fulltext

Identical and shifted identical bands

(  ) R. S. DODDER( 1 ), E. F. JONES( 1 ), J. H. HAMILTON( 1 ), A. V. RAMAYYA( 1 ), P. GORE( 1 ), C. J. BEYER( 1 ), A. P.DELIMA( 1 )( 2 ), J.K. HWANG( 1 ), X. Q. ZHANG( 1 ), S. J. ZHU( 1 )( 3 ), Q. H. LU( 1 ), T. GINTER( 1 ), B. R. S. BABU( 1 ), M. G. WANG( 3 ), J. KORMICKI( 1 )(  ), J. K. DENG( 1 )( 3 ), D. SHI( 1 ), J. D. COLE( 4 ), R. ARYAEINEJAD( 4 ), K. BUTLER-MOORE( 4 ), M. W. DRIGERT( 4 ), W. C. MA( 5 ), G. M. TER-AKOPIAN( 6 ), YU. TS. OGANESSIAN( 6 ), A. V. DANIEL( 6 ), J. O. RASMUSSEN( 7 ), S.J. ASZTALOS( 7 ) I. Y. LEE( 7 ), A. O. MACHIAVELLI( 7 ), M. A. STOYER( 8 ), R. W. LOUGHEED( 8 ) Y. X. DARDENNE( 8 ), S. G. PRUSSIN( 9 ), R. DONANGELO( 10 ) ( 1

) Physics Department, Vanderbilt University - Nashville, TN 37235 (

2

) Physics Department, University of Coimbra - 3000 Coimbra, Portugal (

3

) Physics Department, Tsinghua University - Beijing, PR China (

4

) Idaho National Laboratory - Idaho Falls, ID 83415-2114 (

5

) Department of Physics, Mississippi State University - Mississippi State, MS 39762 (

6

) Joint Institute for Nuclear Research - Dubna 141980, Russia (

7

) Lawrence Berkeley National Laboratory - Berkeley, CA 94720 (

8

) Lawrence Livermore National Laboratory - Livermore, CA 94550 (

9

) Nuclear Engineering Department, University of California - Berkeley, CA 94720 (

10

) Physics Department, University of Rio de Janeiro - Rio de Janeiro, Brazil (ricevuto il 14 Agosto 1997; approvato il 15 Ottobre 1997)

Summary. — Spontaneous fission of252

Cm was studied with 72 large Compton sup-pressed Ge detectors in Gammasphere. New isotopes160

Sm and162

Gd were identified. Through X-ray- and - - coincidence measurements, level energies were established to spins14 + to20 + in152;154;156 60Nd 92;94;96, 156;158;160 62Sm 94;96;98, and 160;162 64Gd 96;98. These nuclei exhibit a remarkable variety of identical bands and bands where the en-ergies and moments of inertia are shifted by the same constant amounts for every spin state from 2+

to 12+

for various combinations of nuclei differing by 2n, 4n, 2p, 4p and. PACS 21.10 – Properties of nuclei; nuclear energy levels.

PACS 27.70 –150A189.

PACS 29.30.Kv – X- and -ray spectroscopy. PACS 27.90 –220A.

PACS 25.85.Ca – Spontaneous fission. PACS 01.30.Cc – Conference proceedings.

( 

)Paper presented at the 174. WE-Heraeus-Seminar “New Ideas on Clustering in Nuclear and Atomic Physics”, Rauischholzhausen (Germany), 9-13 June 1997.

(  

)Also at UNIRIB, ORISE, Oak Ridge, TN 37832, on leave from Inst. Nucl. Physics, Cracow, Poland

950 R. S. DODDER, E. F. JONES, J. H. HAMILTON, A. V. RAMAYYA, ETC.

1. – Introduction

Baktash, Hass, and Nazarewicz [1] have reviewed the totally unexpected discovery of identical bands (IB). Identical bands are two bands which have essentially identical tran-sition energies (differences in energies up to the order of 2-3 keV) and thus essentially identical kinematic (J

1) and dynamic ( J

2) moments of inertia. The initial discovery was

that a superdeformed ( 2

0:6) band in 151

Tb had a band of levels whose transition ener-gies were essentially equal to those of a superdeformed band in152

Dy [2]. The observed difference was much smaller than the approximate 1% variation one would expect in the limit of a rigid body moment of inertia (MOI) because of their mass difference. More dramatic was the difference compared to the 10-15% increase in MOI expected and previ-ously observed in neighboring odd-Anuclei compared to an even-even one because of the

reduction of the pairing correlations by the odd particle. Baktash et al. [1] have reviewed various different classes of IB in superdeformed and normal deformed (

2

0:25) nuclei

for various differences inZ and/or A. Essentially all observed IB are in neutron

defi-cient nuclei with a few discovered in neutron-rich98;100

Sr [3, 4] and108;110

Ru [4, 5] yrast cascades and in the octupole bands in144;146

Ba [4, 6, 7]. We have investigated the neutron-rich nuclei from 142

Ba to 162

Gd which span neu-tron numbers from 86 to 98. The sudden onset of deformation in152;154

64

Gd88;90between N =88and 90, related to the reinforcing of theZ = 64 spherical subshell gap and the N =82strong spherical shell gap [8]. We have identified the new isotopes

160

Sm [4, 7, 11] and162

Gd. The transition energies and MOI’s of the yrast cascades in142,148 56 Ba86,92, 144,152 58 Ce86,94, 150,156 60 Nd90,96, 154,160 62 Sm92,98, and 158,162 64

Gd94,98were compared for

nuclei separated by 2n, 2p,, and 2. A new type of identical band was discovered, one

where the energies and MOI are identical except for a constant shift from1-11%

inde-pendent of spin up to 14+

. We call this new phenomenon shifted identical bands (SIB). The data exhibit a remarkable clustering of similar energies and MOI unrelated to mass differences and present another new challenge for theory. Moreover, in these neutron-rich nuclei one sees for the first time the systematic influence of the spherical subshell gap at

Z= 64 leading to smaller moments of inertia and, presumably, deformations forZ= 64

compared to 62 andZ= 62 compared to 60 as far out asN = 92 to 98 for nuclei with the

sameN.

2. – Results

The spontaneous fission of252

Cf has been studied with 72 large volume Compton sup-pressed Ge detectors and two X-ray detectors in Gammasphere at Lawrence Berkeley National Laboratory. The data were stored in the triple coincidence mode X- - and - - . A - - cube was analyzed with the Radware program and - matrices were built by

gating on specific X-rays; namely, K 1

of Nd, Sm, Gd and a background region just above the Gd K

1

. At Idaho National Engineering Laboratory an X- 252

Cf SF experiment was run for three months with two high resolution X-ray and two large volume Compton sup-pressed gamma-ray detectors in a close geometry. From these data, X- , - , and X-X

matrices were built. Our earlier reported discovery of160

Sm [4, 7] from - - data was

confirmed in the new X- - data. The yrast levels of

156;158;160

Sm are shown in fig. 1. The total projection of the - matrix gated on the Gd X-ray was used to identify in

our work known transitions in160

Gd and new transitions associated with162

Gd. The yrast cascade was confirmed by the - - and X-X data. The relative intensities of the

160,162

Gd transitions are consistent with those expected on the basis of the SF yield data of Wahl [9].

Fig. 1. – Yrast levels in156,160

Sm and160;162 Gd

The160

Gd levels were known to 8+

from Coulomb excitation [10]. The levels of160;162

Gd also are shown in fig. 1.

The energies andJ 1and J 2 MOI of 150,156 Nd,154,160 Sm and 158,162 Gd were com-pared. The154 Sm and158

Gd levels were taken from the most recent Table of Isotopes [10]; the others from our data. The Nd energies were not averaged with other recent results, in order not to introduce any additional uncertainty in the energy differences when compar-ing Nd with Sm and Gd energies from any possible calibration differences in the different data sets.

For the142,148

Ba,144,152

Ce,152,156

Nd isotopes separated by 2n, the variations in

E =E ,
J 1 =J 1, and
J 2 =J

2 are smooth as a function of spin but not constant, e.g.
E=Efor

154

Nd-156

Nd goes from 5.5 to 1.5% for the 2-0 to 16-14 transition. A similar smooth trend is seen for154,156

Sm in
E =E of 7.6 to 5.9% for transitions 2-0 to 14-12. However, for156,158 Sm and158,160

Sm (fig. 2) from the 2-0 to 12-10 transitions
E=E,
J 1 =J 1 and
J 2 =J 2 are 3:4(+1:0;,0:8)%,,3:4(+1:0;,0:8)%,,2:1(+0:5;,1:5)%, and

3.250.25%,,3:15  0:25%, and,3:5  0:5%, respectively, where the0.25 for example is

not a statistical uncertaintly but the maximum upper and lower limits of the number, e.g., the spread in
E=Eis from 3.0% to 3.5%. Thus one can write, for example,E

(I+2! I) 158 = 1:0325E (I +2! I) 160for

I = 0 to 12 and similarly forJ 1 and

J

2. These we

call shifted identical bands. It is truly remarkable how constant is the shift for every spin state forE ;J 1, and J 2for 160 62 Sm98compared to 158 62 Sm96. For158 Gd-160

Gd,
E=E and
J=J show only a smooth variation from 5.6% to 1.9%

from 2-0 to 10-8 transitions. However, 160 64

Gd96 -162

64

Gd98 again have SIB with

E=E,
J 1 =J 1and
J 2 =J 2of 5:3(+1:0;,0:9)%,,5:0(+0:8;,0:9)%, and 6.31.4%, respectively.

As expected from the 2n data, 156

Sm-160

Sm separated by 4n likewise have SIB as a function of spin where the E ;J and J percentage differences are just the sums

952 R. S. DODDER, E. F. JONES, J. H. HAMILTON, A. V. RAMAYYA, ETC.

Fig. 2. – Percentage differences inE ;J1, andJ2for Sm isotopes separated by 2n.

6:6(+0:9;,0:5)%,,6:3(+0:5;,0:7)%, and,5:6(+1:2;,0:6)%, respectively. Similarly for 158,162

Gd, these percentage differences are9:31:0%,,8:60:7%, and7:51:5%.

Perhaps more surprising are the shifted identical bands from 2+

to 12+

separated by two protons as shown in fig. 3. Now the Nd nuclei which have no SIB for two neutrons are involved in shifted identical bands for 2p. For154

!60 Nd94 -156 !62 Sm94,
E=Eand
J 1 =J 1

are,7:4(+0:7;,1:5)%and8:1(+1:6;,0:9)%from 2 + to 12+ , but156 60 Nd96 -158 62 Sm96these and
J 2 =J 2 are ,7:70:3%, 8:4(+0:3;,0:4)% and 8:7(+1:4;,1:2)%, respectively to 14+ . For156 62 Sm94 -158 64 Gd94, 158 62 Sm96 -160 64 Gd96 and 160 62 Sm98 -162 64 Gd98,
E=E,
J 1 =J 1and
J 2 =J 2are ,3:4(+1:2;,0:8)%,3:5(+0:8;,1:2)%,1:7(+1:6;,2:7)%;,3:1(+0:2;,0:2)%, 3:2(+0:2;,0:1)%, 3.11.5%, and;1:2(+0:9;,0:5)%,1:2(+0:5;,0:9)%, 2 to,7, respec-tively. Since150,156

Nd separated by 2n have no shifted identical bands, it is likewise surprising for the 4p cases like154

Nd -158

Gd and156

Nd -160

Gd to have SIB from 2+

to 12+

.

These same nuclei, separated by anparticle likewise exhibit shifted identical bands

as well as one case of two identical bands,156

Sm -160

Gd. The SIB separated by an

par-ticle, fig. 4, with the most constant shift are156 60 Nd96 -160 62 Sm98where
E =E ,
J 1 =J 1, and
J 2 =J 2are ,4:7(+0:3;,0:5)%,4:9(+0:6;,0:3)%, and 4.801.0%. If the 2 + energies are excluded, these values are even more remarkably constant from 4+

to 14+

; namely,

,4:60:2%,4:850:15%, and 5.00.3%, respectively. Note the shifted identical bands

with the most constant shifts as a function of spin involve nuclei withN = 96and 98,

which are the largest neutron numbers for the identified Nd and Sm.

To understand these new phenomena, one needs to extend our knowledge beyond

N =98for these nuclei to see what happens. To extend our knowledge of the Nd, Sm and

Gd nuclei to their unknown isotopes withN>98will require new experimental facilities.

A next generation radioactive ion beam facility which can accelerate very neutron-rich nuclei would allow us to probe the more neutron-rich isotopes of these nuclei to develop

Fig. 3. – Percentage differences inE ;J1, andJ2for Nd-Sm and Sm-Gd isotopes separated by 2p.

an understanding of this phenomena. In conclusion, these152,156

Nd, 156,160

Sm, and

160;162

Gd nuclei exhibit a new phenomena which we have called shifted identical bands where two nuclei separated by 2n, 4n, 2p, 4p orhave identical transition energies,J

1and J

2moments of inertia when these parameters are shifted by the same constant amount

at every spin state from 2+

to 10+

or 14+

(depending on where backbending of the MOI occurs). These shifts are not related to differences in masses. These new phenomena

954 R. S. DODDER, E. F. JONES, J. H. HAMILTON, A. V. RAMAYYA, ETC.

Fig. 4. – Percentage differences inE

;J 1, and

J

2for Nd-Sm isotopes separated by an .

provide a new challenge for nuclear models.

  

Vanderbilt and INEL work was supported by U.S. DOE under DE-FG05-88ER40407 and DE-AC07-76ID01570, respectively, and at the Joint Institute for Nuclear Research by grant 94-02-05584-a of the Russian Federation Foundation of Basic Sciences. Work at Tsinghua U. supported by the National Natural Science Foundation of China. Work at LBNL and LLNL was supported by U.S. DOE grants DE-AC03-76SF00098 and W-7405-ENG48.

REFERENCES

[1] BACKTASHC., HAASB. and NAZAREWICZW., Annu. Rev. Nucl. Part. Sci., 45 (1995) 485. [2] BYRSKIT. et al., Phys. Rev. Lett., 64 (1990) 1650.

[3] LHERSONNEAU G., KRATZ K.-L., AYSTO J., GABELMANN H., KANTELE J. and PFEIFFERB., Inst. Phys. Conf. Ser., 132 (1993) 545.

[4] HAMILTONJ. H. et al., Prog. Part. Nucl. Phys., 35 (1995) 635. [5] LUQ. et al., Phys. Rev. C, 52 (1995) 1348.

[6] ZHUS. J. et al., Phys. Lett. B, 357 (1995) 273.

[7] HAMILTONJ. H. et al., Prog. Part. Nucl. Phys., 38 (1997) 263.

[8] HAMILTONJ. H., Structures of Nuclei Far From Stability, edited by A. BROMLEY(Plenum Press, New York) 1997, pp. 2-98.

[9] WAHLA.C., At. Data Nucl. Data Tables, 39 (1988) 1.

[10] Table of Isotopes, 8th edition, edited by R. B. FIRESTONEet al. (Wiley & Sons, N.Y.) 1996. [11] ZHUS.J. et al., J.Phys. G, 21 (1995) L57-L62.