N U C L E A R P H Y S I C S A

ELSEVIER Nuclear Physics A630 (1998) 257c-267c

A new spin on high spin

Paul Fallon ~

~Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley Ca. 94720.

1. I N T R O D U C T I O N

I would like to talk about a few recent results on "high-spin" nuclear s tructure physics. As an introduction, I will discuss some general aspects of the experimental techniques, then briefly mention a few highlights before moving on to talk about a topic which our group has been pursuing over the last year, namely dipole bands - a topic which causes us to question, or at least think a l i t t le more about, what one means by "rotations" in quantal systems. Final ly I will finish with a brief discussion of GRETA - the next generation Ge spectrometer.

It is well known that the nucleus exhibits both single-particle and collective degrees of freedom, and that these extreme modes of generating angular momentum lead to very different spectra (Fig. 1). By studying the 7-ray emission from high angular momen- tum states, one can obtain a wealth of information on the structure and symmetries of the nucleus. The nucleus of interest is generally produced via a fusion evaporation reac- tion, yielding a system with angular momentum values up to the fission limit. Angular momentum is then lost via the emission of 7-rays. For the highest spin states (I~60h) many 7-rays are produced (M7 ~30) and the decay is extremely complex, involving many pathways of both collective and single-particle character. Clearly one requires a detector system which can pick out the decays of interest and extract the physics. Presently, at the Lawrence Berkeley National Laboratory 88-inch Cyclotron, one uses Gammasphere [1] to study the 7-decays. Gammasphere is a 110 high resolution Germanium detector array; each Ge detector is surrounded by a BGO shield to suppress the background arising from 7-rays which do not deposit their full energy in the Ge crystal. While most experiments employ a fusion-evaporation reaction, other reactions, e.g. transfer, deep inelastic, Coulex and fission can, and have been used, to populate nuclei which can not be reached using fusion-evaporation.

2. G A M M A S P H E R E H I G H S P I N H I G H L I G H T S

It would be impossible to do justice to the range of physics topics addressed with Gammasphere . Instead I refer you to table 1, which is by no means a complete list and is intended to give only a flavor of the physics.

Let us now touch on a few of the topics highlighted in table 1. The study of nuclei at high spin has, over the past few years, exploited the phenomenon of superdeformation (SD) [2]. These structures are associated with the largest deformations and exist at the

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258c P. Fallon/Nuclear Physics A630 (1998) 257c-267c

8000

6000

4000

2000

0 250

o

i

500 750 i000 E n e r g y (keV)

1250 1500

Figure 1. Spectrum of the yrast superdeformed band in 15°Gd, illustrating the two extreme modes of generating angular momentum. At high spins one sees a regular pattern to the 7-ray sequence indicative of a collective rotational degree of freedom. At low spins the nucleus carries spin via single nucleon excitations, leading to a more irregular decay pattern.

highest possible spins, thus providing an excellent laboratory to test our understanding of nuclear properties through the influence of large deformation and Coriolis forces. A subset of the questions addressed include (i) identical bands, (ii) level spins (linking transitions), (iii) deformations (quadrupole moments), and (iv) new regions (SD in A,-~80 and 60 nu- clei). Superdeformation as a phenomenon is well understood. It arises due to the presence of shell gaps which appear in the single-particle energy spectrum at near-integer ratios of

Table 1 Partial list of physics topics studied at Gammasphere.

High Spin • Superdeformation

=~ Identical bands =~ SD-ND Links =~ Deformations

New Regions (A=80,60) • N=Z Nuclei • Octupole Nuclei • AI=2 Stagger (C4) • Band Termination • Dipole (M1) Bands

Neutron Rich • Fission Source • Deep Inelastic/Transfer

Astrophysics • 54Mn, lSlTa, 144pm

Weak Interactions l°C/)-decay: Unitarity of the CKM matrix

t?. Fallon/Nuclear Physics A630 (1998) 257c-267c 259c

the major to minor axis (e.g. a 2:1 axis ratio). These shell gaps can cause local minima in the nuclear potential energy surface if the macroscopic energy surface is sufficiently flat (a reduced fission barrier). A flat potential energy surface occurs in the actinides due to the effect of the Coulomb repulsion, while in lighter mass regions one requires the presence of rotation. This brings me to my first highlight, and that is the recent observation of superdeformation in the A--~60 region (62Zr [3]). By identifying SD bands in this near "light" mass region, it may now be possible to theoretically study these exotic, highly collective, structures using shell model techniques as well as the more usual "mean field" approach. At this point I would like to simply mention the very recent observation [4] of a high-spin structure in 5SCu which decays primarily via p-emission to 5rNi, rather than by "/-decay to low lying SSCu states. This topic is presented in more detail in the contribution by D. Rudolph et al. [5].

Returning to the subject of superdeformation, let us consider the phenomenon of iden- tical bands [6-9] - a classic example being the bands in 192'194Hg (Fig. 2), where the transition energies are identical to ,-~1 keV over almost the full range of the transitions. The remarkable thing about these bands, however, was that while the transition energies were the same, there was evidence that the level spins were different; 192Hg was associated with the "ground state" SD band and had even-integer spins, while the band in 194Hg was proposed to have odd spin values. The result of this was that 1 unit of angular momentum separated states which decay at the same rotational frequency (same E~s). In addition, several other bands were "found" to possess 1 unit of alignment relative to 192Hg, and thus it was suggested [8] that this may arise from an underlying symmetry (pseudo-spin symmetry). At the time this suggestion was first made, the spins were not measured, but inferred from a fitting procedure. Consequently there has been a great deal of discussion as to whether the 1 unit alignment was indeed real. Recently the observa- tion [10] of direct 3' decays from the SD band in 194Hg to the normal deformed levels has enabled a unique determination of the level spins for the identical band in 194Hg which agree with those proposed in Ref 7. Hence the unit alignment is real[ We are now in the position where one can concentrate on the physics and not the fitting. Several groups have at tempted to address the physics of identical bands through systematic studies of the numerous SD bands now known throughout the nuclear chart. Gilles de France [11], in his contribution to these proceedings, describes a study of identical bands in the mass 150 region. I would just like to mention here that, in collaboration with Wojtek Satula (ORNL), we have begun a large study of the moments of inertia (j(2)) and alignments (both experiment and calculation) of SD bands in the mass 190 region. Briefly, our first objective was to address whether or not the observation of identical superdeformed (SD) bands in different nuclei implies "new physics" by asking the obvious question "what does one expect"? This question is really equivalent to asking "what do current models tell us about the relative moments of inertia and spin differences (alignments) between various SD bands"? The level energies and spins for more than 100 SD band configurations in the A=190 region were calculated using the cranked Woods Saxon Strutinsky (TRS) code [12] - modified to include quadrupole pairing. From this, one can determine the spreads in the moments of inertia (as well as alignments etc.) and compare a large variety of SD structures in both experiment and theory. Preliminary results are shown in Fig. 2, where one sees that the TRS calculations are able to reproduce the overall variation in (J(~))

260c P. Fallon /Nuclear Physics A630 (1998) 257c-267c

between SD bands. These calculations are also able to reproduce the observation that 0-quasiparticle (fully paired) bands have a lower j(2) than those with either a blocked neutron or proton, and these "singly" blocked bands have J(2)s which are lower than "doubly" blocked (proton+neutron) bands. At low spin, unpaired particles reduce pair correlations leading to a larger j(2). For higher spins the pairing is reduced in all systems due to the Coriolis force and hence the j(2) will tend to become similar in blocked and unblocked systems. While many of the general features of the data are well reproduced by the calculation, it is not able to predict, case by case, which bands are likely to be most similar, or to reproduce the near perfect 1 unit "alignment" seen, in a few examples, over many transitions. In my opinion, clear evidence for the need for "new" physics has yet to emerge, and although current calculations do not yield "perfect" agreement with experiment, the discrepancies are rather small, and hence a non-heroic ("accidental") ex- planation for the unit alignment is possible (if not likely).

g o o

192Hg 3000

2000

1000

o 1'oo goo

~ 1.2

1.0

0.8 194Hg

,,J 5=00 700 9'00

Energy (keV)

>:

i i

ALIGNMENT

I I i

0600 400 600 800 Egamma (keV)

0.2

g 0.1

2; 0.0 -20

• -~ Calc Expt

-10 0 10 20 A J2%

Figure 2. Superimposed spectra of the yrast superdeformed band in 192Hg and the excited superdeformed band in 194Hg (band 3) illustrating the identical transition energies in these bands. The upper left-hand plot shows the 1 unit spin difference between the levels decaying via "identical" transition energies. The lower portion compares the experimental and calculated variation in the dynamic moments of inertia between SD bands in the A=190 region.

17 Fallon/Nuclear Physics A630 (1998) 257c-267c 261c

Moving on to other exotic structures: • Octupoles - In analogy to molecular HC1, nuclei can attain an octupole (Y3,) de-

formation [13] (Fig. 3) which, among other properties, leads to sequences of states with alternating parity. However, unlike the molecular case, it is not so clear if the concept of a "static" octupole deformation is applicable when describing nuclei. The latest high-spin data on actinide nuclei near 222Ra provide important information on the character of octupole states and, in particular, their spin dependence. An experiment [14] was carried out at Gammasphere using a multinucleon transfer re- action (z32Xe+23~Th) and interleaving bands of alternating parity were observed in 21s'22°'222Rn and 222'224'226Ra. There are noticeable differences between the properties of the bands in the Ra and Rn isotopes. The radon isotopes behave like octupole vibrators while the radium isotopes exhibit a behavior which is characteristic of a stable octupole deformation - illustrated in Fig. 3 (22~Ra) by the tendency at higher spins for the alternating parity bands to become "perfectly" interleaved.

, , -0 I. -I I- 1.27 /~

lO +

0.1 ev " ~

8 +

6 +

4 +

2 + 0 - o +

HCI

9-

•"

5 -

3 -

1-

3 M e V -

2 M e V -

1 M e V

0

(20+) T

( 1 5 +) T

(16 +) T (14 +) " ~

( 12+ ) l ~

(10"~ " ~ ( 8 + ) ~ ' ( 6 + ) - ~ "

14 .8 fm =

(17

(15 '

(13 '

(11 '

~- :

• 0 +

( 1 9 - )

7 - )

5 - )

3 - ) - )

)

222 Ra

Figure 3. The low-lying rotational spectra of 2~2Ra together with that of the HC1 molecule.

262c P Fallon/Nuclear Physics A630 (1998) 257c-267c

A I = 2 stagger - In this context I refer to a few examples [15] of SD bands where one observes a very small, but regular, oscillation (AI=2 stagger) in the transition energies which implies that every second SD state (level) is either shifted upward or downward in energy relative to its unperturbed value (Fig. 4). The shift is of the order of several tens of eV, and is at the limit of experimental accuracy. Nevertheless there is at least one example (149Gd - G. de France's contribution to these proceedings [11]) which has been studied several times and the effect remains; other cases have not been so fortunate. The observed A I = 2 has been associated with a Y44 component to the deformation leading to 4-fold symmetry with respect to the 3 axis (axis perpendicular to the rotation). It has been shown [16] that this symmetry leads to the stagger through a tunneling (mixing) of the 4 states which are based on the position of the total angular momentum relative to the minima in the hexadecapole field.

I+4 I+2 1 Ey

I 'l

I-2 l ~,

I-4 'l

Ey + 2AF

Spin

Figure 4. Schematic representation of a nucleus with a Y44 deformation superimposed on a more "standard" prolate Y20 shape. Rotation is around the "1" axis. The upper left portion illustrates the upward and downward shifts of the band level energies, and the lower picture schematically shows the characteristic pattern of the A I = 2 stagger - as seen for example in 149Gd.

P Fallon/Nuclear Physics A630 (1998) 257c-267c 263c

3. DIPOLE (M1) B A N D S

In this section I would like to turn your attention to another type of structure. From what I have said and from what you already know, one would be tempted to associate the sequence of transitions shown in Fig. 5 with a large prolate deformation. Indeed if all one knew were the transition energies and it was assumed that the decays had an E2 character, then one would obtain a moment of inertia that was comparable with that of SD bands in the A=190 region. However the angular correlation of the 3' rays tell us that the decay of this band proceeds via dipole transitions (M1), and more importantly a measurement of the state lifetimes points to the nucleus having a small quadrupole deformation (oblate) - i.e. it is nearly spherical!

Two obvious questions then arise, (1) how is the nucleus generating angular momentum, and (2) why are these bands so regular (why do they follow an I(I+i) rule reminiscent of a rotational band?). It was proposed [17-18] several years ago that the total spin of the nucleus was derived from a few particles only. In the Pb M1 bands, the orbitals of interest involve a pair of protons (h9/2, i13/2) coupled to j r and two i13/~ neutron holes coupled to j , (Fig. 4). The total spin (J) is then the vector addition of jr and j , . The small deformation means that the collective angular momentum R is small compared with J. Such a situation can be described within the tilted axis cranking (TAC) model. The configurations involved lead to a magnetic dipole moment which precesses around the total spin vector giving rise to the observed M1 radiation, and the strength of the M1 decay is proportional to the perpendicular component of the dipole moment. This component is reduced as the angle between the proton and neutron j-vectors closes. Hence the "shears" mechanism should lead to a characteristic drop in the M1 transition strength - B(M1) value - as a function of increasing spin.

Previous determination of the B(M1) values were inconclusive, indeed in some cases contradictory. So the first thing I will describe are a series of experiments [19,20] to "test" the shears mechanism for generating angular momentum. In general the following results are from an LBNL/LLNL/Bonn/York collaboration, and the B(M1) were obtained by determining the lifetimes of states in the M1 bands. For details on the experimental conditions and analysis, the reader is referred to the cited references. The extracted B(M1) values are shown in Fig. 6 for the bands in 193-199pb. For comparison, the solid lines show the TAC model prediction assuming various configurations. There is good agreement between the TAC predictions and experiment. These data show, for the first time, that the TAC model gives a quantitative description of the M1 bands and, in addition, provides evidence for the concept of magnetic rotation.

In addition to the large number of examples in the Pb region, regular dipole structures (M1 bands) are known in the A ~ l l 0 region of Sb, Sn, In and Cd [21] nuclei. We recently performed an experiment to measure the lifetimes of an M1 band in H°Cd to deduce the behavior of the B(M1) values. As seen in Fig. 7, one now finds regular dipole bands with similar properties in two very different regions of the nuclear chart, and in both cases the B(M1)'s are well described by a "shears"-type mechanism.

The question remains, however, as to how can one get, in so many cases, rotational-like bands from what essentially looks like a single-particle j - j coupling? The deforma- tion is small (near-sphericM) and the number of particles contributing to the total spin is

264c P. Fallon/Nuclear Physics A630 (1998) 257c-267c

35000

26000

17000 O

CD 8000

J3

15

10

5

0

M l ' s

¢D r-4

~ 199 O0 ~q t ~ 0 ~z ze ~ ¢~ Pb(2)

I I " [-.,. Le~

-1000 . . . . . ~" . . . . . . . . . ' ' - " ~ ~

100 200 300 400 500 600

Energy (keV)

Low frequency j

........... High f r e q u e n c y / "

• , , l~p

/ / J / / / . .J '- / / . . i-- _j..

3 J~ J

0 5 10 15 J1

- 1

Figure 5. Schematic representat ion of the angular momentum coupling scheme and the mode of generating angular momentum (the "shears mechanism") as suggested by the TAC model. The neutron (proton) angular momentum vector is represented by j~ ( j r ) while the perpendicular component of the magnet ic moment is labeled by #p~r~. The collective component of the angular momentum is represented by R, the total angular momentum by J , and the t i l t ing angle by 0. The solid (dashed) arrows show the approx- imate coupling at low (high) frequency.

P. Fallon/Nuclear Physics A630 (1998) 257c-267c 265c

m

12

8

4

0

12

8

4

0

12

8

4

0 0.0

193pb

i i i

J , i , i ,

~- l ~ e b

i i i

i J

. ~ 19spb(3)

i , i , i

0.2 0.4 0.6

, c r I ' b '

A B C E l l

i r i

19~pb

2 ~ L "

I I I

, i , i , i

199pb(1 )

" - \ \

, i i , i

0.8 0.0 0.2 0.4 0.6 0.8 0.0 Energy (MeV)

' i , E , i ,

l~'spb

r i i

'"l'b(1) \- .

" " " ~ 2 2 ~ 1 2 5 :

I I i i

i i

199pb(2 )

\ \

i i i

0.2 0.4 0.6 0.8

Figure 6. Exper imenta l ly deduced B(M1) (pN2) values, p lot ted as functions of transi- tion energy (MeV), for the bands in 19a-199Pb [19]. The results for 19a-19rpb [20] are preliminary. The solid lines are the results of TAC model calculations for the suggested configurations of the bands applicable to the 19Spb or 199Pb configurations.

also small; hence we would not associate any appreciable collectivity with these bands. Moreover a (5-interaction does not yield a sequence of states which look like a rotat ional band. A short-range interact ion usually suppresses one state with respect to the others; for unlike particles it is possible that both the jmin and jmax configurations are suppressed. One now speculates as to the nature of the interaction and asks the question, since the spectrum from a "shears" band looks the same as one from a "standard" collective rotat ional nucleus (e.g. a deformed rare earth nucleus), is it also possible that one can think of these dipole bands as arising from a "rotation" - not a rotat ion of the "bulk" shape, but maybe some internal degree of freedom which specifies the orientation, allowing one to define a "rotation" angle [22]? Alternat ively [23] one may ask, what is the simplest interaction which will yield an I ([ + 1) energy dependence? The answer is j . j , where the force is proport ional to cos • (O = angle between j-vectors) . A cos ~5 force corresponds to an odd multiple, the lowest even mult ipole is proport ional to cos 2 ~. This is the familiar Q.Q interaction and can give rise to a rotational-l ike spectrum if I < Imam. The s tudy of rotat ions in a finite quantal system remains a subject of great interest, and it will be of further interest to see how one reconciles the apparent ly "different" concepts of collective rotat ion and shears mechanism.

266c P Fallon/Nuclear Physics A 630 (1998) 257c 267c

30

25 c--

EL

2O

15

6

4

2

0

0.0

199pb

, r i i

0.2 0.4 0.6

24

22

20

18

16

8

6

4

110Cd 0 E , =

0.8 0.0 0.2

Frequency

11oCd

i

0.4 0.6 0 . 8

Figure 7. Spin versus rotational frequency (top) and B(M1) (#~v) versus rotational fre- quency (bottom) for 199pb and ll°Cd (preliminary result). A linear relation between spin and frequency is indicative of a rotational-like behavior. The solid lines represent values obtained with the TAC model.

4. G R E T A - G A M M A R A Y E N E R G Y T R A C K I N G A R R A Y

While the latest generation of detector arrays (Gammasphere, Euroball, GASP) are excellent devices, they employ a "technology" which is probably at the limit of their sensitivity. That is, a device which uses a BGO (Compton) shield to suppress unwanted events is limited in efficiency, since approximately half of the space is taken up by the shield. Removing the BGO and using Ge crystals of a size comparable to that we use now to form a Ge ball will result in too many false summing events, i.e. two V rays deposit energy in a neighboring detector leading to a false energy. One would need ~1000 Ge detectors to negate the effects of multiple hits, and such an array is clearly very expensive.

GRETA [24] uses the idea of tracking to disentangle the multiple hits. Instead of having a very large number of Ge crystals, one has ~100 (same as Gammasphere), but each crystal has a highly segmented outer electrode (6x6 segments). Signals from these "pads" are used to track the Compton scattered v-ray and reconstruct the full energy. The performance of an array based on a highly segmented Ge shell is impressive, resulting in an improved observational limit of 103 over present-day arrays (Gammasphere etc.). Properties of GRETA include:

• A photo-peak efficiency of ~50% for a 1 MeV 7-ray.

• Well-defined interaction points allow one to greatly reduce the effects of Doppler broadening.

• A high efficiency for high-energy v-rays (30% for 15 MeV).

P. Fallon/Nuclear Physics A630 (1998) 257c-267c 267c

To date, much of the effort (I.Y. Lee, K. Vetter, G. Schmid) has gone into trying to understand the characteristics of a segmented Ge detector through simulations of the 7- ray interactions and subsequent charge collection on the electrodes. In addition, a parallel effort has aimed at event reconstruction. While there still remains much to do, a great deal of progress has been made and a first prototype (12-fold segmentation) has recently been delivered to Berkeley for testing. All being well, we anticipate having a full 36-segment prototype in 1998 and a "mini" GRETA (7 detectors) could be planned for operation in 1999 - a full GRETA being possible by 2002.

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of the Conference on Nuclear Structure at the Limits , Argonne National Laboratory, July 22-26 1996. ANL/PHY-97/1 page 1.

11. G. de France, this proceeding. 12. W. Nazarewicz, R. Wyss and A. Johnson, Nucl. Phys. A503 (1989) 285. 13. P.A. Butler and W. Nazarewicz, Rev. Mod. Phys. 68 (1996) 349. 14. J.F.C. Cocks et al., Phys. Rev. Lett. 78 (1997) 2920. 15. S. Flibotte et al., Phys. Rev. Lett. 71 (1993) 4299. 16. I. Hamamoto and B. Mottelson, Phys Lett. B333 (1994) 294; I.M. Pavlichenkov and

S. Flibotte, Phys. Rev C51 (1995) R460; A.O. Macchiavelli et al., Phys. Rev C51 (1995) R1.

17. S. Frauendorf, Nucl. Phys. A557 (1993) 259c. 18. G. Baldsiefen et al., Nucl. Phys. A574 (1994) 521. 19. R.M. Clark et al., Phys. Rev. Lett. 78 (1997) 1868. 20. R.M. Clark et al., to be published; R. Kruecken et al., to be published. 21. S. Juutinen et al., Nucl. Phys. A573 (1994) 306. 22. S. Frauendorf, private communication. 23. A.O. Macchiavelli et al., to be published. 24. I.Y.Lee, Proceeding of the Conference on Nuclear Structure at the Limits , Argonne

National Laboratory, July 22-26 1996. ANL/PHY-97/1 p. 191.