EXPERIMENTAL STUDIES OF VERY HIGH SPIN STATES

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EXPERIMENTAL STUDIES OF VERY HIGH SPIN

STATES

B. Herskind

To cite this version:

JOURNAL DE PHYSIQUE CoZZoque C10, suppZdment au n012, Tome 41, ddcembre 1980, page C10-106

EXPERIMENTAL STUDIES OF VERY HIGH SPIN STATES B. Herskind.

The NieZs Bohr I n s t i t u t e , U n i v e r s i t y o f Copenhagen, DK-4000 Rqskilde, Denmark.

Introduction.

Detailed spectroscopy studies of high spin states are limited to the band struc- tures close to and along the yrast line up to I s 3 . 5 . As discussed in previous talks, these studies have in previous few years given good insight and understanding of how the nuclear coupling schemes are in- fluenced by the interplay of quadrupole and coriolis forces. The success of the cranked shell model calculations as the

one described by Bengtsson and Frauendorf 1)

for the quasiparticle energies in deform- ed nuclei and the shell model type calcu- lations as f .ex. by ~ u d e k ~ ) or those by DGssing, Neergaard and sagawa3) for nuclei near closed shells where not only the ener- gies, but even the static quadrupole mo- ments are reproduced extremely well, is very satisfying.

It would be exciting to extend such studies, both theoretical and experimental, up to the highest spin, nuclei can accomo- date, a limit which is found4) to be s65 fi

for nuclei % A=150. The study of discrete

band structures in this spin region has so

far not been possible, and it has there-

fore been necessary to develop new methods by which one can evaluate at least the gross average properties of high spin sta- tes from the so-called y-ray continuum.

Most of this work is based on measurements of correlations in the y-ray transition energy spectrum (E ) with i) spin by ex-

Y

citation functions, y-ray multiplicity or/

and total energy of the y-cascade ZE ii)

Y' multipolarity by angular correlation or/and conversion coefficient measurements, iii) collectivity by Doppler shift attenuation measurements on reverse reaction products slowed down in fast stopping material.

Recently a series of second generation correlation experiments has been initiated

by studying the transition energy E -E

Y Y

correlations. These measurements have shown how one in a unique way can extract detailed nuclear properties from average values over many bands built on similar particle confi-

gurations. Experiments. are in progress by

a Berkeley-Copenhagen-GSI collaboration, in which the techniques developed for the 1. generation experiments are incorporated in-

to the E -E correlation measurements to

Y Y

study the spin-, multipolarity- or lifetime-

dependence of the structures observed in' the

two-dimensional E -E spectra.

Y Y

The development of large counter arrays

approaching 4n geometry promises to add yet

another dimension to the study of the y-con- tinuum from 'the high spin region. It will be possible with these "Crystal Balls" when com-

T a b l e 1

' Continuum gamma-ray c o r r e l a t i o n e x p e r i m e n t s

Correlation parameters Remarks

FIRST GENERATION Correlation with E _Y E vs. angular momentum

-Y

E vs. E

in * 'max Excitation function

Y

E vs. <My> y-multipolarity as function of E

Y Y

E2 _{Selrction of total y-ray cascade energy}

Y

E vs. y-ray multipolarity -Y

E vs. W(@,$)

Y A r ~ ( l u l o r multipolarity correiation geometry to select E vs. E conversion Convcrs~ori coeff icicnt

Y

E -polarization Ge ( ~ 1 ) polarimeter

Y

E vs. lifetime -Y

E VS. (Tdec + Tfeed) C o r n p a r i s o n E sp~ctrum for recoil in

Y vacuum and szopped

SECOND GENERATION Correlation with E -E _{Y Y}

EY

-

Ey E _Y correlat~on between two y-rays

E

-

E

-

angular momentum

Y Y

Ey

-

Ey

-

y-ray multipolarity Ey

-

Ey

-

lifetime

THIRD GENERATION Large fraction nf y-rays are recorded in individual detector. crystal ball

References

<M > count detectors that fired

-

small correction Y

E E ~

~irect.1~ if eff = 1.0

w(e,@) All available

c10-108 JOURNAL DE PHYSIQUE

energy. Most of the excitation energy is removed through particle emission <$l0 -18 sec. and the nucleus can in the cases where neutron emission is dominant be produced in bound states (no particle emission) with energies 0-10 MeV above the yrast line and with very high angular momentum. The slower

(>10-16sec.) y-emission removes the rest of the excitation energy and angular mo- mentum through y-cascades. A typical decay process is illustrated in fig.1 and fig.2. Statistical calculations and the study of continuum y-ray spectra are consistent with the hypothesis that the y-cascades consist of two parts, namely a few stati- stical y-rays which remove predominantly excitation energy from the nucleus (veri- fied by an exponential tail of high energy transition in the y-spectra) and a long series of yrast-like stretched quadrupole and dipole transitions which remove both

energy and angular momentum with a AE/AI

which in average is roughly equal to the slope of the yrast line, reflected in the observed low energy bump. The flow pattern is illustrated in fig.2.

Several systematic ~ t u d i e s ~ ' ~ ' ~ ) of cbn- tinuum y-ray spectra performed on many nu- clear systems with very different structu- res in the:low spin regions have shown that the statistical transitions are relatively structureless and similar in all cases, on- ly reflecting the temperatuse of the nucleus

at higher excitation,energies whereas the

yrast-like transitions form a low energy bump of high intensity which shows diffe- rent characteristics, depending on the nu-

system.

This is illustrated in fig.3 taken from ref. 7,

,

where fig. 3b shows a typical spec- trum as a result of a 1 2 4 ~ n

+

4 0 ~ r reac- tion leading to evaporation residues of

well deformed 1581159,160~r nuclei. Excita-

tion functions6) and the sum-spectrometer experiment by the Berkeley group discussed later show that this collective low energy bump of stretched E2 transitions increases in energy with increasing Lmax as expected

for a good rotor. In fig.3~1, in contrast

to this very smooth bump observed in gene- ral for good rotors, a distinctly different structure of the bump is observed for the

4 0 ~ r

+

reaction leading to evapora-

tion residues close to the N=82 neutron shell. For these nuclei it is known from discrete spectroscopy up to I%35 that the single particle aspect of the nuclei is do- minating. The analysis of this type of spec-

tra given by the Orsay-Stockholm group 7

shows that the upper part of the collective bump originates from stretched E2 transi- tions probably emitted from a prolate fast spinning nucleus. These data as well as other systematic studies may indicate that the spherical-like nuclei become rotational-like at high spins. More detailed informabion is needed before clear conclusions can be made, but such data indeed point at the in- teresting regions for further study. Other regions where irregularities have been ob- served 3'15) are £.ex. 5 0 ~ i

+

4 0 ~ r -+ " ~ r , 'OT~

+

5 0 ~ i + Ru, 8 2 ~ e

+

4 0 ~ r

* Te, ll0pd

+

4 0 ~ r + Gd, 122,130~e

+

4 8 ~ a -+ ~ f .

STATISTICAL MODEL CALCULATIONS Input Angular Momentum '2'Sn(L0Ar,xn) 1 6 ' - x ~ r E ( A r ) = 147 M e V

E *

~ 5 3 . 8 MeV '0 20 CO 60 80

Fig.1. Statistical model calculation4) for the decay of the 16%r* nucleus from a 147 MeV " ~ r + ' ~ ~ Sn reaction. The angular momen- tum distribution given by the reaction is shown in the top portion of the figure.

The depopulation is indicated as function

of excitation energy and angular momentum for the evaporation residues after emission of 1-5 neutrons. The shaded region of the 3n-5n population shows the portion in which y-emission competes. The entry populations for the residues are projected on the ener- gy and angular momentum axis to display the channel overlap to the left and bottom part of the figure. The predicted entry li- nes are shown for each y-ray emitting re- gion.

Fig.2. Schematic diagram of the visualized y-ray cascades following the particle de-

cay of the 16'~r* shown in fig.1. The con-

tours indicate the y-ray emitting regions of the 3n-5n evaporation residues predic- ted from the statistical model calculations of ref.').

Fig.3. Continuum y-ray spectra (E ) from

m Sn and

'

' ~ n t.argets bombardedYby 185 MeV 'OAr ions. The spectra are collected

in coincidence with at least 4 out of a 6-

c10-110 JOURNAL DE PHYSIQUE

Fig.4. The yrast diagram giving all the known even spin states in ' 6 0 ~ b from the rather complex level scheme of ref.'). The alignment of the v(il312) neutron sta- tes and the *(h11/2) proton states is in- dicated.

The two Moments of Inertia, Jcoll and Jeffz

A typical example of data from a detail-

ed y-spectroscopy experiment is shown in 8

fig.4 for 160yb taken from ref.

.

Essentially all discrete lines in the'

spectra down to a level of %2% of the most

intense lines are used in the construction of the present level scheme. The level

detailed discussion of this type of data and the interpretation ,is given in refs. 8,9,1) One may note here that the second backbend

observed at a frequency %U-.42 MeV is dis-

cussed in a contribution to this conferen- celO) to be experimentally verified via a study of the level scheme of 161yb to ori- ginate from the alignment of hllIZ protons 11)

as earlier predicked by Faessler et al.

.

From these studies it is quite evident that the level schemes for good rotational nuclei show many band crossings in the spin region I%10-30 which can be characterized according to the band crossing frequency, hwc, spin alignment, i, and interaction strength, V, in the vicinity of the cros- sing.

An interesting question now is whether

this type of structure of intermediate .

coupling strength continues to exist also at higher spins or the bands interact even stronger over larger regions for more ex- treme rotations under influence of the strong coriolis force and thereby form a "parallel" strongly coupled band structure as illustrated in f ig.5 by S. B j@rnholmlO)

.

Let us take a closer look at a single band crossing and the resulting y-ray cas- cade passing through it, as shown in fig.6, and try to visualize how an average over

structure observed is surprisingly well ex- many of these bands and band crossings would

plained by rather simple cranked shell mo- be detectable in y-correlation experiments.

del calculations, which both reproduce the The energy of the levels in each sepa-

level oyder, the alignment of several dif- rate band can be written:

ferent. particle configurations and the ro-

E==- 2' R ~ + E Q 1 =- h2 _{( ~ - j & z + E (j}

tational frequencies at which the band wall

P

a

Wcx,U P a

crossings occur, as well as the interaction (1)

transitions, and ja represents the aligned angular momentum, E the energy of the

P

quasiparticle configuration, and R the

collective angular momentum.

For constant dcoll and ja within a

band the transition energies are:

A

-

and the curvature of the band related to the change in E for successive transi-

Y tions are:

where the subscripts (1) and (2) indicate when the 1. or 2. difference in the tran- sition energy is used.

In the continuum y-ray spectra one can not resolve the individual bands, but if

many bands have a similar fcoll and ja,

one may observe such bands in the y-y cor- relation spectrum and an average f ( 2 ) _coll may be extracted.

The effective moment of inertia feff

which is usually extracted from "1.genera- tion" E -spectra, may be visualized as re-

Y

presented by the transitions which could

have passed through the envelope.of the

band crossing (see fig.6). The transitions through this fictive envelope can be writ- ten :

n2

2

ER =

-

I ;E =

-

3 4I;AE =

-.

m2

2"Fe f f

2P:k

Y 2"Feff (2) p

( 4 ) From eqs. (2) and (4) we derive the ratio of the two different moments of inertia

which is an important consequence of the

Since these rules are rather simple, it is useful to discuss and compare the expe- rimental data from the y-continuum in this frame. The y-ray flux measured by an E de-

Y tector in "singles mode" (1.generation ex- periment of table 1) represents the average over many different bands and band cros- sings. This means, that only average quan-

tities can be measured. It is seen from fig.

6 that 3 different quantities are equal for the decay either through the crossing bands or through the fictive envelope band, namely: <M>band/keV = <M> /keV

env (6

Ey ,band(Imax) = Ey ,env('rnax) (7

<Ey>band = <E y env > (8

Therefore, the effective moment of inertia, oreff, of the envelope band may in principle be extracted from the E "singles" spectra

Y in 3 independent ways:

1) According to eq. (6) the height of the yrast bump in the E spectra normalized to

Y

<M>/keV, the number of transitions per keV, (2)

is linearly proportional to Seff.

2) The energy of the upper edge of the yrast bump (or the more sharp multiplicity bump) is in average proportional to Imaxr and since eq.(7) is valid in average one may use the approximation that

I , ,

, is usually evaluated from the experi-

mental Rmax of the reaction or from measured

multiplicity values.

3) The difference in average transition

energy for selected spin intervals (which

can be approximately measured in a sum spec-

trometer-multiplicity (C-M) setup discus- sed later) is

A<E > = 8 ~ ~ / 2 6 ( ~ )

Y ef f (10)

Many measurements have been performed and analyzed according to these approxima- tions, and the different evaluations of

reff

give remarkable agreement, although so far no attempt has been made to distin-

(1) (2

guish between Teff and

reff.

I shall first discuss one of the more general methods, the (C-M) method which has been used to measure eeff, and later the y-y correla-

tion method which can be used to study in more detail the itcoll.

The Sum Spectrometer.

The principles of the C-M method ape

given in re£ .l3), where also the poF'sibi-

lity for channel selection is discussed. This latter point can be appreciated from a look at fig.1 where the projected entry regions on the energy and spin axis are shown. Since the binding energy is larger than the kinetic evaporation energy of the

\ ~

emitted neutrons, one expects small over- lap between the (xn) channels on the ener- gy axis and a good channel selection in the total energy of the y-ray cascades mea- sured in the sum spectrometer. This effect

is very useful for the study of discrete ,

lines in particular if many particle chan- nels are open.

For the study of continuum y-ray spec- tra where one so far only has looked at bulk properties in different mass regions,

the channel selection power is less impor- tant, and one may rather use the,spectro- meter as a "pseudo" spin selector. In the

following discussion we have mostly taken

this view point.

The principles for the spin selections and the subtraction technique are shown in fig.7. If we assume that the statistical transitions first remove a large fraction of the energy in a given y-ray cascade, then the decay corresponding to successive selected high window gates (W5-W4) on the sum spectrum of fig.7a can be constructed. This is shown in fig.7b and 7c. The area of the arrows is made proportional to the number of transitions <M>. If the multipli-

city normalized E spectrum corresponding

Y

to window 4 is subtracted from the E spec- Y

trum of window 5, then the resulting spec-

trum (W5-W4) will correspond essentially to only yrast-like transitions as illustra- ted in fig.7d. It is seen that the sharply selected sum windows

%

> 20% result in transitions from a fairly wide spin inter-

val, but still with a half width of

5

% 20%,

due to the steep slope of the yrast line. A typical setup is shown in fig.8. The target is bombarded with heavy ions in the center of the large NaI crystal (here 20 cm

X 25 cm*) in which the major part of the

y-ray cascade is collected. Two (12.5 X 15

cm0) NaI detectors are placed in

o0

and 90'

with respect to the beam at a distance of 60

cm from the target such that the E spectra Y

can be clearly separated from the neutron background by TOP. The effect from the neu-

trons can not be removed from the sum spec-

JOURNAL DE PHYSIQUE

20 40 60 20 40 60 20 40 60

SPIN ( h ) SPIN ( h ) SPIN ( h )

Fig.7. A principle diagram to show the spin selection and-subtraction technique.

Fig.7a shows a typical ,sum spectrum ( C ) with two window gates W 4 and W5. Fig.7b and 7c

show a typical decay flow corresponding to the respective window gates W 5 and W4, and

fig.7d the expected y-flow along the yrast line only when ( W 5 - W 4 ) are formed.

Fig -8. A typical The ex erimental ref.187.

sum spectrometer setup. details are given in

With this setup one can study the E

-

Y distributions, the y-ray multiplicity <M> and the anisotropy of the transitions as function of the total sum energy of the cascade.

For the ideal sum spectrometer with a

4a geometry and 100% efficiency including

the 2 E detectors, the coincidence to Y

"singles" ratio for counts in the sum cry- stal with one of the transition detectors can be written:

where W is the solid angle of the Ey detec-

tor used for the multiplicity measurement. If a coincidence with the second detector is required, which is often done to clean the spectra for low multiplicity events from £.ex. transfer reactions, the M has to be replaced by (M-l)

.

In a more realistic case there will be a loss due to imperfect summing (Q<4a), and the multiplicity will depend on the ac- tual energy collected in the sum crystal. This effect can be eliminated if both the

"singles" and the coincidence rates are treated separately, both with the E detec-

Y

tor solid angle W included into the large

Cl, (the energy signals E and E x added in Y

one spectrum (Nc/Ns) R+u) and with the E

Y detector excluded from R,(E. and Ex not ad-

Y ded in another spectrum (Nc/Ns)Cl).

The average multiplicity <M> can then be obtained by eliminating the parameter X, the number of transitions actually collected out of M possible, in the two expressions:

which is approximately the same as evalua- ting (MQ+W) from the added and (Mn) from the non-added spectra and then find <M> from the equation:

In a similar way, the E -spectrum corre-

Y

sponding to different values of sum energy has to be corrected by the approximate re- lation :

If the spectra are measured by sum spectro-

meters with SP0.5, the errors in these ap- proximations are negligible.

If one is particularly interested in the data originating from the high spin region, it is an advantage to subdivide the sum cry- stal into several sectors and then require that all the sectors have been activated before an event is stored in the computer. In this case the formulae become more com- plicated and require a numerical solution for <M>. The following equation may be used:

with n being the number of separated seg-

ments. A more detailed discussion of the

sum spectrometer technique is given In refs.

14 and 15.

We shall here only concentrate the dis- cussion on two typical examples of this type of experiments. In a case where the nucleus

C10-116 JOURNAL DE PHYSIQUE

extracted as a function of I, whereas the

analysis is not so straight forward when the nuclear structure is more complicated, perhaps due to large changes in the defor- mation.

The Berkeley group16) applied the me- thod to the well studied case of 4 0 ~ r

+

1 2 4 ~ n at a bombarding energy of 185 MeV ensuring that the highest spin states in the evaporation residues of 1603r were po- pulated. In this experiment several exter- nal E detectors were placed in the vici-

Y

nity of oO, and it was therefore also pos- sible to extract the width of the multipli- city distributions. In fig.9 the measured multiplicity M and width aM are shown as functions of total energy measured in the sum spectrometer. It is seen that the ex- pected proportionality between sum energy and multiplicity is obtained. It is noted also that theOM seems rather wide at high- er multiplicities, indicating that the en- try states have a large spread in spin and excitation energy in accordance with hy- potheses shown in figs.1 and 8. This spread

in I for definite sum energy windows may be smaller for lower mass nuclei with sMal-

ler Zeff since it depends on the slope of the yrast line.

In fig.10a the Ey spectra are shown for

different gates (windows) on the sum ener- gy spectrum (see fig.9a). It is seen that the number of transitions per 200 keV does not chayge mu'ch from window 5 to 8 which

indicates an only slowly increasing 8

ef f as function of spin according to eq.(6).

The edge of the bump increases almost linearly with window number, as expected

from eqs

.

(7) and (9)

.

Because of various background considerations, it is only fea- sible to consider the center region of the sum spectrum. In the lower end the trans- fer reaction channel will contribute sig- nificantly, and in the upper end pile-up effects can be important and therefore have to be evaluated with precaution. The subtraction technique discussed earlier is applied to obtain the result shown in fig.10b. It is seen how the <AE > increa-

Y

ses linearly with the sum energy as expec- ted for constant moment of inertia (see eqs

.

(8) and (10) ) and how both the low and higher energy transitions subtract out.

A numerical evaluation of these data

according to eqs.(8), (10) ,(l21 and (13) is shown in fig.11 where the effective moment

of inertia Jeff is plotted as function of

2 2

h w as frequently used for backbending

plots. The data are in very good agreement with the liquid drop predictions17). This was also found earlier from studies using the y-multiplicity technique on the same

4

reaction channels (see fig.12)

.

The apparent agreement between the two different experimental methods as well as with the theoretical predictions is a strong indication that the deff can be determined reliably from such data on good rotational nuclei. It should be emphasized, however, that the nuclear systems studied in this case are expected to behave like good ro-

tors over the entire angular .momenturn range

0

-0 I O 2 0 3 0 4 0 ' Y ) M

Total y Energy (MeV)

Fig.9. The upper part shows the experi- mental sum spectrum and the xn channel com- ponents obtained by gating on known lines in the coincident Ge-spectrum. The middle part indicates the windows used for the multiplicity evaluation and for the sub-

traction technique discussed in the text. The lower part shows the measured multi- plicities <M> and width O M as function of the total y-ray energy. The points on the dotted line correspond to the measured multiplicity by means of a 00 Ey-counter and no angular correlation correction, whereas the points on the solid line have been corrected for angular correlation ef- fects assuming an 80% stretched quadrupole and a 20% stretched dipole composition of the y-rays.

behave so regularly.

The NBI-GSI group18) has performed a similar type of experiment on the 5 0 ~ i

+

5 0 ~ i + looRu* and 5 0 ~ i

+

'lOpd + l6O3r* giving evaporation residues, 9 6 ~ u

-

9 2 ~ 0

and 154'155*156~r in the vicinity of the closed shells N=50 and N=82. In fig.13 two

sets of E spectra are shown fo= the O0

Y

and 90° counters corresponding to 5 win- dow gates on the sum energy spectrum with increasing energy. These data have been

Trmwtm enrqv (W1

Fig.10, The upper part shows the number of transitions per 200 keV as a function of y-ray energy in a 00 detector for each of the gate windows indicated in fig.9. The lower part shows the subtracted spectra

of f .ex, (window 5-window 4) labeled 5-4.

used to evaluate the multiplicity and ani- sotropy as functions of .E as shown in

Y

figs-lla and llb. If the assumption is

made that the major part of the low ener- gy transitions (E <2.8 MeV) is stretched

Y

the E spectrum can be decomposed into a

Y

(X=l, AI=1) dipole and a ( 1 ~ 2 , AI=2) qua- drupole part. This is shown in the lower .part of fig.14. It is clearly seen that

the upper part of the bump consists of al-

most pure stretched quadrupole transitions in both cases, whereas the lower energy part contains both stretched dipole and quadrupole transitions. It is noted that

the multiplicities ,are especially high at

the outermost edge of the quadrupole bump.

C10-118 JOURNAL DE PHYSIQUE

Fig. 11. The a^ff moment of inertia obtained by means of eq.(10) from data as shown in fig.10, plotted as function of h2w2 for points above

h2<o2=0.2. For comparison the t^coll obtained from the yrast band in 158Er is shown as black dots labeled with I for (I-KE-2).

Fig.12. The same as fig.11, except that the data used is from the multipli-city measurements of ref.4, evaluated by means of eq.(9) for all the points in the right part of the figure. The dashed line shows the prediction from rotating liquid drop calculations.

is shown in fig.15.

The dipole component is in both cases showing an increase in the number of tran-sitions per 60 keV for higher windows which strongly indicates that a dipole component is present also in the decays between the windows corresponding to the highest spin interval which of course as seen from fig. 7 can have rather wide tails in the spin distributions.

The quadrupole part is quite different in the two cases. For the 50Ti + 1 1 0Pd case

there are a low and a higher energy compo-nent which both increase with increasing

spin, whereas for the Ti + Ti case on-ly the high energy part increases in num-ber of transitions for increasing spin in-tervals .

The spectra are in principle very diffe-rent from those observed for the good ro-tors. The increasing number of transitions per energy interval and the almost constant average <E > for different windows may be understood as due to an increasing # f f for

increasing spin. If the data for 50Ti +

50Ti ,50Tj ,IOORU* 192 MeV

I (unfolded 1

-0 l0 do 3 0 40 0 l 0

2'0

3 0 4.0 TRANSITION ENERGY ( M U )

Fi .13. E spectra taken at Ow and 9oW

£0: 5 difIerent window gates on the total

energy spectrum for the 'OTi

+

' O T ~ reac-

tion. The spectra taken with (5"x6") NaI detectors have been unfolded and norma- lized to average multiplicity of corre- sponding windows on the total energy.

TRANSITION M R G Y ( W )

Fig.14. Tlie multl.plicity < M >, the aniso- tropy N (00) /N (go0)

,

and Ey gpectra decom- posed into (h=l,AI=l) and (A=2,AI=2) com- ponents as functions of Ey are shown in the upper, middle and lower part of the figure, respectively, for two different reactions.

( 8 ) , (9) and (10) the result is consistent

with the most simple explanation namely that £or 5 0 ~ i

+

''Opd the deff increases

linearly with spin up to frig at the high-

[

= O T i

+

IIOPd, 223 MeV

TRANSITION ENERGY (MeVI

Fig.15. Decomposed spectra of the (h=l, AI=l) and (X=2;AI=2) components for dif- ferent windows on the total energy for two different reactions.

est spin interval. The 3 narrow energy distributions of both dipole and quadru- pole transitions may indicate triaxial shapes with relatively small changes in particle alignment along a possible axis of collective rotation.

For the 5 0 ~ i

+

5 0 ~ i reaction there are one increasing dipole and only one ipcrea- sing quadrupole component with again al- most constant <E >, but with a large ener-

Y

gy spread in the quadrupole bump. The low quadrupole bump is probably due to the low spin vibrational states through which the decay has to pass before reaching the ground state. This component disappears in the subtracted spectra just like most of the statistical tail. The numerical analy-

sis shows that the Teff increases linearly

with spin but in this case up to deff= 1.3

d indicating that some of the nuclei

rig

populated in the highest spin interval may

JOURNAL DE PHYSIQUE w5 --,

192 MeV

-

W 4

-

/- R' H''

,/;',y

.K;..:/

-

01

I

I

I

I

1

10

20

30

40

50

SPIN

1

Fig.16. The average decay flow of the y-cascades is shown in this yrast diagram. The entry points corresponding to the 5 window gates on the total energy of the cascades and the measured multiplicity are shown as open circles connected by the entry line. From the entry points the direction and length of the vertical lines indicate how much statistical v-rays remove of angular momentum and energy in average for each win- dow. The thick (X=2,AI=2) lines roughly parallel to the yrast line indicate the amount of angular momentum and energy removed by the stretched quadrupole transitions measured for each window interval by the subtraction method, and the thin continuous lines indi- cate the dipole (X=l,AI=l) parts for the same intervals. The dashed lines indicate the slopes corresponding to the energy spread observed for the quadrupole bump of each window interval. The yrast line corresponding to a rotating liquid drop is shown to be steeper at the highest spin than the measured slope of the average flow of the yrast- like transitions.

be superdeformed with a ratio of axis as same nuclei. In other words, if the spread

high as 2:l. This has been anticipated from should be explained by an ensemble of dif-

theoretical calculations of a rotating li- ferent particle aligned configurations it

quid drop with a possible stabilization would mean that at least half of the spin

due to shell

effect^'^).

The wide distri- in some of the states is created by align-

butions of the stretched E2's could be due ment of individual particles ja>I/2 and

to the fact that many particle channels are other states have almost pure collective

open, .but this is not very likely, since rotation.

the overall shape seems unchanged. The It would be interesting to try to con-

spread could also indicate several diffe- struct a decay path which would be consi-

see if the many check points on the ener- gy relations in the data are consistent. This is tried in fig.16. The five entry points are given by the measured sum ener- gy and multiplicity for each energy win- dow, where the measured anisotropies are

taken into account in translating M to I.

From the highest entry point we then mark the loss in energy and angular momentum consistent with the measured subtracted E spectra, and the measured anisotropies.

Y

It is interesting to note that the inter- nal energy balance and multiplicity eva- luations are accurate to within few per- cent from a comparison of the entry points

and sum windows 4, 3 and 2, and that only

the endpoint of the constructed decay flow

deviates slightly from the position of W 1.

The limits of the large spread observed in the E2 bump of -1.2 MeV are indicated with thick dashed lines. Some other experiment performed by the Orsay group is reported as a contribution to this conference.

It has been the purpose of this section of the paper to demonstrate that it is pos- sible to understand the observed bulk pro- perties of the y-continuum spectra from. simple pictures of the nuclear decay from high spin states. On the other hand it is also clear that the underlying structures

step further with this idea and ask how the transition energies in one cascade would be correlated if this underlying rotational picture is roughly correct.

For a perfect rotational nucleus with constant moment of inertia the

-2 _{I 1}

LEy = 8

-

is constant for all y-cas-

23c011

cades, and the pattern shown in fig.17 may be the result of a y-y coincidence experi-

ment if an ideal detector with no compton

scattering were used. One would expect a clean valley along the 45O diagonal corre-

sponding to E yl= Ey2 since in perfect rota-

tional cascades no y-ray has the same ener-

gy as any other. It is noted that the di-

stance between the 1. ridges along the val- .. 2

ley corresponds to 16 L where d

*

Jcol 1 col1

is the moment of inertia of the intraband

transitions (see fig.6)

.

~f we further introduce 10% spread in

the moment of inertia for the bands used in fig.17 and add one extra transition in each band as a typical example of a back- bend, the picture shown in fig.18 can be constructed. It is even more clear from this picture that if rotational structures are dominating in real nuclei, one should be able to detect it by such a simple y-y coincidence experiment. There is, however, one serious experimental difficulty, name-

may be much more complicated than assumed ly that the (photopeak/total) efficiency

above and more refined methods have to be for large collimated NaI detectors is %SO%

developed. and for GeLi detectors only ~ 1 5 % . That means

Second Generation Correlation Experiments. that only s20-25% and 2-3% of the events

In the previous section we used the ro- in a NaI or GeLi coincidence spectrum, re-

tational model as a frame for the analysis spectively, would be due to photopeak X

of the continuum y-ray spectra. photopeak coincidences, or in other words

JOURNAL DE PHYSIQUE

Typical Experimental Arrangement

'v,

'v

f

Fig.17. E -E coincidence pattern for

Y . Y

four rotational bands of constant moment

of inertia. The spacings of adjacent rid- ges and ridges on each side of the equal

energy valley are 8A and 16A respectively,

where A = -h /2fcoll.

IMPERFECT ROTORS

Fig.19. A typical arrangement for Ey-Ey

correlation experiments. Since large pho- topeak/total efficiency is important, the N a I detectors are collimated such that only the center portion of the detector sees the target.

Fig.20. Ey-Ey correlation 2-d spectra ta-

ken-with NaI detectors for the reaction of

118 MeV "C with 12'sn populating residues of the 1 3 = ~ a compound system1').

Fig.18. Ey-Ey coincidence pattern corre-

sponding to the 4 bands shown in fig.17,

plus 4 additional bands with moment of inertia lO%.greater and 4 with 10% smaller

moment of inertia than those shown in fig.

17. The pattern indicated by solid dots cor- responds to non-rotational features (back-

bending) shown as black peaks in the cas-

b e background due t o compton s c a t t e r i n g . To overcome t h i s problem a d a t a reduc- t i o n t e c h n i q u e h a s been developed2') t o i s o l a t e t h e t r u l y c o r r e l a t e d photopeak X photopeak e v e n t s from t h e u n c o r r e l a t e d background of compton s c a t t e r e d e v e n t s . I f t h e number o f t r u l y c o r r e l a t e d e v e n t s i s s m a l l compared t o t h e number o f u n c o r r e l a t e d e v e n t s , t h e p r o b a b i l i t y o f o b t a i n i n g an u n c o r r e l a t e d e v e n t a t e n e r - g i e s ( E i , E . ) i n t h e two-dimensional p l a n e 3 i s

-

The number o f u n c o r r e l a t e d , e v e n t s N . . i n 1 3 t h e spectrum N i j i s t h e n t h e s e p r o b a b i l i - t i e s times t h e t o t a l number of c o u n t s

1

N R k and t h e number o f u n c o r r e l a t e d e v e n t s Ilk i s t h e r e f o r e

..

N i k N9.j N . . = k 1 7

The " c o r r e l a t e d spectrum" ANi (Ei,E.) _l i s t h e n g i v e n

By t h i s p r o c e d u r e one f i n d s a c o r r e l a - t i o n s p e c t r u m which g i v e s t h e d e v i a t i o n from t h e a v e r a g e and i n t h i s way enhances t h e l o c a l s t r u c t u r e s i n t h e s p e c t r a .

The s u b t r a c t e d background i s t o o l a r g e , however, s i n c e t h e p r o j e c t i o n s

1

Nik and

k N,, c o n t a i n a l s o t h e c o r r e l a t e d e v e n t s . I t i s p o s s i b l e t o improve t h e s p e c t r a to- wards t h e a b s o l u t e number o f c o r r e l a t e d e v e n t s by an i t e r a t i o n p r o c e d u r e . The p r o j e c t i o n s o f t h e a b s o l u t e v a l u e s o f t h e c o r r e l a t e d spectrum

1 1 ~ ~ ~ ~ 1

and

I ~ A N ~ ~ ~

k R

g i v e a good approximation t o t h e number o f c o r r e l a t e d e v e n t s i n t h e spectrum and can t h e r e f o r e be used t o c o r r e c t t h e background s u b t r a c t i o n . The n e x t s t e p i n t h e i t e r a - t i o n p r o c e d u r e i s t h e r e f o r e g i v e n by: AN. .(Ei,Ej)p+l = N i j

-

k 1 3

_I

(',Qk-

I

mQk

l

p) ?,k I n t h e f o l l o w i n g we s h a l l u s e t h e c o r r e - l a t e d s p e c t r a ANij(Ei,E.) mostly because

c10-124 JOURNAL DE PHYSIQUE

are needed (>50 mill.) it is necessary to use many counters to obtain sufficient statistics especially in the high energy region.

The result of one of the first experi- ments with NaI counters made at the Stock- holm cyclotron21) for the reaction 118 MeV 12c on 1 2 4 ~ n target populating the residues of the 1 3 6 ~ a compound system is shown in fig.20. The general patterns of this spectrum are as expected with a deep valley along the equal energy diagonal and with pronounced inner 1. ridges, and with outer ridges which become less well defined farther away from the valley. The more detailed analysis of this spectrum is given in a contributed paper to this 21)

conference by M.A. Deleplanque et al.

.

We shall only here emphasize the very in- tense bridge observed to fill the valley

at E = 1120 keV. This bridge contains as

Y

many transitions as the adjacent ridges, indicating that a large fraction of the many rotational-like cascades in the con- tinuum must contain at least two transi- tions of this energy. It is interesting to note that no discrete lines have been observed at this high energy, although the bridge structure observed in the 2-d spectrum is very pronounced. This is be- lieved to be caused by the fact that ma- ny band crossings occur at the same rota- tional frequency hw = Ey/2 = 560 keV.

To understand this multi-band-crossing (MBC) effect it is useful to look at a theoretical calculation where more levels can be systematically included. Let us look at the cranked shell-model calcula-

tion performed for N=90 nuclei which we la- ter also can compare to experimental data for 160yb. Fig.21 shows only the positive

parity levels based o n the i13,2 neutrons

of the Nilsson configurations )66011/2 and 1651)3/2 which because of signature split- ting give 4 different levels as functions

of Rw. A detailed discussion of these dia-

grams is given in refs. 11889) and by Bengt-

sson on this conference.

The four neutron levels labeled here as A, B, C and D can be combined to give the 6 possible 2-quasiparticle levels AB, AC, BC, BD and CD. The energy of these levels is obtained as functions of-hw by simply adding the energy e' of the individual par- ticle levels in the rotating frame as given in fig.20. For the purpose of illustration the levels have been smoothed through the crossings.

The energy in the rotating frame of the resulting six 2-quasiparticle states is plotted as thin fully drawn lines in fig.22.

(The ground state band and its continuation

above the first backbend has 0 energy in

this frame

-

shown as the 0 line). It is

R W ( W ,

Fig.21. Neutron quasiparticle energies

calculated in the rotating frame e t as

function of rotational frequency tlw for the 4 lowest positive parity configura- tions in l6'yb. In the text the levels are referred to as the labels A,B,C,D.

Fi -23. E -E correlation spectra for

thz 1 s 7smY+ 7 6 0 + 6 0 ~ b

+

3n reaction at

80 MeV taken with Ge(Li) detectors. The

data is the same as used earlier by Rie-

dinger et al.') for discrete line speciro-

scopy. The energies for the different band crossings identified in ref.8) are indica- ted on the figure. The channels have been binned together to give 20 keV/channel to obtain better statistics, and then quadra- tically smoothed by the plotting code.

in fig.22), the frequency of the first backbend. The ABCD also crosses all the

I

I

200 400 603

ANGULAR FREQUENCY

h

O ( keV

1

Fbg.22. The levels shown in fig.21 are combined to give the 2-qp. neutron levels shown as thin lines with labels AB,AC,BC, AD,BD and CD on the figure. Similarly the lowest lying 2-qp. proton levels (shown as thick line labeled 2p) are combined wi'th the neutron levels to give the 4-qp. (neu- tron-proton) levels indicated by thick dashed lines. The black dots indicate the energy and frequency where the various levels possibly may interact.

other 2-quasiparticle bands at characteri- stic frequencies for the pairbreaking of the other five 2-quasiparticle states

(uAC,

wBC8 uAD8 uBD, uCD)

.

If we further combine

two highly aligned hllI2 protons, labeled (2p) in the figure, into the diagram, a complicated set of band crossings occur. Many of these crossings will be .blocked, and only the bandcrossings where possible inter'action can take place are marked on the figure with black dots. It is seen

that the allowed crossings line up on

C10-126 JOURNAL DE PHYSIQUE

are all characteristic for the breaking of specific pairs of particles like f.ex. the first backbend discussed above. It is interesting to realize that although one is not able to resolve the individual bands in the continuum of y-rays, one may still be able to identify the highly aligned configurations as bridges in the 2-d spectra and in this way systematical- ly study the details of the nuclear struc- ture which influences the characteristic frequencies for breaking of the particle pairs, as £.ex. the deformations c2 and €4.

Fig.23 shows the data earlier used for detailed spectroscopy studies of 160yb by

Riedinger et

,

resorted into a two-

dimensiona'l spectrum which has been back- ground reduced and binned to 20 keV/chan- nel to obtain better statistics. The posi- tion corresponding to the uAB, uAD, uBC

and w crossings found in ref. 5, for the

2~

individual bands is marked, and it is seen that bridges (or stepping stones) occur in the valley exactly at those places. The AB crossing is however not so clear because the interaction for this crossing is weak and results in a very sharp back- bend. The intensity observed in the val- ley is not caused by the successive transi- tions, but rather by those corresponding to the second ridge, in the present case the 8++6+ (589.5 keV) and the 12++10+

(586.8 keV) transitions. The second back-

l

bend (2p) is only weakly observed because only states of I<30 3 are populated in the present reaction. Therefore only a few bandcrossings above the yrast crossing

can be populated since many of the possible configuration crossings will occur at I>30

R

due to the high alignment of £.ex. the

6-qp. states.

A numerical analysis of the number of

transitions in the bridges is in progress, but it is evident from the preliminary analysis that the intensities in the brid- ges are more than twice the values which can be accounted for by discrete lines

8 1

from the experiment of Riedinger et al.

.

We can therefore conclude that the effect of MBC enhances the bridge structures and that we have a new and interesting possi- bility of a systematic study of the effect of MBC.

Since we in principle understand the structures observed in the lower spin re- gion, it would also be interesting to ex- tend the experiments to the highest spin regions as well. Such experiments were performed by the NBI-Berkeley-GSI collabo-

22)

ration at the 88" cyclotron in Berkeley

.

1 2 4 ~ n was bombarded with 170 and 185 MeV 4 0 ~ r ions leading to evaporation residues of 158'159 * 1603r, the same systems which earlier were studied in detail by the C-M method discussed in the previous section. 4 GeLi detectors were used to collect 6 pairs of coincidences added into the same matrix and a multiplicity filter of NaI detectors ensured that low spin compo- nents were suppressed in a similar arrange- ment as shown in fig.19.

'"~n

(

4 0 ~ r ,

xn)

164-XE~

7

i . 7 5 3 75

E

(40Ar)

=

170

MeV

Fi . 2 4 . E -Ey correlation s zctrum %or " ~ n + * ' ~ r +

B

'

4 - X ~ r reaction taken with GeLi detectors. The transi- tion energies for MBC's in

1 6 0

Ex and those assumed to occur in 1 5 9 r 1 6 0 ~ r from the corresponding ' 6 1 r 1 6 2 ~ b iso- tones are indicated.

C10-128 JOURNAL DE PHYSIQUE

set in at % 1 MeV. The known crossings

can immediately be identified in the lower energy range as given on the figure, from discrete line studies and cranking calcu- lation, but several more bridges corre- sponding to unidentified crossings at

higher energies can also be seen. A more

systematic study of these upper bridges is in progress, but it seems evident that the general structure of band crossings found and studied up to I%30, E ~ 8 5 0 keV

Y

by discrete line spectroscopy continues to persist up to %l MeV corresponding to 1 ~ 4 0 . The general filling of the valley is more clearly verified in the 185 MeV data shown in fig.25. Many other cases

have been in~estigated~~)

,

although not

finally analyzed, in the regions around ll8~e, 1 3 6 ~ d l 1 5 5 ~ r 1 166~b, and it is seen in all these cases that the valley becomes less pronounced at E energies larger than

Y

-1 MeV. It is not clear yet what the cause of this filling is. It may be connected to the loss of pairing above Iz40, and/or with AN=2 couplings to the higher lying shells which are being strongly aligned and there- by lowered in energy. One really strong-

more 'distinct bridge is observed in the

185 MeV data (fig.25) athu~O.55. Calcula- tions show24) that this may be connected with the hgI2 proton orbit, but systematic

studies on .neighbouring nuclei are neces-

sary before more definite conclusions can be made about the details in the high spin region.

As pointed out earlier the distance be-

be compared to the measured Teff discussed

in the sum-spectrometer section.

Fig.26b, c and d show projections across the valley for selected energy interval slices (E1+E2)/2 equal to 750-820 keV, 900-950 keV and 1160-1240 keV, respective-

ly. A tentative location of possible ridges

is shown by dashed arrows. The location of a ridge corresponding to a moment of iner- tia of l50 M~V-' as found for beff for these nuclei (see figs.11 and 12) is also indicated. The width of the valley is clear- ly 25-50% larger than this, indicating an

dcoll smaller than Jeff and an average

particle alignment ja of around 10-20 h,

whereas I is around 45. The general filling

of the valley can also be observed in fig. 26a, where projections of slices along the valley and along the ridge are shown. More detailed theoretical calculations are per- formed by the Lund-group and discussed in

24)

ref.

.

As the last point we will like to dis- cuss the possibility for identifying the lower members of the quasiparticle bands which are f.ex. crossing the ground state

band at higher 'spin. Ohe may say that these

bands will form a second quasi-continuum starting just above the pairing gap as il- lustrated in fig.27. The states in this "second" continuum should be predominant- ly fed by the (xn) channel which has the highest number of neutrons. In the figure

this is shown as a (61-11 channel in contrast

to the (5n) channel. which predominantly

will feed higher spin states first.

tween the ridges'is a measure of the collec- Fig.28 shows the low energy part of an

Fig.26. Projected cuts on the spectrum shown in fig.25. The left side of the figure shows cuts along the 1. ridge

(squares) and along the valley (open circles). The position of the second back- bend (2bb) is indicated. The right side of the figure shows cuts perpendicular to the valley for the shaded areas in fig. 25. The positions corresponding to Jeff =l50 Mev-1-and dco11=95 M ~ V - 1 and 110 M ~ v - ~ are Indicated with arrows.

1 3 0 ~ e -+ 164'1658166~b reaction with a bom- barding energy of 185 MeV. The advantage

gf the iterated correlation spectra is

that photopeak X photopeak correlated

events are enhanced and compton scat- tered events as well as statistical photo- peak events which are randomly distri- buted over the entire 2-d spectrum are

suppressed.

A series of ridges parallel to the two axes can be observed. It is believed that

they represent a continuum of photopeak

coincidences feeding the discrete low

spin levels of the-ground state bands

(gsb) in the 164r165 *166~b nuclei. Some of the most pronounced ridges are marked

I- I

/ no levels

l

Fig.27. A schematic E vs. I diagram to indicate that a sudden change in level density on the border line between the region below and above the pairing gap may be expected. Especially the 6n chan- nels in the reaction 1 3 0 ~ e

+

' O A ~ +

1 6 4 1 1 6 5 f 1 6 6 ~ b are expected to feed the low spin members of the rotational bands above the pairing gap.

with the transitions in the gsb they are in coincidence with. It is seen that all the ridges which belong to the 6n channel feeding the gsb of 1 6 4 ~ b do not extend as high up in enecgy as those belonging to

165~b. Fig.29 shows some typical projec-

JOURNAL DE PHYSIQUE

Fig.28. The low-energy part of a GeLi Er-Ey correlation spectrum, iterated 20 times for the reaction 1 3 0 ~ e

+

' O A ~ +

Is'

r 1 6 6 ~ b with 185 MeV. The figure is a Xerox copy of a colour plot, but it is still possible to see the ridges paral- lel to the axis corresponding to photopeak coincidences with discrete transitions in

the ground state bands of 1s'r'65r'66 _Yb.

The strongest ridges are indicated and reflect £.ex. coincidences with (2++0+),

(4++2+)

,

(6++4+) and (8++6+) in the gsb

of

b.

Fig.29. Projected spectra correspond-

ing to window gates on discrete tfansi- tions ( 2 + + 0 + )

,

(4++2+)

,

(6++4+) and

(21/2+17/2) in the gsb of 16'yb and 1 6 5 ~ b respectively. The shaded areas indicate the continuum (low-spin) y-ray transi- tions, which feed the gsb and are be- lieved to be from rotational bands mainly above the pairing gap.

bands with an Tcoll Q, 90 M~V-l. If this is the case the broad peaks at 180, 270 and 360 keV would then correspond to 6 + 4 , 8+6 and 10+8 intraband transitions in this "second" quasi-continuum above the pairing gap. At the moment, however, we do not know the multipolarity of the transitions,

and much work has to be done before this explanation becomes more than just plau- sible.

In an experiment by Jin Gen-Ming et al.

ref ,25), it has been possible to identify

the low spin ( 4 + , '6 and 8)' members of

2 3

the S-band in 160~y by a ( He,a)

reaction. According to the authors, the energy relations in this band are consi- stent with

rcoll

-

trig. The gsb on the other hand has icoll = 80 ~ e d ' at the lowest spins. It is therefore not unlikely that one should find an average JCol1 of 90

M~v-'

for the low spin members of this quasi-continuum. We may hope that a more detailed study of this region will shed more light on the coriolis attenuation ef- fect, since the band structures at low spin are expected to experience particularly strong changes in the alignments due to the coriolis force. Also the structure should be more sensitive to recoil effects in this region.

Summary.

It has been the purpose of this talk to show that we in the last few years have come far closer towards the understanding of the bulk properties of high spin states, but also to show that many inspiring pro- blems remain to be solved before a more complete insight into the details of the

nuclear phenomena of these states is en- countered.

We have shown that one can speak about two different moments of inertia, the ef-

-

fective moment of inertia Jeff which ex- presses the envelope of the decay pattern and relates to the slope of the yrast line and thereby the shape of the nucleus, and

a collective moment of inertia Jrcoll de-

duced from the second derivative of the rotational energy directly related to collective rotations of the core of the

-

nucleus. The ratio of these ifeff/Jcoll

-

A

gives the average alignment of the

1-1,

many particle configurations on which the rotations are built at high spin. We have shown that there recently have been deve- loped methods by which one experimentally can determine these values from the y-ray spectra. We have also seen how the E -E

Y Y correlation method reveals a new way to study the details of the nuclear configura-

tions, namely by determining the characte-

ristic rotational frequencies h w at which the individual particle pairs break up and align their spins.

A more systematic study and mapping of this effect is in progress in different la- boratories. In principle there is also in- formation about the alignment of the indivi- dual particle configurations in the 2-dimen- sional spectra, but further experiments using more parameters have to be made before

I

we will learn how to extract this informa- tion.

C10- 132 JOURNAL DE PHYSIQUE

spin quasi-continuum above the pairing

gap. An average Tcoll % 90 M~v-' is found

for these bands, although very specula- tive, since f.ex. no spin determination has been made yet.

Acknowledgements.

The work discussed above', much of which

is not published yet, has been made in collaboration with colleagues and visitors at the NBI-Ris0, LBL-Berkeley, GSI-West- germany and AFI-Stockholm. In particular I would like to thank G.B. Hagemann, J.D. Garrett, F.S. Stephens, 0. Andersen, M.A. Deleplanque, R.M. Diamond, C. Ellegaard, Th. Lindblad, S. Ogaza, R.S. Simon, and P.O. Tj0m. Many stimulating discussions with colleagues in Copenhagen and Lund have been most helpful, and I would like

especially to thank Aa. Bohr, B.R. Mottel-

son, S. Bjornholm, S. Frauendorf, G. Lean- der, and B.S. Nilsson for help and encou- ragement.

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