Nuclei Off the Line of Stability - American Chemical Society

49 Shape Competition and Alignment Processes in Light A u and Pt Nuclei 1

1

2

L. L. Riedinger , A. J. Larabee , and J.-Y. Zhang 1

University of Tennessee, Knoxville, TN 37996-1200 Joint Institute for Heavy Ion Research, Oak Ridge, TN 37831

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Calculations are presented and data are reviewed on the properties of the high-j states in the light Au nuclei. Both prolate and oblate structures are observed in this region. It is found that the collective model describes well the bandhead and the high-spin properties of the h9/2 and i13/2 proton states, without resort to an "intruder state" phenomenology. There has been m u c h discussion at this and other conferences about the existence o f nuclear intruder states, i.e. levels outside the m o d e l space f o r a g i v e n nucleus. There is ample evidence [ H E Y 8 3 ] f o r the existence o f intruder states at o r near closed shells, w h i c h demonstrates the importance o f the v a r y i n g particle-hole c o m p o s i t i o n o f these states. A s one proceeds away f r o m the closed shell b y a d d i n g o r subtracting nucléons, at some point there occurs n o r m a l deformed n u c l e i adequately described b y the N i l s s o n m o d e l , i n w h i c h case the s h e l l - m o d e l particle-hole structure o f states becomes irrelevant. O n e important question is f o r h o w m a n y nucléons beyond a closed shell does the intruder description o f certain states g i v e w a y to the collective description. W e pursue here this question f o r the Ζ = 7 9 isotopes o f g o l d and describe experiments and calculations performed o n both the bandhead energies o f h i g h - j states (occasion a l l y c a l l e d intruders) and the bands built o n these states. W e f i n d that the c o l l e c tive picture adequately describes these levels i n a transition region o f competing nuclear shapes. W h i l e oblate structures o c c u r i n the heavier g o l d isotopes, the lighter ones are dominated b y prolate bands. O u r group has performed measurements o n a n u m b e r o f P t and A u n u c l e i . H i g h - s p i n states i n ' A u [ L A R 8 5 ] and i n P t [ W A D 8 5 ] have been studied at the M c M a s t e r U n i v e r s i t y T a n d e m A c c e l e r a t o r w i t h F i n d u c e d reactions. A n array o f 5 G e and 6 N a l counters was used to collect g a m m a - g a m m a coincidence data. A n g u l a r distribution measurements were also performed. B a n d s i n 183,184^ d i e d [CAR85] with a induced reaction at the H o l i f i e l d H e a v y Ion Research F a c i l i t y . T h e S p i n Spectrometer was used w i t h 9 G e counters, six o f w h i c h were C o m p t o n suppressed w i t h N a l annuli. T h e systematics o f the prolate and oblate states observed i n the light 1 8 5

1 8 6

1 8 5

1 9

w

e

r

e

s t u

0097-6156/ 86/0324-0323506.00/ 0 © 1986 American Chemical Society

Meyer and Brenner; Nuclei Off the Line of Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1986.

324

NUCLEI OFF THE LINE OF STABILITY

Ε

Ε (MeV)

( MeV )

1-5 +

0.5+

l.o

+

9/2 -.191

in

Au

-;·.?· -.1β7

0*

0.5 + .238

1.5+

233 Η —

2.0 τ

— Η

163 185 187 189 191 193 ^05 _. -.196 1Β7

-.210

.205

-.201

ΕΧΡ

1-5 + 0.5+

1.0

+

257

1 3 / 2 " ^ in

Au

0.5 +

0+

0 +

102

106 110

A Η

Η

183 185 187 189 191 193

F i g . 2. N i l s s o n c a l c u l a t i o n o f b a n d head energies f o r the I19/2 and 113/2 proton states i n the A u isotopes. A prolate (solid line) and a n oblate (dashed line) solution is g i v e n for most. E q u i l i b r i u m deformations are g i v e n for each. T h e experimental energies are g i v e n for c o m p a r i s o n .

1 14

F i g . 1. E x p e r i m e n t a l systematics o f some prolate (closed squares) and oblate (open squares) states i n H g (Z=80), A u (79), and Pt (78) n u c l e i . H g , A u , and P t n u c l e i are shown i n F i g . 1. T h e first 2 state o f the H g isotopes is remarkably constant i n energy and has been described as a slightly deformed oblate state. A s mapped i n detail i n U N I S O R measurements [ H A M 7 5 ] , there exist r a p i d l y f a l l i n g prolate states i n H g . T h e heavy P t isotopes are evidently s i m i l a r i n ground properties to the H g n u c l e i , but the isotopes b e l o w Ν = 110 m a y be prolate i n shape, j u d g i n g b y the structure o f the 113/2 b a n d i n adjacent o d d - N P t isotopes. A s summarized b y W o o d [ W 0 0 8 1 ] , l o w - l y i n g 0 states i n P t m a y be the oblate states s i m i l a r i n structure to the H g ground configuration. T h u s , Ζ = 79 around Ν = 106 appears to be the point o f crossing +

1 8 4

1 8 8

+

1 8 2

1 8 6


49.

RIEDINGER E T AL.

Shape Competition and Alignment Processes

325

for the oblate and prolate m i n i m a . A s seen i n F i g . 1, the π1ΐ9/2 and πίΐ3/2 states f a l l r a p i d l y i n the l i g h t A u n u c l e i , w h i c h suggests the intruder description, i.e. a different b e h a v i o r o f the n o r m a l 3-hole states (hi 1/2, d3/2, sm) c o m p a r e d to the 1-particle 4-hole levels (I19/2,113/2). T h e structure o f the bands b u i l t o n these states suggests the prolate or oblate nature described i n F i g . 1. A Strutinsky-type N i l s s o n c a l c u l a t i o n o f the bandhead energies for the A u isotopes is s h o w n i n F i g . 2. T h e parameters used i n this N i l s s o n c a l c u l a t i o n were those suggested b y the L u n d group [ B E N 8 5 ] , except for μ = 0.52 for the Ν = 5 and Ν = 6 proton shells. T h i s value better describes levels i n this r e g i o n and became necessary i n order to e x p l a i n i n A u the n e w l y found l / 2 [ 5 3 0 ] band, based partially o n the fia shell state [ L A R 8 5 ] . A s seen i n F i g . 2, there are both prolate and oblate m i n i m a calculated for each o f the quasiparticle states. W h i l e the oblate hm and 113/2 states are rather constant i n energy as a f u n c t i o n o f N , the prolate m i n i m u m falls r a p i d l y , b e c o m i n g l o w e r a t A u for the f o r m e r and at A u for the latter. These calculations m a t c h rather w e l l the observed trend (see F i g . 1), and suggest that it is changing deformation w h i c h is responsible for the " i n t r u d i n g " h i g h - j states, as opposed to the d i f f e r i n g particle-hole character. T h i s c o l l e c t i v e explanation requires a deformation o f -0.173 for the lowest I19/2 state i n A u , but unfortunately the b a n d structure built o n this state is u n k n o w n and thus it is d i f f i c u l t to surmise i f this deformation is reasonable. C a l c u l a t i o n s w i t h a W o o d s - S a x o n potential give results very s i m i l a r to those s h o w n i n F i g . 2 [NAZ85]. It is clear f r o m the calculations o f F i g . 2 that the b a n d structures seen i n the light A u n u c l e i should be dominated b y prolate shapes, as is observed e x p e r i m e n t a l l y i n A u [ L A R 8 5 ] . R o t a t i o n - a l i g n e d bands are b u i l t o n I19/2,113/2, and f7/2 N i l s s o n states, indicative o f Κ = 1/2 bands and prolate shapes. H o w e v e r , the stucture b u i l t o n the h i 1/2 bandhead is more c o m p l e x , as s h o w n i n the partial l e v e l scheme o f F i g . 3. T h e 2 2 0 - k e V bandhead is k n o w n [ B E R 8 3 ] to be a 26 ns isomer, e x p l a i n e d as due to an oblate h i 1/2 to prolate I19/2 transition. T h e sequence of E 2 transitions to the right i n F i g . 3 is s i m i l a r to that seen i n the heavier o d d - A A u n u c l e i [ G O N 7 9 ] , and is explained as the w e a k c o u p l i n g o f the h i 1/2 h o l e state to the slightly oblate H g core. H o w e v e r , the sequence of levels b e g i n n i n g at 1210 k e V is different f r o m anything seen i n the heavier isotopes. T h e strongly-coupled nature o f this n e w band suggests a prolate h i 1/2 structure, w h i c h is expected to lie close i n energy to the oblate band according to the calculations. T h e c o m p l i c a t e d structure s h o w n i n F i g . 3 is therefore quite compatible w i t h the predicted near degeneracy o f prolate and oblate bands i n Au. 1 8 5

1 8 9

1 8 7

1 9 3

1 8 5

1 8 5

F o u r bands are observed to h i g h spins i n

1 8 5

A u and are s h o w n i n the


326


Δ 7rh9/2 α 1/2 s

A

7rh

9 / 2

α = -1/2

+ 7rf7/ α « -1/2 Ο iri a*1/2 2

1 3 / 2

3365.0327.7 •205.7

2831.6-

269.9,

—

3037.3

476 —

2561.7

259 2 •

1B

2302.5-

* P 1 - yrast band

ο vi a = 1/2 1185pt • ^'13/2 " 2 J ν 7Γη ι/ϊ 2 ο =1 Ί • 7rh i/i a = 0j

536.5 277.3,

1 3 / 2

a

9 / 2

s

1 3 /

1263.9

1 β 6

A

9 / 2

2025.2

541.2

1 /

u

1761.2

1 3 / 2

—

212.4J

551.51

(23/2Ί

476

1548.8 338.7

1

628.0 1397.2 19/2"

1210.1714.9

682.3 15/2" 462.3 • ο _Ο Δ

184 w 5

220.0

Pt-yrast band Pt IM Au iri / Au Trh

11/2-

1 3 / 2

185

1 3

, e 5

cj (irh

2

c

9 / 2

)

9 / 2

185

79 106 A u

F i g . 3. A partial l e v e l scheme f o r A u e m p h a s i z i n g the structure b u i l t u p o n the h i i/2 state [ L A R 8 5 ] . T h e 2 2 0 - k e V state has an isomeric decay o f 26 ns to the h9/2 l e v e l . 1 8 5

0.1 Τΐω

0.2 (MeV)

0.3

04

F i g . 4. I n the top t w o panels, the experimental alignment (i) as a function o f rotational frequency f o r bands i n ' A u [ L A R 8 5 ] , P t [ C A R 8 5 ] , and P t [ W A D 8 5 ] . Reference parameters o f JLC= 2 2 * / M e V and «0, = 110 * / M e V are used. I n the bottom panel, the second moment o f inertia is plotted versus frequency f o r selected bands. 1 8 5

1 8 6

1 8 4

2

1 8 5

4

3

alignment v s . rotational frequency graph o f F i g . 4. T h e ol = - 1 / 2 negative parity bands cross a n d interact around I = 2 3 / 2 , w h i c h explains the perturbations i n those t w o bands i n F i g . 4. A l i g n m e n t gains o f different magnitudes are observed i n each o f these bands, suggesting differing alignment processes taking place.


49.

RIEDINGER ET AL.

327

Shape Competition and Alignment Processes

B y comparison, the yrast band o f the core nucleus, P t , is s h o w n i n the second panel o f F i g . 4, as are the two signatures o f the 9/2[624] 113/2 b a n d i n P t . It was previously thought b y some (e.g. [ B E S 7 6 ] ) that the crossing i n P t resulted f r o m the alignment o f in/2 neutrons, as is the case throughout the N = 9 0 to 106 deformed region. O n the other h a n d , our earlier measurements o n Au [ K A H 7 8 ] suggested that the crossing i n P t h a d to result f r o m nhm alignment. It is n o w apparent f r o m the data s h o w n i n F i g . 4 that both o f these quasiparticle alignments take place at nearly the same frequency. T h e third panel i n F i g . 4 contains a plot o f the second moment of inertia versus frequency, w h i c h more sensitively shows crossings for these bands. T h e yrast b a n d o f P t and the πΐΐ3/2 b a n d o f A u have two peaks i n this second-moment plot. T h e Vii3/2band o f P t shows o n l y the first peak, w h i l e the π1ΐ9/2 band o f A u displays the second. These data thus indicate the existence o f a nhm crossing at i w = 0.25 M e V w i t h a Δί = 5.111, and a V113/2 crossing at 1Ι= 0.31 M e V w i t h a Δί = 5 . 7 * . T h e yrast b a n d o f P t is affected b y both crossings, w h i c h explains the large alignment g a i n (9.7-fi) compared to the neighboring o d d - A n u c l e i . O u r measurements o n A u [ L A R 8 5 ] indicate a 7ch9/2vii3/2 b a n d w h i c h shows no crossing, since b o t h alignment processes are b l o c k e d (see F i g . 4). 1 8 4

1 8 5

1 8 4

1 8 5

1 8 4

1 8 4

1 8 5

1 8 5

1 8 5

1 8 4

1 8 6

.20 +

( MeV

F i g . 5. C r a n k e d S h e l l M o d e l frequency f o r the proton I19/2 crossing m i n u s that f o r the neutron 113/2 crossing plotted as a function o f neutron number f o r the Pt isotopes.

)

.10

.05

C r a n k e d S h e l l M o d e l calculations have been performed to learn i f these two c l o s e - l y i n g band crossings c a n be explained w i t h reasonable shape para meters. T h e difference i n the calculated crossing frequencies is s h o w n i n F i g . 5 as a function o f neutron number for the P t isotopes. V a l u e s o f £ a n d tfy were obtained f r o m a potential-energy-surface calculation ( w i t h κ and μ values as g i v e n above) and then used i n the C S M calculation. T h e m i n i m u m i n the curve occurs for P t , i n agreement w i t h the data. N o attempt has yet been made to exactly reproduce these experimental crossing frequencies, since other parameters such as pairing gaps are p o o r l y k n o w n i n this region. Nevertheless, x

1 8 4


328


the calculations do show that it is reasonable for the nhm and ν in/2 crossings, rather w i d e l y split i n other n u c l e i , to be very close i n frequency i n P t . In c o n c l u s i o n , our data o n h i g h - s p i n states i n » A u and i n » P t are mostly indicative o f band structures and alignment processed i n prolate n u c l e i . T h e oblate h i 1/2 b a n d is observed, but is crossed at intermediate spin b y what is probably a prolate h i 1/2 structure. C o l l e c t i v e m o d e l (Nilsson) calculations o f bandhead properties o f the A u isotopes agree w e l l w i t h the observed systematics of the " i n t r u d i n g " hm and 113/2 proton states, c a l l i n g into question the p a r t i c l e hole interpretation o f these states. 1 8 4

1 8 5

1 8 6

184

185

Acknowledgments

T h e authors w i s h to thank W i t e k N a z a r e w i c z and J i m W a d d i n g t o n f o r many h e l p f u l discussions. Research at the U n i v e r s i t y of Tennessee is supported b y the U . S . Department o f E n e r g y under contract N o . D E - A S 0 5 - 7 6 E R O - 4936. T h e Joint Institute for H e a v y Ion Research has as member institutions the U n i v . of Tennessee, V a n d e r b i l t U n i v . , and the O a k R i d g e N a t i o n a l L a b o r a t o r y ; it is supported b y the members and b y the U . S . D O E .

References [BEN85] T. Bengtsson and I. Ragnarsson, Nucl. Phys. A436 14 (1985). [BER83] V. Berg, Z. Hu, J. Oms, and C. Ekstrom, Nucl. Phys. A410 445 (1983). [BES76] S. Beshai, K. Fransson, S.A. Hjorth, A. Johnson, T. Lindblad, and J. Szarkier, Z. Physik A277 351 (1976). [CAR85] M.P. Carpenter, C.R. Bingham, L.H. Courtney, S. Juutinen, A.J. Larabee, Z.M. Liu, L.L. Riedinger, C. Baktash, M.L. Halbert, N.R.Johnson, I.Y.Lee, Y. Schutz, A. Johnson, J. Nyberg, K. Honkanen, D.G. Sarantites, Bull. Am. Phys. Soc. 30 762 (1985). [GON79] Y. Gono, R.M. Lieder, M . Muller-Veggian, A. Neskakis, C. Mayer-Böricke, Nucl. Phys. A327 269 (1979). [HAM75] J.H. Hamilton etal., Phys. Rev. Lett. 35 562(1975). [HEY83] K. Heyde, P. Van Isacker, M . Waroquier, J.L. Wood, and R.A. Meyer, Phys. Rpts. 102 291 (1983). [KAH78] A.C. Kahler, L.L. Riedinger, N.R. Johnson, R.L. Robinson, E.F. Zganjar, A. Visvanathan, D.R. Zolnowski, M.B. Hughes, and T.T. Sugihara, Phys. Lett. 72B 443 (1978). [LAR85] A.J. Larabee, M.P. Carpenter, L.L. Riedinger, L.H. Courtney, J.C. Waddington, V.P. Janzen, W. Nazarewicz, J.Y. Zhang, R. Bengtsson, and G.A. Leander, submitted to Phys. Lett. [NAZ85] W. Nazarewicz et al., to be published. [WAD85] J.C. Waddington, S. Monaro et al., to be published. [WOO81] J.L. Wood, 4th International Conference on Nuclei Far From Stability, Helsingør, 1981, pg 612. RECEIVED July 31, 1986


Nuclei Off the Line of Stability - American Chemical Society

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