The second and third backbendings in 194Hg

Volume 145B, number 1,2

PHYSICS LETTERS

13 September 1984

THE SECOND AND THIRD BACKBENDINGS IN 194Hg H. HOBEL 1, A.P. BYRNE, S. OGAZA 2, A.E. STUCHBERY 3 Department of Nuclear Physics, R.S.P.S., The Australian National University, CanberraACT 2601, Australia and

M. GUTTORMSEN Institute of Physics, University of Oslo, Oslo, Norway ReceNed 19 June 1984

High-spin states in 194Hg ' populated via the reaction 186 w (1 aC, 5n), were investigated by in-beam v-ray spectroscopy using two anti-Compton spectrometers. The level scheme was extended to considerably higher spins. A third backbend in an yrast sequence has been identified for the first time. The level structure is interpreted within the framework of the cranked shell model.

The ground-state bands of the Hg isotopes with A = 188-198 show a strong irregularity around the I ~ = 10+ and 29/2 + states in the even- and odd-mass isotopes, respectively [1,2]. It has been shown that a decoupling of a pair of i 13/2 neutrons is responsible for this effect [3]. Several models have been used recently to describe the level structure theoretically. Kuyucak et al. [4] have extended the interacting boson-fermion approximation to include two- and three-quasiparticle states and can describe the evenand odd-mass Hg isotopes quite well up to ! ~ 20. Using a particle-core coupling model Trefz et al. [5] have reproduced the energy levels of 1 95 - 1 9 BUg u p to 1 ~ 18. Guttormsen et al. [6-8] have used the cranked shell model (CSM) to calculate band crossing frequencies, aligned angular momenta and interaction energies in good agreement with the experimental values. The success of the latter approach can be understood since the Hg isotopes have small moments of inertia (they are weakly oblate deformed [6]) and 1 Permanent address: Institut ftir Strahlen- und Kernphysik, University of Bonn, D-5300, West Germany. 2 Permanent address: Institute of Nuclear Physics, ul. Radzikowskiego 152, P1-31-342 Cracow, Poland. 3 Joint appointment with School of Physics, University of Melbourne, P~kville, 3052, Australia.

low-g2 i 13/2 neutron orbitals lie close to the Fermi surface for oblate deformation. Thus, the Coriolis interaction becomes large even at moderate rotational frequencies. It was the aim of the present work to check the CSM predictions at higher spins where no experimental data existed previously. In particular, the model predictions for the critical frequencies and alignments suggested that the second and third backbendings might be experimentally accessible and these were indeed observed in the present work. Excited states in 194Hg were populated in the reaction 186W(13C, 5n) with 13C beams of 85 MeV from the Canberra 14 lAD Pelletron. At this energy, the 5n and 6n reaction channels are approximately equal in strength. Targets of metallic tungsten (0.5 mg/cm 2) enriched in 186 w to 97% were produced by sputtering onto thin carbon foils or by affLxing fine W-powder to thin mylar foils with a dilute cement solution (~-~-4mg/cm2). Standard in-beam 7-ray spectroscopic techniques were used. In the 77-coincidence experiments 2 × 107 events were collected with two anti-Compton spectrometers consisting of NaI(T1) shields [9] and n-type Ge-detectors (e = 25%, AE = 1.9 keV). Thus even weak transitions could be identified with cer29

Volume 145B, number 1,2

PHYSICS LETTERS

Table 1 Energies, relative "r-ray intensities, angular distribution coefficients and assignments of transitions in 194Hg ' E (keV) a) 97.0 111.0 130.8 c) 208.0 227.6 232.9 235.5 d) 236.3 d) 280.2 305.9 314.7 353.6 383.2 412.9 418.5 423.8 427.9 480.3 485.0 485.2

13, A2 (rel) b) 11.0 8.6 0.6 2.5 12.1 40.3

0.20(4) -0.17(10) 0.08(9) -0.75(3) 0.26(3)"

21.4

22.0 10.7 d) 1.8 0.6 c) 10.0 41.0 4.8 17.0 100 c),d) 1.5 d) d) 10.0

544.6 565.0 574.7 578.4 583.1d) 592.8 606.8 c) 611.2 636.6 643.0 665.8 706.2 710.4 743.6 748.8 803.6 832.6 885.8 c) 891.7 945.2 990.7

A4

0.03(3) -0.09(4)

0.39(4)

-0.11(6)

-0.14(2) 0.41(3) -0.12(12) 0.36(2) 0.37(5) 0.42(7) 0.30(2) -

-0.07(3) -0.18(4) -0.13(3) -0.15(10) -0.09(3) -

0.44(3)

18.2 30.6 23.1 1.7 2.0 7.8 5.8 32.7 97.0 27.5 7.0 10.4 16.1 20.9 57.6 3.1 3.6 4.0 1.9 0.9 2.4

-0.07(4)

0.39(2) 0.30(2) 0.33(2) 0.18(10) -0.05(15) 0.43(5) 0.37(3) 0.29(2) 0.39(4) 0.41(4) 0.39(4) 0.43(4) 0.41(5) -0.19(2) 0.33(9) 0.12(15) 0.40(9) 0.69(26) 0.18(10)

-0.13(3) -0.10(3) -0.13(3) -0.18(7) -0.13(3) -0.10(27) -0.17(6) -0.18(7) -0.16(6) -0.19(6) -0.14(5) -0.04(3) -0.02(13) -0.09(11) -

Assignment

7---* 7-~ 17-~ 19-~ 8-4 9--+ 17-4 16---*

56+ 1618771514-

10 + ~ 9 1 8 - ~ 16(28+) -+ 26 + 1 4 - 4 1319--~ 1714+--+12 ÷ 1 0 - ~ 91 0 - ~ 82+ ~ 0 ÷ (30+)~(28 ÷) 1 2 - ~ 111 5 - ~ 1311---* 98+~ 6÷ 1 4 - ~ 1226 + ~ 24 ÷ 17-~16 ÷ 22 + ~ 20 ÷ 20- --' 181 2 - ~ 104 + ~ 2+ 16 + ~ 14 ÷ 21- ~ 191 3 - ~ 1120 ÷ ~ 18 ÷ 18 + ~ 16 ÷ 5-~ 4+ 2 2 - ~ 2024 + ~ 22 ÷ 23- ~ 21 25 - ~ 23 24- ~ 2220 + ~ 18 ÷

a) Accuracy 0.2-0.4 keV depending on intensity. b) Accuracy 10-40% depending on intensity. ) Transition of similar energy m 1 9 3 Hg; energy and intensity determined from .,t3,-coincidence spectra. d) Doublet; energy and/or intensity determined from "r'rcoincidence spectra. c

30

.

•

13 September 1984

tainty. Energies, intensities and angular distribution coefficients for the transitions in the yrast sequence and in the negative-parity sidebands are summarized in table 1. Details o f the e x p e r i m e n t s and i n f o r m a t i o n on further transitions assigned to 194Hg will be given in a f o r t h c o m i n g publication. The level scheme o f 194Hg is shown in fig. 1. The yrast sequence, previously d e t e r m i n e d up to the 18 + state [10], is n o w e x t e n d e d t o 26 + and possibly up to 30 + . The spin assignments o f 28 and 30 to the 7.30 MeV and 7.78 MeV levels, respectively, are uncertain because the 315 k e V and 4 8 0 k e V transitions are doublets and their multipolarities could not be d e t e r m i n e d f r o m the angular distributions. The two negative-parity side bands, k n o w n h i t h e r t o up to the 1 8 - and 1 7 - states [10], are n o w e x t e n d e d to 2 4 and 2 5 - , respectively. The angular m o m e n t u m p r o j e c t i o n I x on the axis o f r o t a t i o n is p l o t t e d as f u n c t i o n o f rotational freq u e n c y hco in fig. 2. As can be seen, the yrast sequence (upper part of the figure) shows a very sharp first b a c k b e n d i n g w i t h a gain in alignment o f 12 h. This has b e e n interpreted previously as due to the intersection o f the ground-state band with the vi 13/2 band [6]. At/~co = 0.35 MeV a second b a c k b e n d occurs w i t h a gain in alignment o f 6.4 ~ and at the highest observed spins a third - again very sharp - backb e n d can be seen. This is the first time that a third b a c k b e n d has b e e n observed e x p e r i m e n t a l l y . Both negative-parity bands exhibit strong b a c k b e n d s at rico ~ 0.23 MeV w i t h an alignment gain o f about 8.8 h. In addition, the 5 - b a n d shows an u p b e n d i n g at ha) ~< 0.44 MeV. The version o f the CSM used here to interpret the data has b e e n described in detail by Bengtsson and F r a u e n d o r f [11]. In this m o d e l a Nilsson p o t e n t i a l is used to calculate the single particle levels. H o w e v e r , for the very weakly oblate d e f o r m e d Hg isotopes the Nilsson m o d e l parameters have to be adjusted in order to reproduce the e x p e r i m e n t a l energy levels in this mass region [7]. The quasiparticle energies in the rotating frame (routhians) for 194Hg o b t a i n e d in our CSM calculation are shown as f u n c t i o n o f r o t a t i o n a l f r e q u e n c y in fig. 3. F r o m this figure it is apparent that the slopes, ae/3co, o f the n e u t r o n s t a t e s A , B, C and D which result f r o m the i 13/2 levels 3/2 [651] and 5/2 [642] (at/~co = 0) are very steep. H e n c e large alignments are e x p e c t e d for the decoupling o f these particles. The same is true for the p r o t o n states A p

(30*) 7785 (

7305

26"~ ~9

25

6941 24"

th

~24 ÷

23- ~ 6050

o~

22-

QO

22*

2o.~

6645

6411

5578 20* 4986,~

5266

21- .5164 ~I

{..J

l~ =1

20- , /,897

~9- ~4~
~18 ÷ ~ 4275

~J

|

17-~

~1

~I

-'~-~18- ~ 4290 4115 13n~ ~[

15" -~43879 ~

~1

~

13-

I

~1

. ~1 2476

339/~

~ ~+2687/

cO

4+

~ 398/,

~/'-'- ~

~1

c--, 1

0

2*

428

0"

0

5700

~2-

1 4 - ~ 3748

~/

3172,/

~0-~1 z562

e4

6

~

194Hg Fig. 1. Level scheme of 194Hg.

30 i

'ABCDApBEI__~

i

i

I

I

I

I

I

20

10 Ix[~]

~

A

0

S

T

I

BAND

20

10 •

_A F E ~ I

r

L

0.1

~

• 5--BAND o8-- BAND

0.2

0.3

l~t0 [MeV]

I

0.4

0.5

Fig. 2. Angular momentum projection along the axis of rotation as function of rotational frequency; (a) for the yrast sequence, (b)' for the negative-parity side bands.

Volume 145B, n u m b e r 1,2

PHYSICS LETTERS

13 September 1984

x

1.0

1.0

~

~

\\

"" .../19/.H ~'~ E~P ~ Bp

\

\\

~

0.5

A p\

C).5

0 ),ns tU Z "'-0.5

\

\

0

\\ //I

/ / ...." A.....~.x~....-" "',~..-'-';

/ / J NN

0.5

//// _ 5<-":

-1.0

-

-

,¢/

1.0 I

0

03

0.2 0.3 'h ~ [McV]

0.~

0.5

0

0.1

0.2 03 'h w [McVI

O.Z,

0.5

Fig. 3. Calculated routhians for neutrons (left) and p r o t o n s (right) in 194Hg" The parameters used in the CSM calculation are e2 = - 0 . 1 3 , e4 = 0, An = 0.148 7ico0, h n = 6.83 ?/tOO, Ap = 0.158fico0, hp = 6.15 /ito o. The neutron Nilsson model parameters are

(K, t~)n=(0.042, 0.33), (0.036, 0.38) and (0.040, 0~56) for l = 1, 3 and 5, respectively, forNn = 5 and (~,/~)n = (0.0637, 0.42) for the N n = 6 shell. The N n = 5 shell was lifted 0.83 MeV relative to the N n = 6 shell. The Nilsson model parameters for protons are (K, #)p = (0.037, 0.72) and (0.040, 0.86) for l = 2 and 4, respectively, in theNp = 4 shell and (K, ,)p =(0.637, 0.60) for the Np = 5 shell. The Np = 4 shell was lifted to 0.80 MeV. and Bp which result from the h 11/2 levels 1/2 [550] (at ~co = 0). The critical frequencies for the vi23/2_ and vi43/22crossings are clearly lower than the frequency for the 7rh 11/2 alignment. For all band crossings the interaction energies are very small (<10 keV) and the resulting backbending effects can be expected to be strong. All these features of the theoretical routhians are borne out by the experimental data (see fig. 2): the backbendings are very sharp, the aligned angular momenta are close to the maximum possible by the Pauli principle and the crossing frequencies agree roughly with the predicted values. A more quantitative comparison between experimental and calculated results is made in table 2. For the first and second band crossings in the yrast sequence and for the first baekbending in the side bands the agreement is quite good with the set of fixed parameters used in the calculations. Perfect agreement for the first crossing frequency can be obtained with a slightly higher neutron pairing than the one deduced from the odd-even mass differences (which are not very accurately determined). For the second crossing in the yrast sequence and for the crossing in 32

the side bands the pairing has then to be reduced in the calculations in order to achieve agreement with the experiment. This is expected due to the blocking of orbitals by the decoupled particles. There are several possible explanations for the origin of the third backbending in the yrast sequence. It might be caused by an alignment of a pair of h 11/2 protons. The calculated frequency for this effect, however, is appreciably higher (/iw c = 0.46 MeV, see table 2 and fig. 3) than the experimental limit of 0.36 MeV. A variation of the deformation parameters (both e i and 7) and of the pairing A in the CSM calculations of the proton routhians shows that the critical frequency does not depend very much on the deformation as long as the nucleus remains oblate but is strongly dependent on the pairing. If A is decreased by 50% the frequency is reduced to 0.36 MeV which would be compatible with the experimental value. An alternative explanation of the third backbend could be an i 13/2 proton alignment for prolate deformation. The routhian which originates from the proton 1/2 [660] Nilsson orbital (at/76o = 0) decreases very steeply in energy with increasing frequency.

Volume 145B, number 1,2

PHYSICS LETTERS

13 September 1984

Table 2 Crossing frequencies and gains in alignment in 194Hg" (a, n)

(0, +) (0, +) (0, +) (0, -) (1,-) (1, -)

Configurations of crossing bands

10) × A._.BB AB × ABC__D_D ABCD × ABCDApBp AE X ABCE AF X AB___C_CF ABCF X ABCF_ApBp

Frequency hw c (MeV)

Alignment

Alignment

exp.

calc. b)

exp. a)

calc. b)

0.206 0.348 <0.36 0.221 0.236 ~<0.44

0.188 0.355 0.461 0.249 0.249 0.461

11.8 6.4 >9 8.4 8.8 >2

11.6 6.9 9.4 9.2 9.2 9.4

Ai(h)

a) Deduced from the data shown in fig. 2 using the ground-state band as core of reference 1g = g0t~ + 91 to3 with Do = 8.0 h2/ MeV and 91 = 30 h4/MeV3. b) From the CSM calculation presented in fig. 3. This orbital has a rather strong driving force toward prolate deformation. The CSM calculation for e 2 = 0.2 gives a critical frequency of 0.28 MeV and an alignment of i = 10.8 h in agreement with the experimental limits. A third possibility to explain the third backbending might be by a structure of non-collective particle-hole excitations. Certainly states with spins around 30~ can be constructed out o f six quasiparticles involving four neutrons (e.g. vi 13/2) and two protons (e.g. 7rh 11/2)" The negative-parity side bands have been interpreted as semi-decoupled bands with one fully decoupled i 13/2 neutron and one low-/neutron with small alignment [12,13]. Both of these bands show an alignment of ~ 8 h before the backbend (lower part of fig. 2), of which ~6.5 h should be carried by the i l 3/2 neutron and ~ 1 . 5 / i by the accompanying low-/' neutron. The backbending frequency of ~0.23 MeV in these bands is higher than that of the first backbend in the yrast sequence because of the blocking of one i 13/2 neutron orbital. For the same reason there is no additional i13/2 neutron pair available to produce a second neutron band crossing. In summary, the level scheme of 194Hg has been extended to considerably higher spins and a third backbend has been observed. The band structure can be described very well within the framework of the CSM. In the present case the interpretation of the second backbend in terms of a vi43/2 band crossing seems unambiguous. Several suggestions for a theoretical explanation of the third backbending are given.

The authors would like to thank Dr. R. Bengtsson and Dr. W. Nazarewicz for helpful discussions. One of us (H.H.) would like to express his gratitude for the kind hospotality of the Nuclear Physics group during his stay at ANU. [ 1] M. Guttormsen, A. v. Grumbkow, Y.K. Agarwal, K.P. Blume, K. Hardt, H. Hfibel, J. Recht, P. Schfiler, H. Kluge K.H. Maier, A. Maj and N. Roy, Nucl. Phys. A398 (1983) 119. [2] K. Hardt, Y.K. Agarwal, C. Gfinther, M. Guttormsen, R. Kroth, J. Recht, F.A. Beck, T. Byrski, J.C. Merdinger, A. Nourredine, D.C. Radford, J.P. Vivien and C. Bourgeois, Z. Phys. A312 (1983) 251. [3] R. Korth, K. Hardt, M. Guttormsen, G. Mikus, J. Recht, W. Vilter, H. Hfibel and C. Gtinther, Phys. Lett. 99B (1981) 209. [4] S. Kuyucak, A. Faessler and M. Wakai, Nucl. Phys. A420 (1984) 83. [5] M. Trefz, A.A. Raduta, A. Faessler and T.J. Koeppel, Z. Phys. A321 (1983) 195. [6] M. Guttormsen and H. Hfibel, Nucl. Phys. A380 (1982) 502. [7] M. Guttormsen, Y.K. Agarwal, C. Gfinther, K. Hardt, H. Hfibel, A. Kalbus, G. Mikus, J. Recht and P. Schtiler, Nucl. Phys. A383 (1982) 155. [8] M. Guttormsen, K.P. Blume, Y.K. Agarwal, A. v. Grumbkov, K. Hardt, H. Hfibel, J. Recht and P. Schfiler, Z. Phys. A312 (1983) 155. [9] G.D. Dracoulis, Nucl. Instrum. Methods 187 (1981) 413. [10] R.M. Lieder, H. Beuscher, W.F. Davidson, A. Neskasis and C. Mayer-B6ricke, Nucl. Phys. A248 (1975) 317: [ 11 ] R. Bengtsson and S. Frauendorf, Nucl. Phys. A327 (1979) 139. [12] K. Neerg/lrd, P. Vogel and M. Radomski, Nucl. Phys. A238 (1975) 199. [13] H. Toki, K. Neerg~d, P. Vogel and A. Faessler, Nucl. Phys. A279 (1977) 1. 33