- Email: [email protected]
High spin states
Nuclear Physics A396(1983)307c-318c. © North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher.
307c
LBL-14824 HIGH SPIN STATES
F.S. Stephens Nuclear Science Division, Lawrence Berkeley Laboratory University of C a l i f o r n i a , Berkeley, CA 94720 Abstract: Nuclei generate high spins by two methods, alignment of single p a r t i c l e angular momentum and c o l l e c t i v e r o t a t i o n . The competition of these two modes is discussed f i r s t in general terms, then in the spin region below ~40 h, and f i n a l l y fo r the highest spins 40 ~ I ~ 65 Some prognosis f o r future experiments in t h i s f i e l d is given. 1.
Introduction
Nuclei can generate high angular momentum either by alignment along a common axis of the angular momentum of several individual nucleons or by a c o l l e c t i v e r o t a t i o n of the nucleus as a whole. Recent developments in t h i s f i e l d have been centered on understanding the competition of these two modes. This can be i l l u s trated in f i g . i , where level schemes of 158Er and 147Gd are shown1,2). The 158Er scheme is quite regular and the dominant behavior is c o l l e c t i v e r o t a t i o n of a prolate-deformed nucleus as is i l l u s t r a t e d at the l e f t of f i g . I . The 147Gd scheme is quite i r r e g u l a r , with complicated decay pathways and isomeric states (dark l e v e l s ) . I t s dominant behavior is c e r t a i n l y s i n g l e - p a r t i c l e alignment, as is i l l u s t r a t e d at the r i g h t of f i g . i . Yet both of these schemes contain elements of the other type of behavior. There are i r r e g u l a r i t i e s in the 158Er r o t a t i o n a l pattern at spins around 16 and 26, which correspond to single p a r t i c l e alignments, and the 49/2+ isomer at 8.6 MeV in ]47Gd has a quadrupole moment that suggests that the aligned p a r t i c l e s are p o l a r i z i n g the core so a c o l l e c t i v e oblate shape is developing. In t h i s t a l k I w i l l discuss our present understanding of the i n t e r p l a y of these two types of behavior, f i r s t as to the physics involved and then in the experimental data f o r nuclei of t h i s mass region. E(MeV) 12-
28: 52+~[
z
I0
T
49+
B-
6
I2h ÷
13+ g 7-
15BEt
14"7Gd
2
Fig. 1 Level scheme for 158Er and 147Gd, together with i l l u s t r a t i o n s of the dominant source of angular momentum for each case.
308c
F.S. STEPHENS
2. 2.]
Physics of high spin s t a t e s
NUCLEAR SHAPES
One of t h e most i m p o r t a n t f a c t o r s in d e t e r m i n i n g t h e physics of h i g h - s p i n s t a t e s is simply the r o t a t i o n a l b e h a v i o r of r i g i d c l a s s i c a l o b j e c t s . In f i g . 2 t h e moment o f i n e r t i a of such an o b j e c t is compared w i t h t h a t of a r i g i d sphere ( s o l i d l i n e s ) f o r a v a r i e t y of shapes and r o t a t i o n a l axes. The shape and axis is defined by y, which v a r i e s from -120 ° t o 60 ° as t h e o b j e c t v a r i e s from a p r o l a t e shape r o t a t i n g about i t s symmetry a x i s , through o b l a t e and p r o l a t e shapes r o t a t i n g about axes p e r p e n d i c u l a r t o the symmetry a x i s , t o an o b l a t e shape r o t a t i n g about i t s symmetry a x i s . The deformation is given in terms of a q u a n t i t y ~, which is t o lowest o r d e r j u s t AR/R. Values of ¢ around 0.3 are t y p i c a l f o r t h e f a m i l i a r deformed r a r e - e a r t h and a c t i n i d e n u c l e i . The l a r g e s t moments of i n e r t i a , and t h e r e f o r e t h e lowest r o t a t i o n a l e n e r g i e s , occur f o r the range of shapes between y = 0 ° and 60 ° . The v e r y l a r g e s t moment of i n e r t i a is f o r y = 60 ° , an o b l a t e shape r o t a t i n g around i t s symmetry a x i s , and i t is f o r t h i s reason t h e e a r t h has such a shape. The f u l l l i q u i d - d r o p model (LDM) t r e a t m e n t of a r o t a t i n g nucleus 3) includes volume, surface, and Coulomb e n e r g i e s , in a d d i t i o n t o these c l a s s i c a l r o t o r c o n s i d e r a t i o n s , and is shown by t h e dots in f i g . 2. I t is apparent t h a t t h e r e is no strong shape preference in these a d d i t i o n a l LDM terms, so t h a t simple c l a s s i c a l mechanics determine t h e l i q u i d - d r o p shapes. This is i m p o r t a n t , since t h e l i q u i d - d r o p model is our best guide t o such macroscopic n u c l e a r p r o p e r t i e s and is even t h e l i m i t t o which some of t h e microscopic models are n o r m a l i z e d .
~-o6
P4
i
o
e-C~
t2
4
o~>
I0
*5 08 +10 .15
o6 -,~o
-do
G
~o
F20
XBL. 808-11414
Fig. 2. The r a t i o of t h e moment o f i n e r t i a of a r i g i d e l l i p s o i d t o t h a t of a r i g i d sphere vs t h e shape parameter y f o r two values of t h e d e f o r m a t i o n c : 0.3 and ¢ = 0 . 6 . The r i g h t - h a n d scale g i v e s t h e d i f f e r e n c e in r o t a t i o n a l energy in MeV f o r a nucleus w i t h A : 160 and I = 60. The dots g i v e t h e r a t i o s f o r t h e t o t a l l i q u i d - d r o p energy ( r o t a t i o n + surface + Coulomb) o f t h e nucleus. In o r d e r t o see how s i g n i f i c a n t these c l a s s i c a l shape e f f e c t s are, one must choose a mass and spin, and f o r A = 160 and I = 60 h, an energy scale is given on the r i g h t side of f i g . 2. The v a r i a t i o n f o r c = 0.3 of about 10 MeV is l a r g e r than t y p i c a l s h e l l e f f e c t s (-3 MeV) so t h a t f o r t h i s spin t h e e f f e c t s considered here should be dominant. The r o t a t i o n a l energy v a r i e s as 12 so t h a t , f o r 30 h, s h e l l e f f e c t s and these c l a s s i c a l shape e f f e c t s should be about e q u i v a l e n t , and below -20 ~ t h e s h e l l e f f e c t s w i l l dominate. The arguments made here would seem t o apply o n l y f o r c o l l e c t i v e n u c l e a r r o t a t i o n s , and even then o n l y i f t h e n u c l e a r moment o f i n e r t i a has t h e r i g i d body v a l u e , n e i t h e r o f which is o b v i o u s l y t h e
HIGH SPIN STATES
309c
case. In f a c t , however, most people do b e l i e v e t h a t r o t a t i n g n u c l e i at high spins w i l l , on average, have the r i g i d - b o d y moment of i n e r t i a , and t h i s has been shown t o be t h e case f o r an a n i s o t r o p i c harmonic o s c i l l a t o r p o t e n t i a l and independent p a r t i c l e motion 4) . The s m a l l e r moments of i n e r t i a observed at low splns are due l a r g e l y t o t h e p a i r i n g c o r r e l a t i o n s , which should be quenched above -30 h. Furthermore, even in n o n c o l l e c t i v e cases, i t has been shown ( f o r a.Fermi gas) t h a t t h e t r a j e c t o r y of lowest l e v e l s f o l l o w s t h a t given by r o t a t i n g t h e a p p r o p r i a t e l y shaped r i g i d body 5). Thus, these v e r y simple arguments should be v a l i d and shapes in t h e y = 0-60 ° range should dominate at high s p i n , i . e . , above -30 h in t h e A = 160 r e g i o n . Several t y p e s o f m i c r o s c o p i c c a l c u l a t i o n s have now been c a r r i e d out f o r n u c l e i in t h i s r e g i o n and a l l of them agree t h a t t h e y = 0-60 ° range should dominate at high s p i n s , though t h e models show some d i f f e r e n c e s w i t h i n t h e y = 0-60 ° range. 2.2
LEVEL STRUCTURES
A general q u e s t i o n a r i s e s as t o how one can r e c o g n i z e these shapes e x p e r i m e n t a l l y . That i s , what kind of n u c l e a r s t r u c t u r e is expected f o r shapes in t h i s y = 0-60 ° r e g i o n . I t has been recognized since 1952 t h a t a deformed nucleus can r o t a t e c o l l e c t i v e l y around an a x i s p e r p e n d i c u l a r t o t h e symmetry a x i s 6). The p r o l a t e y = 0 ° shape is o f t h i s t y p e and e s s e n t i a l l y a l l t h e r o t a t i o n a l n u c l e i known have y - v a l u e s equal t o or near 0 °. On t h e o t h e r hand, a nucleus cannot r o t a t e c o l l e c t i v e l y around a symmetry a x i s : those degrees of freedom are c o n t a i n e d in t h e s i n g l e - p a r t i c l e m o t i o n . Thus t h e y = 60 ° o b l a t e n u c l e i do not have c o l l e c t i v e r o t a t i o n , but b u i l d up t h e i r a n g u l a r momentum by a l i g n i n g along a common a x i s t h e c o n t r i b u t i o n of v a r i o u s s i n g l e p a r t i c l e s . These are t h e two basic b e h a v i o r s discussed in Section I . The k i n d o f s t r u c t u r e associated w i t h the t r i a x i a l n u c l e a r shapes between y = 0 ° and 60 ° has been e l u c i d a t e d r e c e n t l y - - s i n c e t h e f i r s t clues t o t h i s were found in t h e backbending phenomenon d i s c o v e r e d / ) in 1971. The s i t u a t i o n is d e p i c t e d in f i g . 3. For e x a c t l y a x i a l l y symmetric shapes (upper l e f t ) o n l y c o l l e c t i v e r o t a t i o n is p o s s i b l e , and d i f f e r e n t c o n f i g u r a t i o n s g i v e r i s e t o bands t h a t extend over broad r e g i o n s of s p i n . In f a c t , what is observed t o happen is i n d i c a t e d at t h e upper 2O
'2//
15 IO
5
.
.
.
.
t
I : Zjo + ~®co,
w 15
~
',
1
7\, -
f
I
I
/
jo ~)"
v
B
z
I¢
,/
/,( o
ig"
//°
/I/ 0
0
20
40
0
I
20
4~) XBLB04~44
Fig. 3. Schematic excitation energy vs spin plots for various relative amounts of collective angular momentumand single-particle rotation-aligned angular momentum. Bandhead(pure s i n g l e - p a r t i c l e ) energies are shown in the lower two panels, The solid curves correspond to real bands, whereas the dashed curve is the envelope of the real bands.
310c
F.S. STEPHENS
r i g h t , where bands w i t h d i f f e r e n t c o n f i g u r a t i o n have d i f f e r e n t amounts of s i n g l e - p a r t i c l e angular momentum a l i g n e d w i t h t h e r o t a t i o n axis and t h e r e b y g i v e r i s e t o s l i g h t l y n o n a x i a l shapes and a p a t t e r n of crossing bands. Sequences w i t h spins up t o -40 h have now been observed w i t h t h r e e successive alignments (band c r o s s i n g s ) t h a t p r o v i d e about h a l f t h e t o t a l angular momentum o f t h e nucleus. As w moves c l o s e r t o 60 ° ( l o w e r l e f t ) t h e p r o p o r t i o n of s i n g l e - p a r t i c l e t o c o l l e c t i v e a n g u l a r momentum becomes l a r g e r , and t h e r o t a t i o n a l bands become less c o l l e c t i v e w i t h s m a l l e r moments of i n e r t i a . This s i t u a t i o n p r o b a b l y occurs in n u c l e i l i k e 154Er in t h e I = 30-40 h r e g i o n 8) and in 154Dy near 9) I = 40 h, but is c e r t a i n l y the least documented of the regions of f i g . 3. F i n a l l y , at t h e lower r i g h t o f f i g . 3, t h e c o l l e c t i v e motion is v e r y weak or e n t i r e l y absent, and we now susRect many n u c l e i in t h e N = 82, Z = 64 r e g i o n are of t h i s t y p e . So f a r o n l y 147Gd has q ~ r u p o l e ~ents measured t o i n d i c a t e a nonspherical shape 2), but n u c l e i l i k e *m~Dy and ±UUGd are v e r y l i k e l y o f t h i s t y p e . I t is not so easy t o d i s t i n g u i s h these s p e c t r a from those of n u c l e i w i t h s p h e r i c a l shapes, but quadrupole moments can do t h i s , and t h e r e may be a d d i t i o n a l f e a t u r e s of t h e spectra t h a t can help (the r o t a t i o n about t h e p e r p e n d i c u l a r axes?). In any case, t h e main p o i n t here is t h a t t h e r e are c h a r a c t e r i s t i c spectra associated w i t h t h e shapes between w = O° and 60 ° , and these are r a t h e r easy t o d i s t i n g u i s h e x p e r i m e n t a l l y . Furthermore, t h e range o f s p e c t r a l types is (or can be) c o n t i n u o u s , as i t must be since y is ( o r can be) c o n t i n u o u s . I t should be recognized t h a t t h e r e is no simple path through f i g . 3 along which n u c l e i e v o l v e w i t h i n c r e a s i n g spin. I t was c l e a r in f i g . 2 t h a t t h e w = 0 t o 60 ° r e g i o n was q u i t e f l a t in t h e LDM l i m i t so t h a t s h e l l e f f e c t s determine j u s t where in t h i s range a given nucleus w i l l be. Some n u c l e i l i k e 154Dy r e c e n t l y discussed by Khoo 9~ seem t o progress from upper r i g h t t o lower l e f t and p r o b a b l y on t o lower r i g h t as t h e spin goes from 20 t o 40 h. However, i t s neighbor 152Dy s h i f t s from l o w e r - r i g h t - t y p e b e h a v i o r in t h e 20-40 h range t o some t y p e (as yet not well s p e c i f i e d ) of c o l l e c t i v e b e h a v i o r at h i g h e r sp i n~- i 0 ) . The s h e l l e f f e c t s determine such s p e c i f i c b e h a v i o r s . However, one g e n e r a l i z a t i o n we can make t h a t w i l l be i n t e r e s t i n g f o r t h e highest spin regions is t h a t more s i n g l e - p a r t i c l e angular momentum g e n e r a l l y i n d i c a t e s b e h a v i o r c l o s e r t o t h e = 60 ° l i m i t , and c o n v e r s e l y a l a r g e r f r a c t i o n of c o l l e c t i v e a n g u l a r momentum u s u a l l y means a s h i f t towards w = 0°3. 3.1
Nuclear s t r u c t u r e below ~40 h
THE NEW SPECTROSCOPY
One of t h e i m p o r t a n t t h i n g s we have learned about s t u d y i n g n u c l e i at high spins i s the importance of using t h e r o t a t i o n a l frequency, m, as a parameter r a t h e r than t h e a n g u l a r momentum, I . The reason f o r t h i s is t h a t I c o n t a i n s comparable c o n t r i b u t i o n s from two s o u r c e s - - c o l l e c t i v e r o t a t i o n and s i n g l e p a r t i c l e a l i g n m e n t . Thus, i t is not a good v a r i a b l e t o study e i t h e r b e h a v i o r . On t h e o t h e r hand, m is r e l a t e d o n l y t o t h e c o l l e c t i v e r o t a t i o n , and thus is a v a r i a b l e t h a t p r o v i d e s a p o s s i b i l i t y t o separate these two aspects of high a n g u l a r momentum states. Furthermore, although I is t h e quantized q u a n t i t y , ~ is even more r e a d i l y a c c e s s i b l e e x p e r i m e n t a l l y . For a l l but t h e lowest s p i n s , i t is adequate t o use w = E~/2, where Ey is t h e c o l l e c t i v e r o t a t i o n a l t r a n s i t i o n . There is r e a l l y n o t h i n g more r e a d l l y measured than these E~ v a l u e s . Thus our p l o t s and analyses w i l l g e n e r a l l y be in terms of t h e a n g u l a r frequency, ~,. A l a r g e amount o f work has r e c e n t l y been done in s t u d y i n g d e t a i l e d n u c l e a r l e v e l s in t h e I = 0 t o -30 h range. Our understanding of nuclear b e h a v i o r in t h i s spin r e g i o n has progressed enormously, and I want t o give.%Qu some c l u e as t o what t o expect in such s t u d i e s . IA s i n g l e l e v e l scheme, of 16Uyb, is shown in f i g . 4 on an energy vs spin p l o t z l ) . The v a r i o u s bands are connected and one sees in a d d i t i o n t o two band crossings along t h e y r a s t l i n e , a v e r y large number (shown or i m p l i e d ) above i t . The o r g a n i z a t i o n of such i n f o r m a t i o n is now r a t h e r f a r advanced, and I want t o o u t l i n e t h a t f o r you.
HIGH SPIN STATES
311c
12
a. 16+
io
,6Oyb
,~-
-
3O
38~b -
~o-
/J Ali~n mlnl 40 -
L >~
,,
38+
o
6
, / '
28 16+ 12"
f'"
4"
4~
$
alignm0n~s
~
I__2
iG+_
2
O~ ~/ 0
~
L I0
• 20 I(~)
, 30
8-
-
.
.
24 ÷
-
38*
0 40
0
Oi
02
O~ ~
x~L e09-11~7~
Fig. 4. R o t a t i o n a l band t r a j e c t o r i e s on an E vs I p l o t f o r the l e v e l s of 160yb. The observed l e v e l s are i n d i c a t e d by t h e h o r i z o n t a l marks. From r e f . 11.
04 (MeV)
05
06
~em.m~
Fig. 5. Plots of the moment of i n e r t i a ( t o p ) , spin ( m i d d l e ) , and spin alignment (bottom) vs the r o t a t i o n a ] ~§quency f o r the y r a s t sequence in ~ Er. From r e f . I .
The f i r s t step of r e d u c t i o n is shown in f i g . 5 where f o r 158E~ (very s i m i l a r t o ]60yb) the p r o p e r t i e s of t h e y r a s t sebuence are p l o t t e d l ) against m. At the t o p the moment of i n e r t i a , ~ O (defined here as I/m or approximately as 21/E~), is shown, and two s i z e a b l e d i s c o n t i n u i t i e s (a backbend and an upbend) are c l e a r . These are the band crossings I have been d i s c u s s i n g , and i t is now known t h a t the f i r s t of these at h~ ~ 0.25 MeV corresponds t o the alignment of two i13/2 neutrons and t h e second at bm ~ 0.42 MeV t o an a d d i t i o n a l alignment of two h i i 1 2 neutrons. The middle curve shows I p l o t t e d against ~, and regions corresponding t o t h r e e bands are r a t h e r e a s i l y seen, the lower two of which have been e x t r a p o l a t e d t o higher f r e q u e n c i e s (dashed l i n e s ) . The increase in aligned angular momentum f o r each band change, i , can be estimated by s u b t r a c t i n g the spin in the lower band from t h a t in the upper at a given frequency. The assumption here i s t h a t the c o l l e c t i v e c o n t r i b u t i o n s t o the two bands are the same at the same r o t a t i o n a l frequency. The bottom curve shows the aligned angular momentum f o r each case, about I0 b f o r the i13/2 neutrons and 5-6 h f o r the h i i / 2 protons. Thus, associated w i t h a band c r o s s i n g , or alignment, are t h r e e q u a n t i t i e s - - a c r i t i c a l frequency f o r the c r o s s i n g , ~c; an aligned angular momentum, i , and an i n t e r a c t i o n between the bands, V, which determines how sharp the crossing i s , i . e . , a l a r g e backbend, an upbend, or a crossing so smoothed out i t may be hard t o t e l l t h e r e was any band crossing at a l l . Part of the new spectroscopy i s t h e i d e n t i f i c a t i o n of observed band crossings w i t h those c a l c u l a t e d using these t h r e e measurable c h a r a c t e r i s t i c s . This i s , however, by no means the l i m i t of t h i s new game. The next level of a n a l y s i s can be v i s u a l i z e d using f i g . 6. Here are shown12) aligned angular momentum p l o t s f o r one band in 162yb and two in 163yb. The alignment f o r t h e y r a s t sequency of 162yb is r a t h e r s i m i l a r t o the f i r s t of i58Er, and gives alignment, c r i t ! c a l , f~equ~ncy~ and b a c k b ~ shape ( i n t e r a c t i o n ) t h a t are q u i t e comparable. The oanos ape e a t ano F in ±o~yb are s i m i l a r in t h a t the same i13/2 p a i r a l i g n s , but t h e r e is in a d d i t i o n an e x t r a odd neutron, E or F. To lowest o r d e r t h i s i1312 alignment ought t o come at the same frequency in any band ( c o n f i g u r a t i o n ) . i n which i t occurs. This is a p p r o x i m a t e l y t r u e in f i g . 6, but not q u i t e . In Ib3yb where E or F is blocked, t h e crossing frequency is s l i g h t l y lower than in 162yb where t h e r e is no b l o c k i n g . Thus in higher
312c
F.S. STEPHENS
P6-i
•
~
]
-
-
1 6 2 y b
12
163yb
......
4= v
•
F
~
-
8
A--
J 4 0
] OH
I 02
t 03 (. (MeV)
Fig. 6.
t 04
r
05
xBLBeB - ~oJo
Spin alignments vs r o t a t i o n a l frequency f o r measured level sequences of
162yb and 163yb. The odd q u a s i - p a r t i c l e o r b i t s occupied in 163yb are denoted by E and F. More d e t a i l on these c o n f i g u r a t i o n s can be found in r e f . 13. o r d e r the remaining c o n f i g u r a t i o n does a f f e c t the crossing frequency due t o r e s i d u a l i n t e r a c t i o n s among the p a r t i c l e s , and in t h i s case i t is thought t h a t most of the s h i f t is due t o changes in the p a i r i n g c o r r e l a t i o n s and thus the p a i r i n g gap. Systematic studies of these small s h i f t s due t o c o n f i g u r a t i o n have been made by G a r r e t t , Herskind, and others 13) in Copenhagen and have led t o the determination of p a i r i n g gaps f o r i n d i v i d u a l c o n f i g u r a t i o n (bands). Even more d e t a i l e d studies of t h i s t y p e may give i n f o r m a t i o n about quadrupole p a i r i n g in nuclei. I b e l i e v e i t is very s i g n i f i c a n t t h a t we have a nuclear p r o p e r t y - - a n g u l a r frequency--which we can vary f o r v i r t u a l l y any c o n f i g u r a t i o n in any nucleus and observe c e r t a i n c h a r a c t e r i s t i c f e a t u r e s - - a l i g n m e n t s . The behavior of these alignments in various c o n f i g u r a t i o n s can give i n f o r m a t i o n on many nuclear p r o p e r t i e s . This is indeed a new type of nuclear spectroscopy. 3.2
NUCLEAR QUAKES
These alignments in nuclei are not r e a l l y so d i f f e r e n t from what happens in some other areas of physics. I f we t u r n around our p e r s p e c t i v e and t h i n k of a nucleus slowing down from a high i n i t i a l spin obtained ( f o r example) in a nuclear r e a c t i o n , then the r o t a t i o n a l frequency slowly decreases, producing an increase in the r o t a t i o n a l p e r i o d . This r e g u l a r increase in p e r i o d (slowing down) is sometimes i n t e r r u p t e d by r a t h e r s i z e a b l e decreases. These correspond t o i n t e r n a l rearrangements, "nuclearquakes", and are j u s t our alignment process. I t is amusing t o compare i t w i t h another type of quake--a "starquake". Neutron stars or " p u l s a r s " also have r e g u l a r l y i n c r e a s i n g . ~ # r i o d s t h a t o c c a s i o n a l l y decrease suddenly. The slowing down of t h e nucleus Ib~Er i s compared w i t h the p u l s a r Vela in f i g . 7. The behaviors are q u i t e s i m i l a r , though the percentage changes in t h e nuclear case are much l a r g e r . Both o r d i n a t e and abscissa d i f f e r by about 20 orders of magnitude between these two cases, which i n d i c a t e s t h a t the size of the " g l i t c h " corresponds t o the amount of r e g u l a r change occurring over roughly the same number o f periods ( ~ I 0 8 ) . The p u l s a r g l i t c h e s are not too well understood at present but probably have t o do w i t h a sudden breaking of the s o l i d crust on t h e neutron s t a r . The nuclear g l i t c h is much b e t t e r understood as the udden p a i r i n g of two h i g h - j p a r t i c l e s . In the case of t h i s f i r s t backbend in ~°Er, the p a r t i c l e s are the i1312 neutrons. Above I ~ 14 t h i s p a i r of aligned p a r t i c l e s contributes -10 h along the rotation axis, but t h i s is lost below I ~ 14 when the p a r t i c l e s suddenly couple to spin nearly zero and begin t o
~
H I G H SPIN S T A T E S
313c
"G 8
'_o
"°I ./1 /
/"
O.6
-9
i,, ÷
,;..,/"
. /
20 +
Z
o!5Time (10"11,!os)
o
,!5
0.0892095
~_0~892090
'f
L
0.0892085
Fig. 7.
Jan
I Feb
I Mot 1969 XSLB2~-I0500
Plots of rotational period vs time for the nucleus 158Er (top) and the pulsar Vela (bottom).
participate in the pairing correlations. The angular momentumhas to be made up by the collective rotation, which must speed up, thereby decreasing the period. 4.
Nuclear structure "above -40 b
The previous studies have all been based on the analyses of spectra with intense resolved y-ray lines. Below about 40 h where the population following heavy-ion fusion reactions "condenses" into a few (<%10) paths, one can make the kinds of detailed spectroscopic studies just described. However, above -40~ the population is spread over too many states and the y-ray spectrum cannot at present be resolved. In studying the unresolved spectra from these highest spin states, the approach has necessarily been less detailed, involving shapes and moments of i n e r t i a . 4.1
MOMENTSOF INERTIA
As a consequence of the interplay between collective and single p a r t i c l e motions, there are a variety of moments of i n e r t i a one can measure and compare with detailed nuclear model calculations. The f i r s t distinction to make is between kinematic and dynamic values. The lowest order equation for rotational motion is the usual: h2 h2 12 E = ~ l ( I + 1) ~2--'~
(1)
where the one can generally be neglected compared with I for the spins we want to consider. A moment of i n e r t i a may be defined from the f i r s t derivative of this energy with respect to spin:
h2
= I
-- h ~
(2)
314c
F.S. STEPHENS
where ~ I ) is c a l l e d the " k i n e m a t i c " moment of i n e r t i a because i t has t o do with the motion of the system--the r a t i o of angular momentum t o angular f r e q u e n c y I t is also apparent t h a t the second d e r i v a t i v e leads t o a d e f i n i t i o n :
.#2)
/d2Ey1
d1
where ~l(2) is c a l l e d the "dynamic" moment o f i n e r t i a since i t has t o do with the way the system w i l l respond t o a f o r c e . I f t h e r e is only the k i n e t i c energy term as given in Eqn. I , these are equal; but, in general, when t h e r e are a d d i t i o n a l l-dependent terms in the Hamiltonian these two moments of i n e r t i a w i l l differ. In the present case, the C o r i o l i s f o r c e p e r t u r b s the i n t e r n a l nuclear s t r u c t u r e , g i v i n g r i s e , in lowest order, t o an ( l . j ) term, so t h a t M~z) # ,j~2). This s i t u a t i o n is not uncommon in o t h e r branches of physics. The arguments c a r r y over i n t o t r a n s l a t i o n a l motion, where p212m is analogous t o 12/2,41, and a d d i t i o n a l momentum-dependent terms in the Ham]J~onian give r i s e t o two observed masses. Bohr and Mottelson have pointed outZ"1 that an e l e c t r o n moving in a c r y s t a l l a t t i c e is a close analog, where the kinematic mass determine.~ the level d e n s i t y and r e l a t e d s t a t i s t i c a l mechanical p r o p e r t i e s ; whereas the response of the e l e c t r o n t o an e x t e r n a l force depends on a d i f f e r e n t , dynamic mass. These two moments of i n e r t i a can be defined in p r i n c i p l e f o r any sequence of states d e s i r e d , but c e r t a i n ones occur r a t h e r n a t u r a l l y in the decay processes. So long as the p a r t i c l e c o n f i g u r a t i o n is f r o z e n , so t h a t one is confined t o a band, the a p p r o p r i a t e moments of i n e r t i a a r e ~ (1) J(2) I f t h e r e is no band and ~band" p e r t u r b a t i o n (alignment, shape change, e t c . ) of the i n t e r n a l s t r u c t u r e along t h i s band, these correspond t o " c o l l e c t i v e " values, and t h i s is an approximation we w i l l g e n e r a l l y assume in the f o l l o w i n g . However, a s i n g l e decay pathway involves a sequence of bands having d i f f e r e n t alignments. Then the o v e r a l l v a r i a t i o n of spin w i t h frequency i s d i f f e r e n t and defines " e f f e c t i v e " moments of i n e r t i a (1) e f f and ,j~2) ~ff" This ~ _ _2 f) f is a s l i g h t l y d i f f e r e n t moment of i n e r t i a than has been p r e v i o u s l y defined, but seems t o be an a p p r o p r i a t e one, both e x p e r i m e n t a l l y and t h e o r e t i c a l l y . I t is defined f o r any frequency and in regions of backbends contains c o n t r i b u t i o n s from both bands, g i v i n g r i s e t o very high values.
There are several reasons f o r p r e f e r r i n g t h i s ~ . ~ :
i)
it
is easy t o
measure e x p e r i m e n t a l l y ; 2) i t can be measured with high r e s o l u t i o n (small m i n t e r v a l s ) g i v i n g more d e t a i l e d i n f o r m a t i o n ; 3) i t s i n t e g r a l gives the usual ~ ( i ) . and 4) the mathematical r e l a t i o n s h i p s we want t o use r e q u i r e an
,(2) "~band
(4)
~eff 4.2
EXPERIMENTAL DATA
For the unresolved spectra from the highest spin s t a t e s , the p o p u l a t i o n is spread over many bands in many decay sequences. Nevertheless, the average band moments of i n e r t i a can be determined by looking f g r successive r o t a t i o n a l t r a n s i t i o n s as c o r r e l a t i o n s in y-y coincidence s p e c t r a l b ) . The general p r i n c i p l e here is t h a t no two y rays in a r o t a t i o n a l sequence have the same energy, so t h a t a
HIGH SPIN STATES
315c
plot of E (1) vs E (2) should have no counts along the diagonal, "valley".
Y
(2)
Y
i.e.,
a
The width of this valley is related tO,~band. The overall spin and
y-ray energies and t h e i r variations are also measurable giving the1~verage effect i v e moments of inertia. Recently a new method has been developed ) for ^(2) from the height of the y-ray spectrum. T h i s is limited to obtaining ~eff regions of the spectrum containing only rotational E2 transitions, so the number of y rays (related to AI) in a given y-ray energy interval (related to ae) gives
L~2 ~ " and "~eff' ,(2) we can obtain a value for dl/dm or~Peff. Since we have--~2)~' ~Pbanu information about ai in these unresolved regions. The heavy lines in f i g . 8 correspond t o ~ (2) values16) for three systems eff whose principal products in the high spin region are: 160Er (solid line), 162yb (dotted l i n e ) , and 166yb (dashed l i n e ) . The general rise at low frequencies in all these nuclei is due to the quenching of the pairing correlations, and the i r r e g u l a r i t i e s below he - 0.3 MeV result from p a r t i a l l y resolved individual y-ray transitions and the known alignments (backbends), which cause several transitions to pile up at the same frequency.
The--~b 2) and values from the correlation data
are plotted as lighter lines in the regions where they have been determined. The rise in the effective moments of inertia above frequencies of 0.5 MeV seemto be associated with a drop in the band values. This suggests that alignments are becoming more important contributors of angular momentum. The higher values for the Yb (Z = 70) nuclei compared with 160Er (Z = 68) suggests that protons play an important role here, which is in accord with calculations that predict proton h9/2 and i131~ alignments in this frequency region. Thus the present, somewhat qualitative work indicates that single particle alignment and collective rotation continue t h e i r competiton to carry the angular momentummost e f f i c i e n t l y , though f i g . 8 suggests that single-particle motion carries a larger fraction at the highest spins. Accordingto the general arguments of section 2, this could i n d i c a t e a s h i f t away from y ~ 0 ° i n t o the t r i a x i a l region. i
!
i
I
i
I
7
i
,,,.." j
2oo
."P ...., ...........
/<;~;'
CM
"~
~00
~
.
V
Od
0
0.2
i
,
i
I
0.4
i
L
I
0.6
l~w (MeV)
I
I
I
0.8
XBL 823-233B
Fig. 8. 4~(e2~ as a f u n c t i o n of he f o r the systems 124Sn + 4OAr ( t h i c k s o l i d l i n e ) , 126Te + 4OAr (dotted l i n e ) , 130Te + 4OAr ( t h i c k dashed l i n e ) . Also shown are some values of~#{bZnJd'-" f o r 124Sn + 4OAr ( t h i n s o l i d l i n e s ) and 130Te + 4OAr ( t h i n dashed l i n e s ) . j(2)
I t is somewhat puzzling that these~eff values do not show any detailed structure at the highest frequencies.
An interesting explanation could be that
316c
F.S. STEPHENS
t h e r e are e s s e n t i a l l y no conserved quantum numbers at these f r e q u e n c i e s , and a l l bands behave s i m i l a r l y . But t h i s seems u n l i k e l y , both from t h e o r e t i c a l grounds and from t h e absence of h i g h l y c o r r e l a t e d y - r a y spectra ( w e l l - d e v e l o p e d v a l l e y s t r u c t u r e ) t h a t should r e s u l t . More l i k e l y t h e i r r e g u l a r i t i e s are washed out because t h e observed p o p u l a t i o n is spread o v e r many c o n f i g u r a t i o n s and a broad temperature r e g i o n . R e s t r i c t i n g these p o p u l a t i o n spreads should then r e v e a l a wealth of detailed information. We are here at t h e f o r e f r o n t o f t h e h i g h - s p i n s t u d i e s and t h e l a s t c o n c l u s i o n s (or p o s s i b i l i t i e s ) have been r a t h e r s p e c u l a t i v e . N e v e r t h e l e s s , i f we cannot e v e n t u a l l y r e s o l v e t h e y - r a y s p e c t r a , then I b e l i e v e our understanding of t h i s spin r e g i o n w i l l come from such s t u d i e s . 5.
Future prospects
The f u t u r e prospects f o r t h i s f i e l d of h i g h - s p i n n u c l e a r physics look b r i g h t j u s t now. We seem t o have a good basic understanding of t h e physics i n v o l v e d , and f u r t h e r m o r e the t h e o r e t i c a l techniques e x i s t t o c a l c u l a t e most, i f not a l l , t h e q u a n t i t i e s subject t o measurement. Progress in a f i e l d n e a r l y always comes from such c a r e f u l comparisons of e x p e r i m e n t a l r e s u l t s w i t h t h e e x p e c t a t i o n s c a l c u l a t e d from t h e best e x i s t i n g t h e o r i e s . E x p e r i m e n t a l l y t h e study of h i g h - s p i n s t a t e s has always produced i n n o v a t i v e methods. M u l t i p l i c i t y filters, sum spectrometers, and c o r r e l a t i o n techniques are a few examples. At t h i s conference we are going t o hear r e s u l t s from yet another new method. There e x i s t now two m u l t i p l e - d e t e c t o r , 4~, Nal systems, one b u i l t at Oak Ridge w i t h 72 d e t e c t o r s and the o t h e r at Heidelberg w i t h 162 d e t e c t o r s . These instruments measure n e a r l y a l l t h e y rays e m i t t e d in an event and thus g i v e , event by e v e n t , t h e t o t a l y - r a y energy and m u l t i p l i c i t y , as well as the i n d i v i d u a l y - r a y energies and a n g u l a r d i s t r i b u t i o n s . I t is r e a l l y hard t o imagine what such i n f o r m a t i o n w i l l t e l l us about t h e y - r a y cascades from the highest spin s t a t e s . I w i l l mention j u s t one p o s s i b i l i t y t h a t seems t o me both t h e most obvious and t h e most e x c i t i n g r e s u l t we might hope f o r . A simultaneous measurement of both multiplicity and t o t a l y - r a y energy enables one t o l o c a l i z e a r e g i o n of t h e ( E , I ) plane from which t h e d e e x c i t i n g y rays can be i s o l a t e d . In Fig. 9 1 have shown t h e r e g i o n d e l i m i t e d by 20% FWHM in m u l t i p l i c i t y and 15% FWHM in t o t a l energy 32
]
i
i
[
I
i
28 t/
24 20
8 4
G 0
I0
20
30
40
50
60
70
I XBL 8 2 ~ 2 6
Fig. 9. A r e g i o n o f t h e E vs I plane is shown f o r a nucleus around A = 160, where the r e g i o n decaying m a i n l y by y rays is i n d i c a t e d (between t h e y r a s t l i n e and t h e e n t r y l i m i t ) , as is t h e r e g i o n (shaded) t h a t can be l o c a l i z e d by t h e 4~ Nal b a l l s .
HIGH SPIN STATES
317c
(something l i k e t h a t e x p e c t e d ) . While t h i s is not such a small r e g i o n , i t can be located in such a way as t o i s o l a t e r a t h e r small regions of p o p u l a t i o n - - f o r example, along t h e y r a s t l i n e as i n d i c a t e d . One or two Ge d e t e c t o r s placed i n s i d e the 4~ b a l l s under these c o n d i t i o n s might be able t o resolve the c o i n c i d e n t y - r a y spectrum. Such a p o s s i b i l i t y would r e v o l u t i o n i z e our study of the highest spin s t a t e s , and b r i n g us t o the level of d e t a i l e d spectroscopy described in section 3 f o r the spin region below -30 . These Nal d e t e c t o r systems are not the only hope in t h i s f i e l d , however. The development of Compton-suppressed Ge d e t e c t o r s has proceeded r a p i d l y in the l a s t few years, p a r t i c u l a r l y at Copenhagen and Daresbury. We at Berkeley have opted t o b u i l d a system of 21 such Ge d e t e c t o r s in close p r o x i m i t y t o an a p p r o x i mately 4~ b a l l made out of bismuth germanate. A drawing of t h i s system is shown in f i g . i 0 . While our 4~ b a l l w i l l have somewhat lower r e s o l u t i o n than the /'
Fig. 10. A sketch of the d e t e c t o r system under c o n s t r u c t i o n at Berkeley, which c o n s i s t s o f an inner -4x b a l l made of 44 elements of bismuth germanate, and an a r r a y of 21 Compton-suppressed Ge d e t e c t o r s outside t h i s b a l l .
e x i s t i n g 4~ Nal b a l l s , we hope t o compensate w i t h the power of the Ge a r r a y , which w i l l take Compton-suppressed quadrupole coincidences at a r a t e comparable t o t h a t at which most e x i s t i n g Ge arrays take double coincidences. I f the high r e s o l u t i o n in the ( E , I ) plane of t h e Nal b a l l s should f a i l t o produce resolved spectra from the highest spin s t a t e s , we f e e l t h e r e is hope t h a t such an instrument might. In any case, i t is i d e a l l y suited f o r a wide v a r i e t y of nuclear spectroscopic studies. I am c o n f i d e n t t h a t over the coming years these 4~ systems w i l l teach us many t h i n g s about h i g h - s p i n s t a t e s . This work was supported by the D i r e c t o r , O f f i c e of Energy Research, D i v i s i o n of Nuclear Physics of t h e O f f i c e of High Energy and Nuclear Physics of t h e U.S. Department o f Energy under Contract DE-ACO3-76SFO0098.
318c
F.S. STEPHENS References
i. 2.
3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
J. Burde, E.L. Dines, S. Shih, R.M. Diamond, J.E. Draper, K.H. Lindenberger, C. Schuck, and F.S. Stephens, Phys. Rev. Lett. 48 (1982) 530 O. Hausser, H.-E. Mahnke, J.F. Sharpey-Schafer, M.C. Swanson, P. Taras, D. Ward, H.R. Andrews, and T.K. Alexander, Phys. Rev. Lett. 44 (1980) 132: O. Hausser, H.-E. Mahnke, J.F. Sharpey-Schafer, M.L. Swanson, P. Taras, D. Ward, H.R. Andrews, and T.K. Alexander, Phys. Rev. Lett. 44 (1980) 132: O. Bakander, C. Baktash, J. Borggreen, J.B. Jensen, J. Kownacki, J. Pedersen, G. Sletten, D. Ward, H.R. Andrews, O. Hausser, P. Skensved, and P. Taras, preprint (1982) S. Cohen, F. P l a s i l , and W.J. Swiatecki, Ann. Phys. 82 (1974) 557 A. Bohr and B.R. Mottelson, Mat. Fys. Medd. Dan. Vid~--Selsk., 3(], no. 2 (1955) A. Bohr and B.R. Mottelson, Nuclear Structure, vol. 2. (Benjamin, Reading, Mass., 1975) p. 80 A. Bohr, Mat. Fys. Medd. Dan. Vid. Selsk., 2__66,no. 14 (1952) A. Johnson, H. Ryde, and J. Sztarkier, Phys. Lett. 34B (1971) 605 C. Baktash, E. der Mateosian, O.C. Kistner, and A.W. Sunyar, Phys. Rev. Lett. 42 (1979) 637 A. Pakkanen, Y.H. Chung, P.J. Daly, S.R. Faber, H. Helppi, J. Wilson, P. Chowdhury, T.C. Khoo, I. Ahmad, J. Borggreen, Z.W. Grabowski, and D.C. Radford, Phys. Rev. Lett. 48 (1982) 1530 B. Hass, H.R. Andrews, O. Hausser, D. Horn, J.F. Sharpey-Schafer, P. Taras, W. Trautmann, D. Ward, T.L. Khoo, and R.K. Smither, Phys. Lett. B84 (1979) 178 B. Herskind, J. de Physique 4_!I (1980) CI0-I06 B. Herskind, private communication (1982) J.D. Garrett and J.J. Gaardhoje, XIV Masurian Summer School on Nuclear Physics (Mikolajki, Poland, 1980) A. Bohr and B.R. Mottelson', Physica Scripta 24 (1981) 71 O. Andersen, J.D. Garrett, G.B. Hagemann, B. Herskind, D.C. H i l l i s , and L.L. Riedinger, Phys. Rev. Lett. 43 (1979) 687 M.A. Deleplanque, H.J. Kbrne-~-, H. Kluge, A.O. Macchiavelli, N. Bendjaballah, R.M. Diamond, and F.S. Stephens, submitted to Phys. Rev. Lett.
307c
LBL-14824 HIGH SPIN STATES
F.S. Stephens Nuclear Science Division, Lawrence Berkeley Laboratory University of C a l i f o r n i a , Berkeley, CA 94720 Abstract: Nuclei generate high spins by two methods, alignment of single p a r t i c l e angular momentum and c o l l e c t i v e r o t a t i o n . The competition of these two modes is discussed f i r s t in general terms, then in the spin region below ~40 h, and f i n a l l y fo r the highest spins 40 ~ I ~ 65 Some prognosis f o r future experiments in t h i s f i e l d is given. 1.
Introduction
Nuclei can generate high angular momentum either by alignment along a common axis of the angular momentum of several individual nucleons or by a c o l l e c t i v e r o t a t i o n of the nucleus as a whole. Recent developments in t h i s f i e l d have been centered on understanding the competition of these two modes. This can be i l l u s trated in f i g . i , where level schemes of 158Er and 147Gd are shown1,2). The 158Er scheme is quite regular and the dominant behavior is c o l l e c t i v e r o t a t i o n of a prolate-deformed nucleus as is i l l u s t r a t e d at the l e f t of f i g . I . The 147Gd scheme is quite i r r e g u l a r , with complicated decay pathways and isomeric states (dark l e v e l s ) . I t s dominant behavior is c e r t a i n l y s i n g l e - p a r t i c l e alignment, as is i l l u s t r a t e d at the r i g h t of f i g . i . Yet both of these schemes contain elements of the other type of behavior. There are i r r e g u l a r i t i e s in the 158Er r o t a t i o n a l pattern at spins around 16 and 26, which correspond to single p a r t i c l e alignments, and the 49/2+ isomer at 8.6 MeV in ]47Gd has a quadrupole moment that suggests that the aligned p a r t i c l e s are p o l a r i z i n g the core so a c o l l e c t i v e oblate shape is developing. In t h i s t a l k I w i l l discuss our present understanding of the i n t e r p l a y of these two types of behavior, f i r s t as to the physics involved and then in the experimental data f o r nuclei of t h i s mass region. E(MeV) 12-
28: 52+~[
z
I0
T
49+
B-
6
I2h ÷
13+ g 7-
15BEt
14"7Gd
2
Fig. 1 Level scheme for 158Er and 147Gd, together with i l l u s t r a t i o n s of the dominant source of angular momentum for each case.
308c
F.S. STEPHENS
2. 2.]
Physics of high spin s t a t e s
NUCLEAR SHAPES
One of t h e most i m p o r t a n t f a c t o r s in d e t e r m i n i n g t h e physics of h i g h - s p i n s t a t e s is simply the r o t a t i o n a l b e h a v i o r of r i g i d c l a s s i c a l o b j e c t s . In f i g . 2 t h e moment o f i n e r t i a of such an o b j e c t is compared w i t h t h a t of a r i g i d sphere ( s o l i d l i n e s ) f o r a v a r i e t y of shapes and r o t a t i o n a l axes. The shape and axis is defined by y, which v a r i e s from -120 ° t o 60 ° as t h e o b j e c t v a r i e s from a p r o l a t e shape r o t a t i n g about i t s symmetry a x i s , through o b l a t e and p r o l a t e shapes r o t a t i n g about axes p e r p e n d i c u l a r t o the symmetry a x i s , t o an o b l a t e shape r o t a t i n g about i t s symmetry a x i s . The deformation is given in terms of a q u a n t i t y ~, which is t o lowest o r d e r j u s t AR/R. Values of ¢ around 0.3 are t y p i c a l f o r t h e f a m i l i a r deformed r a r e - e a r t h and a c t i n i d e n u c l e i . The l a r g e s t moments of i n e r t i a , and t h e r e f o r e t h e lowest r o t a t i o n a l e n e r g i e s , occur f o r the range of shapes between y = 0 ° and 60 ° . The v e r y l a r g e s t moment of i n e r t i a is f o r y = 60 ° , an o b l a t e shape r o t a t i n g around i t s symmetry a x i s , and i t is f o r t h i s reason t h e e a r t h has such a shape. The f u l l l i q u i d - d r o p model (LDM) t r e a t m e n t of a r o t a t i n g nucleus 3) includes volume, surface, and Coulomb e n e r g i e s , in a d d i t i o n t o these c l a s s i c a l r o t o r c o n s i d e r a t i o n s , and is shown by t h e dots in f i g . 2. I t is apparent t h a t t h e r e is no strong shape preference in these a d d i t i o n a l LDM terms, so t h a t simple c l a s s i c a l mechanics determine t h e l i q u i d - d r o p shapes. This is i m p o r t a n t , since t h e l i q u i d - d r o p model is our best guide t o such macroscopic n u c l e a r p r o p e r t i e s and is even t h e l i m i t t o which some of t h e microscopic models are n o r m a l i z e d .
~-o6
P4
i
o
e-C~
t2
4
o~>
I0
*5 08 +10 .15
o6 -,~o
-do
G
~o
F20
XBL. 808-11414
Fig. 2. The r a t i o of t h e moment o f i n e r t i a of a r i g i d e l l i p s o i d t o t h a t of a r i g i d sphere vs t h e shape parameter y f o r two values of t h e d e f o r m a t i o n c : 0.3 and ¢ = 0 . 6 . The r i g h t - h a n d scale g i v e s t h e d i f f e r e n c e in r o t a t i o n a l energy in MeV f o r a nucleus w i t h A : 160 and I = 60. The dots g i v e t h e r a t i o s f o r t h e t o t a l l i q u i d - d r o p energy ( r o t a t i o n + surface + Coulomb) o f t h e nucleus. In o r d e r t o see how s i g n i f i c a n t these c l a s s i c a l shape e f f e c t s are, one must choose a mass and spin, and f o r A = 160 and I = 60 h, an energy scale is given on the r i g h t side of f i g . 2. The v a r i a t i o n f o r c = 0.3 of about 10 MeV is l a r g e r than t y p i c a l s h e l l e f f e c t s (-3 MeV) so t h a t f o r t h i s spin t h e e f f e c t s considered here should be dominant. The r o t a t i o n a l energy v a r i e s as 12 so t h a t , f o r 30 h, s h e l l e f f e c t s and these c l a s s i c a l shape e f f e c t s should be about e q u i v a l e n t , and below -20 ~ t h e s h e l l e f f e c t s w i l l dominate. The arguments made here would seem t o apply o n l y f o r c o l l e c t i v e n u c l e a r r o t a t i o n s , and even then o n l y i f t h e n u c l e a r moment o f i n e r t i a has t h e r i g i d body v a l u e , n e i t h e r o f which is o b v i o u s l y t h e
HIGH SPIN STATES
309c
case. In f a c t , however, most people do b e l i e v e t h a t r o t a t i n g n u c l e i at high spins w i l l , on average, have the r i g i d - b o d y moment of i n e r t i a , and t h i s has been shown t o be t h e case f o r an a n i s o t r o p i c harmonic o s c i l l a t o r p o t e n t i a l and independent p a r t i c l e motion 4) . The s m a l l e r moments of i n e r t i a observed at low splns are due l a r g e l y t o t h e p a i r i n g c o r r e l a t i o n s , which should be quenched above -30 h. Furthermore, even in n o n c o l l e c t i v e cases, i t has been shown ( f o r a.Fermi gas) t h a t t h e t r a j e c t o r y of lowest l e v e l s f o l l o w s t h a t given by r o t a t i n g t h e a p p r o p r i a t e l y shaped r i g i d body 5). Thus, these v e r y simple arguments should be v a l i d and shapes in t h e y = 0-60 ° range should dominate at high s p i n , i . e . , above -30 h in t h e A = 160 r e g i o n . Several t y p e s o f m i c r o s c o p i c c a l c u l a t i o n s have now been c a r r i e d out f o r n u c l e i in t h i s r e g i o n and a l l of them agree t h a t t h e y = 0-60 ° range should dominate at high s p i n s , though t h e models show some d i f f e r e n c e s w i t h i n t h e y = 0-60 ° range. 2.2
LEVEL STRUCTURES
A general q u e s t i o n a r i s e s as t o how one can r e c o g n i z e these shapes e x p e r i m e n t a l l y . That i s , what kind of n u c l e a r s t r u c t u r e is expected f o r shapes in t h i s y = 0-60 ° r e g i o n . I t has been recognized since 1952 t h a t a deformed nucleus can r o t a t e c o l l e c t i v e l y around an a x i s p e r p e n d i c u l a r t o t h e symmetry a x i s 6). The p r o l a t e y = 0 ° shape is o f t h i s t y p e and e s s e n t i a l l y a l l t h e r o t a t i o n a l n u c l e i known have y - v a l u e s equal t o or near 0 °. On t h e o t h e r hand, a nucleus cannot r o t a t e c o l l e c t i v e l y around a symmetry a x i s : those degrees of freedom are c o n t a i n e d in t h e s i n g l e - p a r t i c l e m o t i o n . Thus t h e y = 60 ° o b l a t e n u c l e i do not have c o l l e c t i v e r o t a t i o n , but b u i l d up t h e i r a n g u l a r momentum by a l i g n i n g along a common a x i s t h e c o n t r i b u t i o n of v a r i o u s s i n g l e p a r t i c l e s . These are t h e two basic b e h a v i o r s discussed in Section I . The k i n d o f s t r u c t u r e associated w i t h the t r i a x i a l n u c l e a r shapes between y = 0 ° and 60 ° has been e l u c i d a t e d r e c e n t l y - - s i n c e t h e f i r s t clues t o t h i s were found in t h e backbending phenomenon d i s c o v e r e d / ) in 1971. The s i t u a t i o n is d e p i c t e d in f i g . 3. For e x a c t l y a x i a l l y symmetric shapes (upper l e f t ) o n l y c o l l e c t i v e r o t a t i o n is p o s s i b l e , and d i f f e r e n t c o n f i g u r a t i o n s g i v e r i s e t o bands t h a t extend over broad r e g i o n s of s p i n . In f a c t , what is observed t o happen is i n d i c a t e d at t h e upper 2O
'2//
15 IO
5
.
.
.
.
t
I : Zjo + ~®co,
w 15
~
',
1
7\, -
f
I
I
/
jo ~)"
v
B
z
I¢
,/
/,( o
ig"
//°
/I/ 0
0
20
40
0
I
20
4~) XBLB04~44
Fig. 3. Schematic excitation energy vs spin plots for various relative amounts of collective angular momentumand single-particle rotation-aligned angular momentum. Bandhead(pure s i n g l e - p a r t i c l e ) energies are shown in the lower two panels, The solid curves correspond to real bands, whereas the dashed curve is the envelope of the real bands.
310c
F.S. STEPHENS
r i g h t , where bands w i t h d i f f e r e n t c o n f i g u r a t i o n have d i f f e r e n t amounts of s i n g l e - p a r t i c l e angular momentum a l i g n e d w i t h t h e r o t a t i o n axis and t h e r e b y g i v e r i s e t o s l i g h t l y n o n a x i a l shapes and a p a t t e r n of crossing bands. Sequences w i t h spins up t o -40 h have now been observed w i t h t h r e e successive alignments (band c r o s s i n g s ) t h a t p r o v i d e about h a l f t h e t o t a l angular momentum o f t h e nucleus. As w moves c l o s e r t o 60 ° ( l o w e r l e f t ) t h e p r o p o r t i o n of s i n g l e - p a r t i c l e t o c o l l e c t i v e a n g u l a r momentum becomes l a r g e r , and t h e r o t a t i o n a l bands become less c o l l e c t i v e w i t h s m a l l e r moments of i n e r t i a . This s i t u a t i o n p r o b a b l y occurs in n u c l e i l i k e 154Er in t h e I = 30-40 h r e g i o n 8) and in 154Dy near 9) I = 40 h, but is c e r t a i n l y the least documented of the regions of f i g . 3. F i n a l l y , at t h e lower r i g h t o f f i g . 3, t h e c o l l e c t i v e motion is v e r y weak or e n t i r e l y absent, and we now susRect many n u c l e i in t h e N = 82, Z = 64 r e g i o n are of t h i s t y p e . So f a r o n l y 147Gd has q ~ r u p o l e ~ents measured t o i n d i c a t e a nonspherical shape 2), but n u c l e i l i k e *m~Dy and ±UUGd are v e r y l i k e l y o f t h i s t y p e . I t is not so easy t o d i s t i n g u i s h these s p e c t r a from those of n u c l e i w i t h s p h e r i c a l shapes, but quadrupole moments can do t h i s , and t h e r e may be a d d i t i o n a l f e a t u r e s of t h e spectra t h a t can help (the r o t a t i o n about t h e p e r p e n d i c u l a r axes?). In any case, t h e main p o i n t here is t h a t t h e r e are c h a r a c t e r i s t i c spectra associated w i t h t h e shapes between w = O° and 60 ° , and these are r a t h e r easy t o d i s t i n g u i s h e x p e r i m e n t a l l y . Furthermore, t h e range o f s p e c t r a l types is (or can be) c o n t i n u o u s , as i t must be since y is ( o r can be) c o n t i n u o u s . I t should be recognized t h a t t h e r e is no simple path through f i g . 3 along which n u c l e i e v o l v e w i t h i n c r e a s i n g spin. I t was c l e a r in f i g . 2 t h a t t h e w = 0 t o 60 ° r e g i o n was q u i t e f l a t in t h e LDM l i m i t so t h a t s h e l l e f f e c t s determine j u s t where in t h i s range a given nucleus w i l l be. Some n u c l e i l i k e 154Dy r e c e n t l y discussed by Khoo 9~ seem t o progress from upper r i g h t t o lower l e f t and p r o b a b l y on t o lower r i g h t as t h e spin goes from 20 t o 40 h. However, i t s neighbor 152Dy s h i f t s from l o w e r - r i g h t - t y p e b e h a v i o r in t h e 20-40 h range t o some t y p e (as yet not well s p e c i f i e d ) of c o l l e c t i v e b e h a v i o r at h i g h e r sp i n~- i 0 ) . The s h e l l e f f e c t s determine such s p e c i f i c b e h a v i o r s . However, one g e n e r a l i z a t i o n we can make t h a t w i l l be i n t e r e s t i n g f o r t h e highest spin regions is t h a t more s i n g l e - p a r t i c l e angular momentum g e n e r a l l y i n d i c a t e s b e h a v i o r c l o s e r t o t h e = 60 ° l i m i t , and c o n v e r s e l y a l a r g e r f r a c t i o n of c o l l e c t i v e a n g u l a r momentum u s u a l l y means a s h i f t towards w = 0°3. 3.1
Nuclear s t r u c t u r e below ~40 h
THE NEW SPECTROSCOPY
One of t h e i m p o r t a n t t h i n g s we have learned about s t u d y i n g n u c l e i at high spins i s the importance of using t h e r o t a t i o n a l frequency, m, as a parameter r a t h e r than t h e a n g u l a r momentum, I . The reason f o r t h i s is t h a t I c o n t a i n s comparable c o n t r i b u t i o n s from two s o u r c e s - - c o l l e c t i v e r o t a t i o n and s i n g l e p a r t i c l e a l i g n m e n t . Thus, i t is not a good v a r i a b l e t o study e i t h e r b e h a v i o r . On t h e o t h e r hand, m is r e l a t e d o n l y t o t h e c o l l e c t i v e r o t a t i o n , and thus is a v a r i a b l e t h a t p r o v i d e s a p o s s i b i l i t y t o separate these two aspects of high a n g u l a r momentum states. Furthermore, although I is t h e quantized q u a n t i t y , ~ is even more r e a d i l y a c c e s s i b l e e x p e r i m e n t a l l y . For a l l but t h e lowest s p i n s , i t is adequate t o use w = E~/2, where Ey is t h e c o l l e c t i v e r o t a t i o n a l t r a n s i t i o n . There is r e a l l y n o t h i n g more r e a d l l y measured than these E~ v a l u e s . Thus our p l o t s and analyses w i l l g e n e r a l l y be in terms of t h e a n g u l a r frequency, ~,. A l a r g e amount o f work has r e c e n t l y been done in s t u d y i n g d e t a i l e d n u c l e a r l e v e l s in t h e I = 0 t o -30 h range. Our understanding of nuclear b e h a v i o r in t h i s spin r e g i o n has progressed enormously, and I want t o give.%Qu some c l u e as t o what t o expect in such s t u d i e s . IA s i n g l e l e v e l scheme, of 16Uyb, is shown in f i g . 4 on an energy vs spin p l o t z l ) . The v a r i o u s bands are connected and one sees in a d d i t i o n t o two band crossings along t h e y r a s t l i n e , a v e r y large number (shown or i m p l i e d ) above i t . The o r g a n i z a t i o n of such i n f o r m a t i o n is now r a t h e r f a r advanced, and I want t o o u t l i n e t h a t f o r you.
HIGH SPIN STATES
311c
12
a. 16+
io
,6Oyb
,~-
-
3O
38~b -
~o-
/J Ali~n mlnl 40 -
L >~
,,
38+
o
6
, / '
28 16+ 12"
f'"
4"
4~
$
alignm0n~s
~
I__2
iG+_
2
O~ ~/ 0
~
L I0
• 20 I(~)
, 30
8-
-
.
.
24 ÷
-
38*
0 40
0
Oi
02
O~ ~
x~L e09-11~7~
Fig. 4. R o t a t i o n a l band t r a j e c t o r i e s on an E vs I p l o t f o r the l e v e l s of 160yb. The observed l e v e l s are i n d i c a t e d by t h e h o r i z o n t a l marks. From r e f . 11.
04 (MeV)
05
06
~em.m~
Fig. 5. Plots of the moment of i n e r t i a ( t o p ) , spin ( m i d d l e ) , and spin alignment (bottom) vs the r o t a t i o n a ] ~§quency f o r the y r a s t sequence in ~ Er. From r e f . I .
The f i r s t step of r e d u c t i o n is shown in f i g . 5 where f o r 158E~ (very s i m i l a r t o ]60yb) the p r o p e r t i e s of t h e y r a s t sebuence are p l o t t e d l ) against m. At the t o p the moment of i n e r t i a , ~ O (defined here as I/m or approximately as 21/E~), is shown, and two s i z e a b l e d i s c o n t i n u i t i e s (a backbend and an upbend) are c l e a r . These are the band crossings I have been d i s c u s s i n g , and i t is now known t h a t the f i r s t of these at h~ ~ 0.25 MeV corresponds t o the alignment of two i13/2 neutrons and t h e second at bm ~ 0.42 MeV t o an a d d i t i o n a l alignment of two h i i 1 2 neutrons. The middle curve shows I p l o t t e d against ~, and regions corresponding t o t h r e e bands are r a t h e r e a s i l y seen, the lower two of which have been e x t r a p o l a t e d t o higher f r e q u e n c i e s (dashed l i n e s ) . The increase in aligned angular momentum f o r each band change, i , can be estimated by s u b t r a c t i n g the spin in the lower band from t h a t in the upper at a given frequency. The assumption here i s t h a t the c o l l e c t i v e c o n t r i b u t i o n s t o the two bands are the same at the same r o t a t i o n a l frequency. The bottom curve shows the aligned angular momentum f o r each case, about I0 b f o r the i13/2 neutrons and 5-6 h f o r the h i i / 2 protons. Thus, associated w i t h a band c r o s s i n g , or alignment, are t h r e e q u a n t i t i e s - - a c r i t i c a l frequency f o r the c r o s s i n g , ~c; an aligned angular momentum, i , and an i n t e r a c t i o n between the bands, V, which determines how sharp the crossing i s , i . e . , a l a r g e backbend, an upbend, or a crossing so smoothed out i t may be hard t o t e l l t h e r e was any band crossing at a l l . Part of the new spectroscopy i s t h e i d e n t i f i c a t i o n of observed band crossings w i t h those c a l c u l a t e d using these t h r e e measurable c h a r a c t e r i s t i c s . This i s , however, by no means the l i m i t of t h i s new game. The next level of a n a l y s i s can be v i s u a l i z e d using f i g . 6. Here are shown12) aligned angular momentum p l o t s f o r one band in 162yb and two in 163yb. The alignment f o r t h e y r a s t sequency of 162yb is r a t h e r s i m i l a r t o the f i r s t of i58Er, and gives alignment, c r i t ! c a l , f~equ~ncy~ and b a c k b ~ shape ( i n t e r a c t i o n ) t h a t are q u i t e comparable. The oanos ape e a t ano F in ±o~yb are s i m i l a r in t h a t the same i13/2 p a i r a l i g n s , but t h e r e is in a d d i t i o n an e x t r a odd neutron, E or F. To lowest o r d e r t h i s i1312 alignment ought t o come at the same frequency in any band ( c o n f i g u r a t i o n ) . i n which i t occurs. This is a p p r o x i m a t e l y t r u e in f i g . 6, but not q u i t e . In Ib3yb where E or F is blocked, t h e crossing frequency is s l i g h t l y lower than in 162yb where t h e r e is no b l o c k i n g . Thus in higher
312c
F.S. STEPHENS
P6-i
•
~
]
-
-
1 6 2 y b
12
163yb
......
4= v
•
F
~
-
8
A--
J 4 0
] OH
I 02
t 03 (. (MeV)
Fig. 6.
t 04
r
05
xBLBeB - ~oJo
Spin alignments vs r o t a t i o n a l frequency f o r measured level sequences of
162yb and 163yb. The odd q u a s i - p a r t i c l e o r b i t s occupied in 163yb are denoted by E and F. More d e t a i l on these c o n f i g u r a t i o n s can be found in r e f . 13. o r d e r the remaining c o n f i g u r a t i o n does a f f e c t the crossing frequency due t o r e s i d u a l i n t e r a c t i o n s among the p a r t i c l e s , and in t h i s case i t is thought t h a t most of the s h i f t is due t o changes in the p a i r i n g c o r r e l a t i o n s and thus the p a i r i n g gap. Systematic studies of these small s h i f t s due t o c o n f i g u r a t i o n have been made by G a r r e t t , Herskind, and others 13) in Copenhagen and have led t o the determination of p a i r i n g gaps f o r i n d i v i d u a l c o n f i g u r a t i o n (bands). Even more d e t a i l e d studies of t h i s t y p e may give i n f o r m a t i o n about quadrupole p a i r i n g in nuclei. I b e l i e v e i t is very s i g n i f i c a n t t h a t we have a nuclear p r o p e r t y - - a n g u l a r frequency--which we can vary f o r v i r t u a l l y any c o n f i g u r a t i o n in any nucleus and observe c e r t a i n c h a r a c t e r i s t i c f e a t u r e s - - a l i g n m e n t s . The behavior of these alignments in various c o n f i g u r a t i o n s can give i n f o r m a t i o n on many nuclear p r o p e r t i e s . This is indeed a new type of nuclear spectroscopy. 3.2
NUCLEAR QUAKES
These alignments in nuclei are not r e a l l y so d i f f e r e n t from what happens in some other areas of physics. I f we t u r n around our p e r s p e c t i v e and t h i n k of a nucleus slowing down from a high i n i t i a l spin obtained ( f o r example) in a nuclear r e a c t i o n , then the r o t a t i o n a l frequency slowly decreases, producing an increase in the r o t a t i o n a l p e r i o d . This r e g u l a r increase in p e r i o d (slowing down) is sometimes i n t e r r u p t e d by r a t h e r s i z e a b l e decreases. These correspond t o i n t e r n a l rearrangements, "nuclearquakes", and are j u s t our alignment process. I t is amusing t o compare i t w i t h another type of quake--a "starquake". Neutron stars or " p u l s a r s " also have r e g u l a r l y i n c r e a s i n g . ~ # r i o d s t h a t o c c a s i o n a l l y decrease suddenly. The slowing down of t h e nucleus Ib~Er i s compared w i t h the p u l s a r Vela in f i g . 7. The behaviors are q u i t e s i m i l a r , though the percentage changes in t h e nuclear case are much l a r g e r . Both o r d i n a t e and abscissa d i f f e r by about 20 orders of magnitude between these two cases, which i n d i c a t e s t h a t the size of the " g l i t c h " corresponds t o the amount of r e g u l a r change occurring over roughly the same number o f periods ( ~ I 0 8 ) . The p u l s a r g l i t c h e s are not too well understood at present but probably have t o do w i t h a sudden breaking of the s o l i d crust on t h e neutron s t a r . The nuclear g l i t c h is much b e t t e r understood as the udden p a i r i n g of two h i g h - j p a r t i c l e s . In the case of t h i s f i r s t backbend in ~°Er, the p a r t i c l e s are the i1312 neutrons. Above I ~ 14 t h i s p a i r of aligned p a r t i c l e s contributes -10 h along the rotation axis, but t h i s is lost below I ~ 14 when the p a r t i c l e s suddenly couple to spin nearly zero and begin t o
~
H I G H SPIN S T A T E S
313c
"G 8
'_o
"°I ./1 /
/"
O.6
-9
i,, ÷
,;..,/"
. /
20 +
Z
o!5Time (10"11,!os)
o
,!5
0.0892095
~_0~892090
'f
L
0.0892085
Fig. 7.
Jan
I Feb
I Mot 1969 XSLB2~-I0500
Plots of rotational period vs time for the nucleus 158Er (top) and the pulsar Vela (bottom).
participate in the pairing correlations. The angular momentumhas to be made up by the collective rotation, which must speed up, thereby decreasing the period. 4.
Nuclear structure "above -40 b
The previous studies have all been based on the analyses of spectra with intense resolved y-ray lines. Below about 40 h where the population following heavy-ion fusion reactions "condenses" into a few (<%10) paths, one can make the kinds of detailed spectroscopic studies just described. However, above -40~ the population is spread over too many states and the y-ray spectrum cannot at present be resolved. In studying the unresolved spectra from these highest spin states, the approach has necessarily been less detailed, involving shapes and moments of i n e r t i a . 4.1
MOMENTSOF INERTIA
As a consequence of the interplay between collective and single p a r t i c l e motions, there are a variety of moments of i n e r t i a one can measure and compare with detailed nuclear model calculations. The f i r s t distinction to make is between kinematic and dynamic values. The lowest order equation for rotational motion is the usual: h2 h2 12 E = ~ l ( I + 1) ~2--'~
(1)
where the one can generally be neglected compared with I for the spins we want to consider. A moment of i n e r t i a may be defined from the f i r s t derivative of this energy with respect to spin:
h2
= I
-- h ~
(2)
314c
F.S. STEPHENS
where ~ I ) is c a l l e d the " k i n e m a t i c " moment of i n e r t i a because i t has t o do with the motion of the system--the r a t i o of angular momentum t o angular f r e q u e n c y I t is also apparent t h a t the second d e r i v a t i v e leads t o a d e f i n i t i o n :
.#2)
/d2Ey1
d1
where ~l(2) is c a l l e d the "dynamic" moment o f i n e r t i a since i t has t o do with the way the system w i l l respond t o a f o r c e . I f t h e r e is only the k i n e t i c energy term as given in Eqn. I , these are equal; but, in general, when t h e r e are a d d i t i o n a l l-dependent terms in the Hamiltonian these two moments of i n e r t i a w i l l differ. In the present case, the C o r i o l i s f o r c e p e r t u r b s the i n t e r n a l nuclear s t r u c t u r e , g i v i n g r i s e , in lowest order, t o an ( l . j ) term, so t h a t M~z) # ,j~2). This s i t u a t i o n is not uncommon in o t h e r branches of physics. The arguments c a r r y over i n t o t r a n s l a t i o n a l motion, where p212m is analogous t o 12/2,41, and a d d i t i o n a l momentum-dependent terms in the Ham]J~onian give r i s e t o two observed masses. Bohr and Mottelson have pointed outZ"1 that an e l e c t r o n moving in a c r y s t a l l a t t i c e is a close analog, where the kinematic mass determine.~ the level d e n s i t y and r e l a t e d s t a t i s t i c a l mechanical p r o p e r t i e s ; whereas the response of the e l e c t r o n t o an e x t e r n a l force depends on a d i f f e r e n t , dynamic mass. These two moments of i n e r t i a can be defined in p r i n c i p l e f o r any sequence of states d e s i r e d , but c e r t a i n ones occur r a t h e r n a t u r a l l y in the decay processes. So long as the p a r t i c l e c o n f i g u r a t i o n is f r o z e n , so t h a t one is confined t o a band, the a p p r o p r i a t e moments of i n e r t i a a r e ~ (1) J(2) I f t h e r e is no band and ~band" p e r t u r b a t i o n (alignment, shape change, e t c . ) of the i n t e r n a l s t r u c t u r e along t h i s band, these correspond t o " c o l l e c t i v e " values, and t h i s is an approximation we w i l l g e n e r a l l y assume in the f o l l o w i n g . However, a s i n g l e decay pathway involves a sequence of bands having d i f f e r e n t alignments. Then the o v e r a l l v a r i a t i o n of spin w i t h frequency i s d i f f e r e n t and defines " e f f e c t i v e " moments of i n e r t i a (1) e f f and ,j~2) ~ff" This ~ _ _2 f) f is a s l i g h t l y d i f f e r e n t moment of i n e r t i a than has been p r e v i o u s l y defined, but seems t o be an a p p r o p r i a t e one, both e x p e r i m e n t a l l y and t h e o r e t i c a l l y . I t is defined f o r any frequency and in regions of backbends contains c o n t r i b u t i o n s from both bands, g i v i n g r i s e t o very high values.
There are several reasons f o r p r e f e r r i n g t h i s ~ . ~ :
i)
it
is easy t o
measure e x p e r i m e n t a l l y ; 2) i t can be measured with high r e s o l u t i o n (small m i n t e r v a l s ) g i v i n g more d e t a i l e d i n f o r m a t i o n ; 3) i t s i n t e g r a l gives the usual ~ ( i ) . and 4) the mathematical r e l a t i o n s h i p s we want t o use r e q u i r e an
,(2) "~band
(4)
~eff 4.2
EXPERIMENTAL DATA
For the unresolved spectra from the highest spin s t a t e s , the p o p u l a t i o n is spread over many bands in many decay sequences. Nevertheless, the average band moments of i n e r t i a can be determined by looking f g r successive r o t a t i o n a l t r a n s i t i o n s as c o r r e l a t i o n s in y-y coincidence s p e c t r a l b ) . The general p r i n c i p l e here is t h a t no two y rays in a r o t a t i o n a l sequence have the same energy, so t h a t a
HIGH SPIN STATES
315c
plot of E (1) vs E (2) should have no counts along the diagonal, "valley".
Y
(2)
Y
i.e.,
a
The width of this valley is related tO,~band. The overall spin and
y-ray energies and t h e i r variations are also measurable giving the1~verage effect i v e moments of inertia. Recently a new method has been developed ) for ^(2) from the height of the y-ray spectrum. T h i s is limited to obtaining ~eff regions of the spectrum containing only rotational E2 transitions, so the number of y rays (related to AI) in a given y-ray energy interval (related to ae) gives
L~2 ~ " and "~eff' ,(2) we can obtain a value for dl/dm or~Peff. Since we have--~2)~' ~Pbanu information about ai in these unresolved regions. The heavy lines in f i g . 8 correspond t o ~ (2) values16) for three systems eff whose principal products in the high spin region are: 160Er (solid line), 162yb (dotted l i n e ) , and 166yb (dashed l i n e ) . The general rise at low frequencies in all these nuclei is due to the quenching of the pairing correlations, and the i r r e g u l a r i t i e s below he - 0.3 MeV result from p a r t i a l l y resolved individual y-ray transitions and the known alignments (backbends), which cause several transitions to pile up at the same frequency.
The--~b 2) and values from the correlation data
are plotted as lighter lines in the regions where they have been determined. The rise in the effective moments of inertia above frequencies of 0.5 MeV seemto be associated with a drop in the band values. This suggests that alignments are becoming more important contributors of angular momentum. The higher values for the Yb (Z = 70) nuclei compared with 160Er (Z = 68) suggests that protons play an important role here, which is in accord with calculations that predict proton h9/2 and i131~ alignments in this frequency region. Thus the present, somewhat qualitative work indicates that single particle alignment and collective rotation continue t h e i r competiton to carry the angular momentummost e f f i c i e n t l y , though f i g . 8 suggests that single-particle motion carries a larger fraction at the highest spins. Accordingto the general arguments of section 2, this could i n d i c a t e a s h i f t away from y ~ 0 ° i n t o the t r i a x i a l region. i
!
i
I
i
I
7
i
,,,.." j
2oo
."P ...., ...........
/<;~;'
CM
"~
~00
~
.
V
Od
0
0.2
i
,
i
I
0.4
i
L
I
0.6
l~w (MeV)
I
I
I
0.8
XBL 823-233B
Fig. 8. 4~(e2~ as a f u n c t i o n of he f o r the systems 124Sn + 4OAr ( t h i c k s o l i d l i n e ) , 126Te + 4OAr (dotted l i n e ) , 130Te + 4OAr ( t h i c k dashed l i n e ) . Also shown are some values of~#{bZnJd'-" f o r 124Sn + 4OAr ( t h i n s o l i d l i n e s ) and 130Te + 4OAr ( t h i n dashed l i n e s ) . j(2)
I t is somewhat puzzling that these~eff values do not show any detailed structure at the highest frequencies.
An interesting explanation could be that
316c
F.S. STEPHENS
t h e r e are e s s e n t i a l l y no conserved quantum numbers at these f r e q u e n c i e s , and a l l bands behave s i m i l a r l y . But t h i s seems u n l i k e l y , both from t h e o r e t i c a l grounds and from t h e absence of h i g h l y c o r r e l a t e d y - r a y spectra ( w e l l - d e v e l o p e d v a l l e y s t r u c t u r e ) t h a t should r e s u l t . More l i k e l y t h e i r r e g u l a r i t i e s are washed out because t h e observed p o p u l a t i o n is spread o v e r many c o n f i g u r a t i o n s and a broad temperature r e g i o n . R e s t r i c t i n g these p o p u l a t i o n spreads should then r e v e a l a wealth of detailed information. We are here at t h e f o r e f r o n t o f t h e h i g h - s p i n s t u d i e s and t h e l a s t c o n c l u s i o n s (or p o s s i b i l i t i e s ) have been r a t h e r s p e c u l a t i v e . N e v e r t h e l e s s , i f we cannot e v e n t u a l l y r e s o l v e t h e y - r a y s p e c t r a , then I b e l i e v e our understanding of t h i s spin r e g i o n w i l l come from such s t u d i e s . 5.
Future prospects
The f u t u r e prospects f o r t h i s f i e l d of h i g h - s p i n n u c l e a r physics look b r i g h t j u s t now. We seem t o have a good basic understanding of t h e physics i n v o l v e d , and f u r t h e r m o r e the t h e o r e t i c a l techniques e x i s t t o c a l c u l a t e most, i f not a l l , t h e q u a n t i t i e s subject t o measurement. Progress in a f i e l d n e a r l y always comes from such c a r e f u l comparisons of e x p e r i m e n t a l r e s u l t s w i t h t h e e x p e c t a t i o n s c a l c u l a t e d from t h e best e x i s t i n g t h e o r i e s . E x p e r i m e n t a l l y t h e study of h i g h - s p i n s t a t e s has always produced i n n o v a t i v e methods. M u l t i p l i c i t y filters, sum spectrometers, and c o r r e l a t i o n techniques are a few examples. At t h i s conference we are going t o hear r e s u l t s from yet another new method. There e x i s t now two m u l t i p l e - d e t e c t o r , 4~, Nal systems, one b u i l t at Oak Ridge w i t h 72 d e t e c t o r s and the o t h e r at Heidelberg w i t h 162 d e t e c t o r s . These instruments measure n e a r l y a l l t h e y rays e m i t t e d in an event and thus g i v e , event by e v e n t , t h e t o t a l y - r a y energy and m u l t i p l i c i t y , as well as the i n d i v i d u a l y - r a y energies and a n g u l a r d i s t r i b u t i o n s . I t is r e a l l y hard t o imagine what such i n f o r m a t i o n w i l l t e l l us about t h e y - r a y cascades from the highest spin s t a t e s . I w i l l mention j u s t one p o s s i b i l i t y t h a t seems t o me both t h e most obvious and t h e most e x c i t i n g r e s u l t we might hope f o r . A simultaneous measurement of both multiplicity and t o t a l y - r a y energy enables one t o l o c a l i z e a r e g i o n of t h e ( E , I ) plane from which t h e d e e x c i t i n g y rays can be i s o l a t e d . In Fig. 9 1 have shown t h e r e g i o n d e l i m i t e d by 20% FWHM in m u l t i p l i c i t y and 15% FWHM in t o t a l energy 32
]
i
i
[
I
i
28 t/
24 20
8 4
G 0
I0
20
30
40
50
60
70
I XBL 8 2 ~ 2 6
Fig. 9. A r e g i o n o f t h e E vs I plane is shown f o r a nucleus around A = 160, where the r e g i o n decaying m a i n l y by y rays is i n d i c a t e d (between t h e y r a s t l i n e and t h e e n t r y l i m i t ) , as is t h e r e g i o n (shaded) t h a t can be l o c a l i z e d by t h e 4~ Nal b a l l s .
HIGH SPIN STATES
317c
(something l i k e t h a t e x p e c t e d ) . While t h i s is not such a small r e g i o n , i t can be located in such a way as t o i s o l a t e r a t h e r small regions of p o p u l a t i o n - - f o r example, along t h e y r a s t l i n e as i n d i c a t e d . One or two Ge d e t e c t o r s placed i n s i d e the 4~ b a l l s under these c o n d i t i o n s might be able t o resolve the c o i n c i d e n t y - r a y spectrum. Such a p o s s i b i l i t y would r e v o l u t i o n i z e our study of the highest spin s t a t e s , and b r i n g us t o the level of d e t a i l e d spectroscopy described in section 3 f o r the spin region below -30 . These Nal d e t e c t o r systems are not the only hope in t h i s f i e l d , however. The development of Compton-suppressed Ge d e t e c t o r s has proceeded r a p i d l y in the l a s t few years, p a r t i c u l a r l y at Copenhagen and Daresbury. We at Berkeley have opted t o b u i l d a system of 21 such Ge d e t e c t o r s in close p r o x i m i t y t o an a p p r o x i mately 4~ b a l l made out of bismuth germanate. A drawing of t h i s system is shown in f i g . i 0 . While our 4~ b a l l w i l l have somewhat lower r e s o l u t i o n than the /'
Fig. 10. A sketch of the d e t e c t o r system under c o n s t r u c t i o n at Berkeley, which c o n s i s t s o f an inner -4x b a l l made of 44 elements of bismuth germanate, and an a r r a y of 21 Compton-suppressed Ge d e t e c t o r s outside t h i s b a l l .
e x i s t i n g 4~ Nal b a l l s , we hope t o compensate w i t h the power of the Ge a r r a y , which w i l l take Compton-suppressed quadrupole coincidences at a r a t e comparable t o t h a t at which most e x i s t i n g Ge arrays take double coincidences. I f the high r e s o l u t i o n in the ( E , I ) plane of t h e Nal b a l l s should f a i l t o produce resolved spectra from the highest spin s t a t e s , we f e e l t h e r e is hope t h a t such an instrument might. In any case, i t is i d e a l l y suited f o r a wide v a r i e t y of nuclear spectroscopic studies. I am c o n f i d e n t t h a t over the coming years these 4~ systems w i l l teach us many t h i n g s about h i g h - s p i n s t a t e s . This work was supported by the D i r e c t o r , O f f i c e of Energy Research, D i v i s i o n of Nuclear Physics of t h e O f f i c e of High Energy and Nuclear Physics of t h e U.S. Department o f Energy under Contract DE-ACO3-76SFO0098.
318c
F.S. STEPHENS References
i. 2.
3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
J. Burde, E.L. Dines, S. Shih, R.M. Diamond, J.E. Draper, K.H. Lindenberger, C. Schuck, and F.S. Stephens, Phys. Rev. Lett. 48 (1982) 530 O. Hausser, H.-E. Mahnke, J.F. Sharpey-Schafer, M.C. Swanson, P. Taras, D. Ward, H.R. Andrews, and T.K. Alexander, Phys. Rev. Lett. 44 (1980) 132: O. Hausser, H.-E. Mahnke, J.F. Sharpey-Schafer, M.L. Swanson, P. Taras, D. Ward, H.R. Andrews, and T.K. Alexander, Phys. Rev. Lett. 44 (1980) 132: O. Bakander, C. Baktash, J. Borggreen, J.B. Jensen, J. Kownacki, J. Pedersen, G. Sletten, D. Ward, H.R. Andrews, O. Hausser, P. Skensved, and P. Taras, preprint (1982) S. Cohen, F. P l a s i l , and W.J. Swiatecki, Ann. Phys. 82 (1974) 557 A. Bohr and B.R. Mottelson, Mat. Fys. Medd. Dan. Vid~--Selsk., 3(], no. 2 (1955) A. Bohr and B.R. Mottelson, Nuclear Structure, vol. 2. (Benjamin, Reading, Mass., 1975) p. 80 A. Bohr, Mat. Fys. Medd. Dan. Vid. Selsk., 2__66,no. 14 (1952) A. Johnson, H. Ryde, and J. Sztarkier, Phys. Lett. 34B (1971) 605 C. Baktash, E. der Mateosian, O.C. Kistner, and A.W. Sunyar, Phys. Rev. Lett. 42 (1979) 637 A. Pakkanen, Y.H. Chung, P.J. Daly, S.R. Faber, H. Helppi, J. Wilson, P. Chowdhury, T.C. Khoo, I. Ahmad, J. Borggreen, Z.W. Grabowski, and D.C. Radford, Phys. Rev. Lett. 48 (1982) 1530 B. Hass, H.R. Andrews, O. Hausser, D. Horn, J.F. Sharpey-Schafer, P. Taras, W. Trautmann, D. Ward, T.L. Khoo, and R.K. Smither, Phys. Lett. B84 (1979) 178 B. Herskind, J. de Physique 4_!I (1980) CI0-I06 B. Herskind, private communication (1982) J.D. Garrett and J.J. Gaardhoje, XIV Masurian Summer School on Nuclear Physics (Mikolajki, Poland, 1980) A. Bohr and B.R. Mottelson', Physica Scripta 24 (1981) 71 O. Andersen, J.D. Garrett, G.B. Hagemann, B. Herskind, D.C. H i l l i s , and L.L. Riedinger, Phys. Rev. Lett. 43 (1979) 687 M.A. Deleplanque, H.J. Kbrne-~-, H. Kluge, A.O. Macchiavelli, N. Bendjaballah, R.M. Diamond, and F.S. Stephens, submitted to Phys. Rev. Lett.