson and R. E. Bell, Can. J. Phys. 30 (1952) 459 26) R. K. Sheline, personal communication (1964) 27) B. P. Maier et al., to be published