A rotational band of 19 (possibly 20) transitions extending to spin ∼ 131 2 h {combining short stroke overlay} has been observed in 151Dy with an average dynamic moment of inertia I(2) = 79 h {combining short stroke overlay}2 MeV-1. This band is identified as a superdeformed band in 151Dy. The value of I(2) agrees with cranked Strutinsky calculations. Similarities as well as striking differences with the superdeformed bands of neighboring nuclei are observed

Ahmad, I.

Beard, K.

Chasman, R.R.

Drigert, M.W.

Garg, U.

Hass, M.

Janssens, R.V.F.

Khoo, T.L.

Körner, H.-J.

Ma, W.C.

Pilotte, S.

Rathke, G.-E.

Taras, P.

Wolfs, F.L.H.

Carolina Digital Repository

Volume 209, number 2,3 PHYSICS LETTERS B 4 August 1988 A SUPERDEFORMED BAND IN lSlDy'~ G.-E. R A T H K E  a, R.V.F. JANSSENS a, M.W. D R I G E R T  b, I. A H M A D  a, K. BEARD ¢, R.R. C H A S M A N  a, U. G A R G  c, M. HASS a,l, T.L. K H O O  a, H.-J. K O R N E R  a,2, W.C. MA a,3, S. P ILOTTE d, p. TARAS d and F.L.H. W O L F S  a a Argonne National Laboratory, Argonne, IL 60439, USA b Idaho National Engineering Laboratory, EG & G Idaho Inc., Idaho Falls, ID 83415, USA " University o f  Notre Dame, Notre Dame, IN  46556, USA d Universitb de MontrbaL Montreal Quebec, Canada H3C 3J7 Received 6 April 1988 A rotational band of 19 (possibly 20) transitions extending to spin ~ 131/2 h has been observed in ~StDy with an average dynamic moment of inertia j~2~= 79 h 2 MeV -~. This band is identified as a superdeformed band in ~5~Dy. The value of j~2~ agrees with cranked Strutinsky calculations. Similarities as well as striking differences with the superdeformed bands of neighbor- ing nuclei are observed. With  the discovery of  a band  of  19 discrete transi-  t ions in ~ 52Dy [ 1 ] corresponding to the rota t ion o f  a superdeformed nucleus ( f l~  0.6 ) it became clear that  detai led gamma-ray  spectroscopy can be per formed up to very high spin in weakly popula ted  potent ia l  energy min ima  of  very large deformat ions .  This fas- cinating result provides  incentive to map  regions of  the nuclear  chart  where superdeformat ion  occurs for an unders tanding of  the underlying microscopic  structure. While  rota t ional  bands  with f l~  0.45 have been found in several nuclei with mass around A = 130 [ 2,3 ], very few cases are known so far in the A = 150 region. In fact, discrete bands have been reported only in 152Dy, 149Gd [4] ,  and 148Gd [5] .  Addi t ional ,  but  weaker, evidence for superdeformat ion  has come from studies of  energy correlat ions in the quasicon- t inuum in light Dy, Er [6] and  G d  [7] nuclei. In Work supported by the US Department of Energy, Nuclear Physics Division, under Contract No. W-31-109-Eng-38, by NSF under Grant No. PHY 84-16025 and by the Natural Sci- ences and Engineering Research Council of Canada Permanent address: The Weizmann Institute, 76 100 Rehovot, Israel. 2 Permanent address: Technische Universit~it Miinchen, D-8046 Garching, Fed. Rep. Germany. 3 Present address: Tsinghua University, Beijing, P. R. China. contrast ,  theoret ical  studies [8 -10]  predict  many  nuclei  in the A = 150 region to be superdeformed at high spin and these calculations require further ex- per imenta l  verif ication.  In this letter we present  evi- dence for superdeformat ion  in ~51Dy based on a rota t ional  band  extending over  19 (possibly 20) t ransi t ions with an essentially constant  energy differ- ence o f  51 keV and an average dynamic  moment  of  inert ia  of  79 h 2 MeV-~.  The exper iment  was carried out  at the ATLAS ac- celerator  with the Argonne-Not re  Dame  gamma-ray  facility which consists of  an inner  array of  50 hexag- onal BGO elements  surrounded by 12 Compton  sup- pressed germanium spectrometers  ( C S G )  arranged in two rings. The array covers ~ 80% of  4g a round  the target. It is used as a gamma-ray  ca lor imeter  and pro- vides a measure  of  the gamma-ray  multiplici ty.  The sensi t ivi ty of  the CSGs was necessary for detect ion of  very weak gamma-rays.  The states in ~ 5 ~Dy were pop- ulated with the 122Sn(345, 5n) reaction at 174.5 MeV. Wi th  this choice of  beam energy and projec t i le - tar -  get combinat ion ,  the ~5~Dy final nucleus is popula ted  with a m a x i m u m  angular m o m e n t u m  in excess of  65 h and an exci tat ion energy of  33 MeV, assuming a kinetic  energy of  2 MeV per  neutron.  These condi-  t ions are s imilar  to those used in refs. [ 1,4,5 ] where 0370-2693 /88 /$  03.50 © Elsevier Science Publishers  B.V. ( Nor th -Hol land  Physics Publishing Divis ion  ) 177 Volume 209, number 2,3 PHYSICS LETTERS B 4 August 1988 discrete superdeformed bands have been observed. The target consisted of four stacked ~2Sn self-sup- porting foils (three 200 gg/cm 2 and one 300 gg/cm ~ thick). With a threshold of 5 on the number of array elements firing in coincidence with 2 CSGs or more, a total of 3.2 × 10 s events were recorded. In addition to the energy and time information measured in the CSGs, the gamma-ray sum-energy, the prompt and delayed multiplicities and the hit pattern of the array were stored on magnetic tape. In the analysis, at least 18 detectors of the BGO array were required to fire in coincidence with the CSGs. This procedure enhances the relative yield of the high spin states in 15tDy by selecting events with high gamma-ray multiplicity and also reduces the contribution of some of the other evaporation chan- nels. (The coincidence matrix still contains contri- butions from the 4n ( t£Dy) and 6n (~S°Dy) channels with 14 and 28% intensities, respectively. ) The num- ber of events in the final gamma-gamma-coinci- dence matrix was 1.5× 10 ~. A new band of 19 transitions extending from 577 to 1490 keV was observed in spectra generated from the matrix. The band was seen in individual spectra gated on each transition. The spectrum shown in fig. 1 was obtained by summing the spectra in coinci- dence with the cleanest coincidence gates (577, 682, 734, 940 and 1194 keV). All the transitions belong- ing to the band are visible with, perhaps, the excep- tion of the two highest transitions for which firm assignments were made on the basis of the inspection of the individual coincidence spectra. All other tran- sitions appearing in fig. 1 and in the individual coin- cidence spectra could be assigned to known transitions in tSIDy [11] or to contaminants in tS2"lS°Dy. The coincidence data also revealed the presence of a weak line at 522 keV which may be the lowest transition in the band. However, strong con- taminant peaks in tSZDy and in ~ D y  at the same en- ergy preclude a definitive assignment. With the exception of the weakest lines, the stretched-E2 char- acter of the transitions was established from the an- gular distribution measured at 34.5 °, 90 ° and 145.5 ° with respect to the beam. The average moment of inertia of the new band is consistent with a superdeformed shape. In addition, 0 5OO- 2~ 4 0 0 -  ~ ~ ~ ~ ~ co ~ co 300 - ~ r - .  200 I00 0 09 eJ 0,.! + I 600 tO0 CO _ _  CO d ~- o ~I- 0 - -  I000 ENERGY (keV) r Q  - -  ,/ v 1200 t f )  ~ 4  A o,1 Od ,~-  Od ( M  i ~- r6 _ ro if) 03 ~,r - -  - -  to)  o J  v - -  ,q,- t¢~ i 14;0 Fig. 1. Gamma-ray spectrum in ~ D y  obtained by summing coincidence gates on the selected transitions (577, 682, 734, 940, and 1194 keV ) in the superdeformed band. Note that the higher part of the spectrum was compressed by a factor of 2. The Doppler correction is different for the upper part of the spectrum because of the shorter emission times of the high energy transitions (see text for details). The transition energies and the proposed spin assignments are included. The placement of the lowest transition is tentative. All the transitions belonging to the band are visible with, perhaps, the exception of the two highest transitions for which firm assignments were made on the basis of the inspection of the individual coincidence spectra. 178 Volume 209, number 2,3 PHYSICS LETTERS B 4 August 1988 it has many properties similar to those observed in the superdeformed bands in the neighboring ~52Dy and ~49Gd [1,4] nuclei. Therefore, this band is henceforth referred to as the superdeformed (SD) band and it is assumed to correspond to the rotation of the ~5~Dy nucleus with a very large prolate defor- mation (axis ratio of 2:1 ). From several coincidence spectra gated on gamma- rays in the SD band and in the yrast band it was pos- sible to derive an intensity of 1.8% for the total flow through the SD band under the multiplicity condi- tion mentioned above. This number corresponds to an absolute intensity of 1.3% of all ~5~Dy decays (i.e. when the multiplicity condition is removed), and to about 0.6% of the estimated total evaporation resi- due yield. The intensity distribution along the SD band, de- rived from the coincidence spectra, is shown in fig. 2. The decreasing intensity seen at the highest spins pre- sumably reflects the initial feeding population. At lower spin, the intensity remains essentially constant over a total of 8 transitions. Decay out of the SD band towards the yrast line occurs rather abruptly over a range of 2 or 3 transitions. Transitions which link the SD band to the known yrast states could not be iden- tified and it is likely that many different decay paths share the intensity. This is corroborated by the feed- ing pattern into the yrast line which was found to be spread over 4 states (the relevant yrast level struc- ture is given as an insert in fig. 2) in the following 1.5 •z LO uJ I -  z '~' 0 . 5  t ) I 5 5 / 2  t+} + t titt I I I 75 /2  95/2 II 5 /2  SPIN (f i )  57/2_ . -/~6% H083.2 16% 5 3 / ~ - / 2 o o / ,  I 5 , / 2 ~ J  °I I oo5.3 j2a°/o I 49/2-  * ~13nS l + I 135 /2  Fig. 2. Relative intensity of the gamma-rays in the superde- formed band of ~5~Dy as deduced from the coincidence spectra. The inset presents the feeding from the superdeformed band into the yrast levels. way: (36+8)% to the 57/2 level, (16+9)% to the 53/2 level, (20+12)% to the 51/2 level and (28+ 11 )% to the 49/2 isomer. Therefore, the aver- age spin on entry into the yrast states is 53/2 h. The spin of the lowest level in the SD band is esti- mated to be 51/2 h. This value follows from the deexcitation pattern out of the SD band (fig. 2), the average spin of entry into the yrast line (53/2 h) and the assumption ofa  AI= 1.5 h angular momentum re- moval by the transitions linking the SD states and the yrast line. This value of Al is plausible since the deex- citing transitions are most likely statistical [ 1,4 ] and the SD band will be about 3 MeV above the yrast line at the point of deexcitation, if one assumes that it be- comes yrast at I =  115/2 h as predicted [8,9]. The highest spin reported here is 131/2 h. The data also contain information on the lifetimes in the SD band. Under the experimental conditions, the average time the 151Dy recoils take to escape the target is 43 fs. Gamma-rays from the highest spin states can be emitted before the nuclei leave the tar- get. By comparing the gamma-ray energies in the for- ward and backward CSGs it was found that the Doppler shifts for the 9 highest transitions decrease with spin and are different from the average shift for the strongest yrast transitions (which are emitted outside the target because of their ps lifetimes). Thus, deexcitation between the 131/2 and 99/2 levels pro- ceeds in less than 43 fs, a time scale comparable to the one reported by Bentley et al. [ 1 ] for 152Dy. This indicates that the transitions reported here are highly collective as expected for a SD band. A preliminary analysis of the Ev-E v correlation matrix indicates that the discrete band accounts for at least 75% of the in- tensity in the superdeformed ridge. Any underlying correlated continuum radiation is very weak. It is interesting to compare the data for ~5~Dy with the results reported for the SD bands observed in 152Dy [1] and ~49Gd [4]. (Equivalent information on 148Gd is not available.) The gamma-ray intensity flowing through the SD band is comparable in J52.tS~Dy and 149Gd. The three experiments report numbers of the order of 1% of the ground state pop- ulation and the number of transitions reported is the same as well. The intensity pattern as a function of spin is remarkably similar: in the two Dy nuclei 80% of the feeding has occurred at spin 50 (99/2) h and 50% population is achieved at spin 56 (115/2) h. The 179 Volume 209, number 2,3 PHYSICS LETTERS B 4 August 1988 corresponding numbers are not that different for t49Gd where 80 (50)% population is in the SD band at spin 103/2 (115 /2)  h. This pattern is in contrast with the one observed in rotational bands with smaller deformations in the rare earth nuclei: the side feed- ing into discrete states extends to very low spin, even when states with I ~  50 h are seen. In the three cases the decay out o f  the band is presumed to occur via statistical transitions and, again, occurs within the same spin range: the average deexcitation spin is 27 h in 152Dy and 28 h in J~ Dy and 149Gd. Finally, the mean entry spin into the yrast line is identical in the two odd-even nuclei (26.5 h) and smaller in J52Dy (21.5 h). Since these three experiments have been per- formed at similar excitation energies and angular momenta,  these comparisons suggest that the feeding mechanisms in and out of  the SD bands are similar in the three nuclei. Even at the highest spins, a single band carries all the intensity. For J52Dy it has been suggested [ 8 ] and calculated [ 9 ] that this is due to a large gap in the single-particle spectrum at Z =  66 and N =  86. A similar gap would have to be present for Z = 6 4  and N = 8 5  and could become smaller for Z = 6 4 ,  N = 8 4  (in order to account for the weaker population in 148Gd [ 5 ] ). Assuming that the deex- citation towards the yrast line occurs when the poten- tial energy barrier between the SD states and yrast states can be penetrated effectively so that statistical decay out of  the band competes with collective in- band transitions [ 8 ], the comparison suggests that the SD minima have similar properties in the three nuclei. The static and dynamic moments  of  inertia .,¢(~) and j (2 )  for all the SD bands under discussion are presented in fig. 3. Similarities as well as striking dif- ferences can be seen. In the Dy isotopes the values of  ,4 (~) and j ( 2 )  become essentially constant at the highest spins ( I >  44 h) and have values very close to each other, the difference being somewhat larger in ~ ~ Dy. This indicates that both nuclei rotate like rigid bodies. The value measured for ~(2) is somewhat smaller in 15 ~Dy (81 h 2 M e V -  1 versus 83 h 2 M e V -  ~ ) and is in good agreement with calculations by Chas- man (ref. [9] and table 1 in ref. [ 7 ] ) w h e r e  the drop in the value of  j (2 )  is due to a smaller deformation. The striking difference in the general behavior of  ~¢(~) and 0¢(2) should, however, also be pointed out. We note that for ~51Dy the value of  ~(])  exceeds that o f  105 I 0 0  9 5  9o] 85  8O 75, 8.' 9C 8~ 7C 6~ 2O %: f. o x × x × x  × ~ . × × y ( l l  x * × x x  { + ~ l z )  151Dy * ÷ *  + +  , * * y ( 2 )  • * * + ~ i ,I. ~ { % I 0  D y  × × x × x x x × x × × x × x x × ~  x x × x x * ,  x x ~ ~ x  x x * , * x x x x x q "( l l  • " * ~, 149 * Gd y(z) 148Gd • • • • * * ,~ { ,~y(2I  (* S P I N  { '~ )  Fig. 3. Static ( J ~ =  (2~-1)h2/ET) and dynamic (,ff(2)=4h2/ AE~) moments of inertia for the nuclei ~5~Dy (top), 152Dy (mid- dle) and 149Gd (bottom) asa function of spin. The j(z) moment of inertia for ~48Gd has been added for comparison, assuming that the spin of the lowest member of the band is •=24 h. , i f ( 2 ) .  In contrast, , i f ( 2 )  > ~ ( 1 )  in 152Dy, a fact for which there is, to our knowledge, no explanation. Further- more, while J(~) is seen to decrease and j (2 )  to in- crease with spin in ~5~Dy, the opposite happens in 152Dy. While the changes in the value of  j (2 )  are only of  the order of  4% in the two Dy nuclei, much larger variations are seen in the Gd isotopes: the decrease of  j (2 )  persists over the entire spin range and the ab- solute value is smaller as well. These results can again be accounted for in the calculations by Chasman [ 9 ]. The Gd isotopes are calculated to be less deformed and the changes in ~(2) are attributed to the spin de- pendence of  the shell corrections. In the case of  the Dy isotopes, the shell corrections as a function of  spin remain essentially unchanged. An alternative expla- nation for the decrease invokes residual pairing [ 4,8 ]. In conclusion, a band of  19 (possibly 20) transi- tions corresponding to rotation of  a superdeformed ~5~Dy nucleus has been observed. The properties o f  the band resemble closely those reported for the su- perdeformed band in 152Dy. This indicates that the mean field properties are not modified greatly by the removal of  a single neutron. 180 Volume 209, number 2,3 PHYSICS LETTERS B 4 August 1988 Th i s  expe r imen t  is the first one  pe r fo rmed  wi th  the  full A r g o n n e - N o t r e  D a m e  g a m m a - r a y  facility. The  au thors  express their  gra t i tude  to V. K u b i l i u s  for his des ign work, to J. Ray,  J. T i m m ,  J. Joswick, a n d  A. H o r v a t h  for the i r  technical  assistance,  to P. Wi l t  for help wi th  the electronics,  an d  to T. Moog for the da ta  acqu i s i t ion  software. O n e  of  the au thors  (G . -E .R . )  would  like to t hank  the  A l e x a n d e r - v o n - H u m b o l d t -  St i f tung for g ran t ing  a F e o d o r - L y n e n - S t i p e n d i u m .  Note added. After  this  let ter  was s u b m i t t e d  for pub-  l icat ion,  we lea rned  abou t  the results  o f  recent  work by  Bengtsson,  Ragna r s son  a n d  Aberg [ 12 ] where  the inf luence of  particles excited in to  high N-shells on  the d y n a m i c  m o m e n t  of  iner t ia  j r 2 )  is calculated.  The  difference in  the va lues  o f  j r 2 )  for ~52Dy a n d  ~5~Dy can  be expla ined,  at least qual i ta t ively ,  by the differ- ence in the respect ive con t r i bu t ions  of  i~3/2 p ro tons  and  J15/2 n e u t r o n s  for the two nuclei .  In  par t icular ,  the rise seen in  ~ 5 ~Dy is ca lcula ted  to or ig inate  m a i n l y  f rom the c o n t r i b u t i o n  o f  the four  i~3/2 pro tons .  References [ 1 ] P.J. Twin et al., Phys. Rev. Lett. 57 (1986) 811; M.A. Bentley et al., Phys. Rev. Lett. 59 (1987) 2141. [2] E.M. Beck et al., Phys. Lett. B 195 (1987) 531, and refer- ences therein. [3] R. Wadsworth et al., J. Phys. G 13 (1987) L207, and ref- erences therein. [4] B. Haas et al., Phys. Rev. Len. 60 (1988) 503. [ 5 ] M.A. Deleplanque et al., preprint; P. Taras et al., private communication. [ 6 ] M.J.A. de Voigt et al., Phys. Rev. Lett. 59 ( 1987 ) 270. [ 7 ] M.W. Drigert et al., Phys. Lett. B 201 (1988) 223; G. Hebbinghaus et al., Phys. Rev. Lett. 59 (1987) 2024. [8] I. Ragnarsson and S. Aberg, Phys. Lett. B 180 (1986) 191. [9] R.R. Chasman, Phys. Lett. B 187 (1987) 219. [ 10] J. Dudek et al., Phys. Rev. Lett. 59 (1987) 1405. [ 11 ] B. Haas et al., Nucl. Phys. A 362 ( 1981 ) 254. [ 12 ] R. Bengtsson, I. Ragnarsson and S. ~.berg, Lund preprint MPh-88/01. 181 

A superdeformed band in 151Dy

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A superdeformed band in 151Dy

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