Evidence for reduced neutron pairing correlations in 165Yb

Volume 142B, number 4

PHYSICS LETTERS

26 July 1984

EVIDENCE FOR REDUCED NEUTRON PAIRING CORRELATIONS IN 165yb C. SCHUCK I, N. BENDJABALLAH 2, R.M. DIAMOND, Y. ELLIS-AKOVALI 3, K.H. LINDENBERGER 4, J.O. NEWTON s, F.S. STEPHENS Nuclear Science Division, Lawrence Berkeley Laboratory, University o f California, Berkeley, CA 94720, USA

and J.D. G A R R E T T and B. HERSKIND The Niels Bohr lnstitute, University of Copenhagen, DK 2100 Copenhagen, Denmark

Received 3 January 1984

Three rotational sequences in 16syb have been extended to high spins by using the 13°Te(4°Ar, 5n) amd lS°Nd(2°Ne, 5n) reactions. Evidence is presented for a reduction of the neutron pairing correlations at the highest rotational frequencies (hw > 0.40 MeV), but no quantitative measure of this reduction can be made. There appears to be a conflict with the expectations of simple CSM calculations.

Discrete line studies o f rapidly rotating nuclei have focused on band crossings corresponding to the alignment o f high4, low-~ quasiparticles [ 1]. In the yrast sequence o f the N = 90 even-even isotones 158Er [2] and 160yb [3,4], two band crossings have been established at angular frequencies ~ o = 0.27 and 0.41 MeV. These crossings are interpreted as the alignment o f a pair o f i13/2 quasineutrons [ 1] and a pair o f h11/2 quasiprotons [5,6]. The present letter reports data for several configurations in an odd4V nucleus, 165yb (N = 95), which has a somewhat larger deformation and so delays the quasiproton crossing to a higher rotational frequency. As a result the rotational sequences based on specific neutron configurations can be studied to higher frequency than in the lighter, 1 Permanent address: Centre de Spectrom~trie Nucl6aire et de Spectrom&rie de Masse, 91406 Orsay, France. 2 Permanent address: CEN - CDTB, PB 1017 Alger-Gate, Algeria. 3 Permanent address: Nuclear Data Project, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA. 4 Permanent address: Hahn-Meitner Institute, Berlin, Germany. s Permanent address: Australian National University, Canberra, Austrafia. 0.370-2693/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

less deformed nuclei. In fact, the quasiproton band crossing has been observed at h ~ = 0 . 4 8 - 0 . 5 0 MeV in the two N = 96 isotones 168Hf [7,8] and 170W [9]. Rotational decay sequences in 165 Yb established in previous studies [10] have been extended to higher angular momentum by using the 130Te(4°Ar, 5n) and 150Nd(20Ne, 5n) reactions [ 11], with beams from the 88-inch cyclotron o f the Lawrence Berkeley Laboratory. G a m m a - g a m m a coincidences were obtained from an array o f five Ge(Li) detectors, four o f them set at 153 ° with respect to the beam direction. An additional coincidence was required with one or more o f five 7.6 × 7.6 cm NaI detectors used as a multiplicity filter. Angular distribution measurements were obtained from the fifth Ge(Li) detector positioned alternatively at 0 ° and 87 °. The extension o f the (rr, a) = ( - , 1/2) and ( - , - 1 / 2 ) sequences is based on the relative intensities o f the transitions in the 7 - 7 coincidence data. More details on the experimental set-up and analysis can be found in ref. [11]. The resuiting level scheme for 165yb is presented in fig. 1. The experimental results are analyzed in the next few paragraphs and then will be discussed. The component o f the total angular momentum aligned with the rotation 253

Volume 142B, number 4

PHYSICS LETTERS .....

61/2'*--~

26 July 1984

7844

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....

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95

Fig. 1. Level scheme o f 16syb populated by the lS°Nd (2°Ne, 5n) and the 13°Te(4°Ar, 5n) reactions. The numbers between parentheses are the relative intensities o f the 7 transitions obtained with the 2°Ne reaction.

Ix= [ ( I + { ) 2 - K 211/2,

(1)

is presented in fig. 2 as a function of the angular frequency

E(I + 1 ) - E ( I - 1)., hw(I) =ix(i + 1) - I x ( I - 1) '

(2)

for four rotational sequences in 165yb together with similar values for the yrast sequence of the neighbouring even-even isotopes 164yb [11] and 166yb [12]. For hw > 0.28 MeV in the negative-parity b ands o f 165 Yb and after the blocked b and crossing at ~ 6o ~ 0.36 MeV in the positive-parity b a n d , I x is observed to increase linearly with the frequency for these seniority-three configurations. The kinematic moments o f inertia 9(1)/h 2 = Ix~bin 254

,

(3)

are presented as a function o f frequency in fig. 3a. For h6o > 0.3 MeV the 9 (1) values for the seniority three (v = 3) sequences in 165yb are only slightly frequency dependent. In the frequency region where such data exist for the v = 2 yrast sequences in 164,166yb [ 13], the 9(1) values are slightly smaller than those o f the v = 3 configurations. However, all 9 (1)/~2 values, if extrapolated, seem to converge at the largest rotational frequencies to values close to 65 MeV-1. This is only slightly lower than that of the moment o f inertia o f a deformed (e 2 = 0.24) rigid r o t o r , ~ f i g / h 2 = 73 MeV -1 . The dynamic moments o f inertia (2) l-t,2 = 9 band'-

dlx/hdm=

Ix(I+ 1) - I x ( I - 1) h [ w ( I + I) - w ( I - 1)] '

(4)

are shown as a function o f the frequency in fig. 3b.

Volume 142B, number 4

PHYSICS LETTERS .m

1

30

I

I

I

-

They are much more sensitive to changes in the local structure than 3 (1)/h2, but are nearly constant for the negative-parity states for 0.36 < h w < 0.44 MeV. The excitation energies in a rotating frame (routhians or e') calculated relative to a reference configuration with a moment o f inertia equal to 61.2 h 2 MeV -1 (corresponding to the moment o f inertia o f the "linear" region o f the I x versus Ptco plots in fig. 2)

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d /

/~164yb 20

_

~

'

~

Y

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_

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......

o J

~=__1'

o

164 166 . . .

I,(-.-',~)

.....

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.z

.4 ~ ( M e V )

Fig. 2. Plot of Ix versushco for four rotational bands in 165yb and the yrast sequences in 164,166yb.

'>

I

T

(2 _1__ . . . . . . . . . . . . . .

(5)

are shown in fig. 4a for the four bands in 165yb and in fig. 4b for two bands in 164,166yb. E ( w ) is the, energy above the ground state in the laboratory frame. From the experimental results a striking feature that emerges in the nearly constant value o f 9 (1) above h w = 0.36 MeV for all three configurations in 165yb. Two mathematically equivalent statements are that 9 (b2~)d is nearly equal to 9 (1) and that t h e I x versus h w curve is approximately straight with an intercept near zero. To understand this behavior we can begin by considering the properties o f a system with no pairing correlations, because the three quasi-neutrons and the high rotational frequency are expected to result in a strong reduction o f pairing. With no

{" (÷&) -.--

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26 July 1984

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/

30

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0.2

0.3

(-,- ~) -*-

164,is

0.4

30

0.2 0.5 hca (MeV)

I

0.5

I

0.4

0.5

Fig. 3. (a) Plot of Q (1)/h2 versus Pito for four rotational bands in 165Yb and the yrast bands in 164,166yb" (b) Plot of Q (2)/pt2 versus hco for three bands in 1 6 5 Yb and the yrast bands in 164,166yb" 255

Volume 142B, number 4

PHYSICS LETTERS

a

/

0.6

P

¢

,'B(+,- I/2) >

0.4

"~ 0.2

"~.~ -0.2

0.1

b

.~" 0.2

........- J 164 Yb

1.0

,

,

0.3

0.4

1 ~ (MeV)

164yb

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/

:~ 0.5 e'A+ e ' E ~ ~ e ~

o,i C

0'2

+ e,B I

o'.3

l~w

(MeV)

0.4

I=

/ AE

> 0.8

uo

0.4 0.22 I

0.36 I

15~(MeV)

It

Fig.4. (a)Plot of routhians relative to the 9 = 61.2/'/ 2 MeV -1 reference versus hto for four rotational bands in 16syb. (b) Plot of routhians relative to the same reference versus h e for two different two-particle configurations in 164yb and 166yb together with the constructed two-particle routhians in 165Yb. (c) Plot of a, the difference between the average of the twoparticle routhians in the even--even nuclei and the sum of e)t+ el3 versus hco in 16syb. pairing (neutron or proton), g(1) should average to the deformed rigid-rotor value, but should not be constant due to the occurrence o f particle alignments which cause jumps in ~ (1). All CSM calculations o f high-spin nuclear behavior [ 14,15] predict that part of the angular momentum will continue to come in these sudden alignments leaving significantly less available for the collective motion. Between alignm e n t s 9 band (2) should therefore be less than 9 (1) (around 1/2 to 2/3 on average), causing 9 (1) to drop slowly there. Thus 9 (1) is expected to oscillate around the rigid-rotor value. If the shape, deformation, and configuration are frozen,9 (b2a~)d itself is ex256

26 July 1984

pected to decrease slowly as the more easily available angular momentum is used up, but that is a higher order effect. This described behavior is not very similar to that observed. However, there are no quasi-protons in the observed bands of 165yb, so that the proton pairing correlations are almost surely not quenched. This means that the protons will contribute less angular momentum at a given frequency, resulting in an ~ (l) lower than the rigid-body value (as observed). It also means that the proton pairing will be continuously reduced by the Coriolis interaction (Coriolis antipairing) as co increases. This will, by itself, contribute to an increasing .c)(b2a)ndvalue, and together with the lowered 9 (bhd expected after the (neutron) alignments, could give a nearly constant ~ (b2a~)d ~ D (1) as observed. If so, this is a somewhat accidental cancellation o f two opposite tendencies. But other examples are known where 9 band(2)~ 9 (1) and 9 (b2~)d is quite constant over a wide range o f frequency [16,17]. Thus there may be more fundamental reasons for this behavior, but they are not apparent in present CSM calculations. The above discussion requires that the neutron pairing be rather low, but gives no quantitative measure of it. It should also be noted that the moments o f inertia o f the seniority three neutron states in 165yb are larger, but only slightly so, than the seniority two states of the neighboring even-even 164,166yb, indicating possibly not much further decrease in neutron pairing correlations with an additional unpaired particle. An alternate explanation would be a deformation change, but it should be noted that the increase in deformation necessary to produce a constant 9 (I) over this frequency range is Axe ~ 0.05. This seems rather unlikely in this mass region where centrifugal stretching is still supposed to be small at these rotational frequencies [ 1 8 - 2 0 ] . Finally, we can make a measurement o f the change in the total pairing correlation energy as a function o f high rotational frequency. Consider the difference between the routhian o f the two-quasineutron band AB, @i13/2) 2, and the sum o f its one-quasineutrino constit tuents,/5 = e~LB -- e)t - eB, with reference states chosen such that the lowest real state in both even and odd nuclei has e' = 0 at co = 0. At co = 0, 8 is a measure o f the neutron pairing correlation energy, being roughly equal to twice the o d d - e v e n mass difference. For non-zero co, with the assumption that

PHYSICS LETTERS

Volume 142B, number 4

the only change is the loss in neutron and proton pairing and not, for example, a change in deformation or shell effect, = +e'(n, co, AB) -

e'(n,co = 0, 0)

+ e'(n, co = 0, g) - e ( n' ,

co, B)+e'(n, co = 0 , g)

- e'(p, co, 0) + e'(p, co = 0, 0 ) . !

.

!

- e'(n, co, A)

(6)

Here e (p, w, 0) and e (n, w, A) are (negative) pairing correlation energies at rotational frequency co for protons and neutrons in the zero quasiparticle and one-quasineutron configuration A, respectively, and e'(n, co = 0, g) is the pairing energy o f the odd-mass ground state at co = 0. The first six terms are the changes in neutron pairing, but the last two represent changes in the proton pairing. Although the total pairing energy falls steeply with co (fig. 4c), it is not, in general, possible to separate the effects o f the neutrons and o f the protons although calculations show that the major effect in the range o f co we have observed experimentally is due to loss o f neutron pairing. However, it should be noted that at still larger co, where the proton as well as the neutron pairing has been quenched, all the terms will approximately cancel but for e'(p, co = 0, 0), leaving a large negative value o f 5. Thus the (extrapolated) crossing o f the horizontal axis in fig. 4c is not the value o f co where the neutron pairing vanishes, but depends upon the relative quenching o f the neutron and proton pairing and upon the value chosen for the reference moment o f inertia. But clearly by co = 0.36 the neutron pairing has been greatly diminished. Thus there are a number o f features about the highspin states in 165yb for ~co = 0 . 3 - 0 . 5 MeV that suggest that the neutron pairing correlations are substantially reduced. Although it cannot be ruled out by the experiments performed so far that part o f the effects are not due to a shape change, such a deformation change is not predicted theoretically for this frequency range. However, the nearly equal and (large) constant

26 July 1984

values o f 9 (1) and ~ (2) observed in this and in other recent studies at high rotational frequencies pose a real challenge; such a situation is not expected from simple theory for the unpaired system, and too many examples are accumulating to believe it is accidental. Future experiments (observation o f the next few states) and better calculations that simultaneously take into account changes with pairing, shell effects, and deformation may solve this problem, but it is possible that some physics is missing from the picture. We would like to thank Thomas DCssing for enlightening advice and comments. This work was supported by the Director, Office o f Energy Research, Division o f Nuclear Physics o f the Office o f High Energy and Nuclear Physics o f the US Department o f Energy under Contract DE-AC03-76SF00098.

References [1] F.S. Stephens and R.S. Simon, Nucl. Phys. A183 (1972) 257. [2] I.Y. Lee et al., Phys. Rev. Lett. 38 (1977) 1454. [3] F.A. Beck et al., Phys. Rev. Lett. 42 (1979) 493. [4] L.L. Riedinger et al., Phys. Rev. Lett. 44 (1980) 568. [5] A. Faessler and M. Ploszajczak, Phys. Lett. 76B (1978) 1. [6] R. Holzmann et al., Phys. Rev. Lett. 50 (1983) 1834. [7] R. Chapman et al., Phys. Rev. Lett. 51 (1983) 2265. [8] R.V.F. Janssens et al., Phys. Lett. 106B (1981) 475. [9] J. Recht et al., Phys. Lett. 122B (1983) 207. [10] N. Roy et al., Nucl. Phys. A382 (1982) 125. [11 ] C. Schuck et al., Proc. XXth Intern. Meeting on Nuclear physics (Bormio, Italy, 1982) p. 197; Proc. INS Intern. Symp. on Dynamics of nuclear collective motion (Mt. Fuji, Japan, 1982) p. 474. [12] S. Jonson et al., Lund-N.B.I., preprint (1983). [13] W. Walus et al., Phys. Scr. 24 (1981) 324. [14] H. Sagawa and T. D~ssing, Phys. Lett. 96B (1980) 238. [15] J. Zhang and S. Aberg, Nucl. Phys. A390 (1982) 314. [16] T.L. Khoo et al., Phys. Scr. T5 (1983) 16. [17] J.B. Bacelar et al., N.BJ.-Daresbury preprint (1983). [18] G. Andersson et al., Nucl. Phys. A268 (1976) 205. [19] S. Cwiok, private communication. [20] T. Udagawa and R.K. Sheline, Phys. Rev. 147 (1966) 671.

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