of Tennessee,. Knoxville, Tennessee 3'7996-2200. J. C. %addington. McMaster University,. Hamilton, Ontario, L85 4M' Canada. M. P. Fewell, N. R. Johnson, ...
PHYSICAL REVIE% C
section is intended for the accelerated publication
The Rapid Communications
accompanied by an abstract Pag.e proofs are sent to authors, corrections unless requested by the author.
but, because
of important
of the
new results
rapid publication
Shape effects in hit/2 and g7/2 bands in
M.
anuscripts
schedule, publication
submitted
to this section are
is not delayed for receipt of
' Tm
'
A. J. Larabee, L. H. Courtney, S. Frauendorf, and L. L. Ricdinger Department of I'hysics and Astronomy, The University of Tennessee, Tennessee 3'7996-2200
Knoxville,
J. C. %addington McMaster University,
Ontario, L85
Hamilton,
4M' Canada
M. P. Fewell, N. R. Johnson, I. Y. Lce, and F. K. McGowan Oak Ridge Rational Laboratory, Oak Ridge, Tennessee 3783'0 [,'Received 27 February 1984)
The i&3l2 2
7 2
I.
523] and
neutron
7 2
I.
404] bands are observed in ' Tm to
backbend.
Before the backbend,
[404] none, which is interpreted
as resulting
the
2
I= 612
[523]
and
43
2,
band exhibits
from the very different
respectively,
large signature
driving
influences
The i&3l2 neutron alignment hl&l2, and g7l2 orbits, respectively, on the core triaxiality. naure splitting in each band as a result of its dominant driving force to positive values
8 {Ml;I in terms
I —1)/8 (E2;I
of calculated increases
I —2)
well beyond the
splitting,
of the
A
the
= 2,
changes the sig-
of y. Measured
values increase dramatically after the backbend, and this is explained Ml transition rates and decreases in the E2 rates.
in the
The triaxial %=90 nuclei are generally viewed as rather soft with shapes that may be profoundly affected by rotation One approach to determine and by quasiparticle alignment. the nuclear shape is to study the energy splitting between the two signatures of medium-to-high E bands, since recent calculations ' have shown this to be rather sensitive to the size of y, the core triaxiality parameter. %C present here the best example to data of the very different polarizing influences on the soft X = 90 core by two different quasipartiTm. clc cxcltatlons ln Two E = 2 bands are observed, based on the hlll2 and g7l2 quasiproton orbitials. These two bands have very different degrees of signature splitting (i.e. , the energy difference between the favored and unfavored components of the band), which are explained here as the effect of the IIIII2 and g7/t2 orbitals having dlstlnctly dlffcI'cnt values of p. In addition, 8 (Ml )/8 (E2) rattos arc Illcasurcd II1 botll ballds and found to reflect the differences in signature splittings. Furthermore, the 8(M1)/8(E2) values increase dramatically after the backbcnd in each band and the classical vector model of Ref. 3 is used to explain this as an effect of enhanced MI and decreased E2 matrix elements. TIll (Flg. 1) llas been constructed Tllc level scllcIIlc foI' from experiments involving the ' Sm(I~N, 3n) reaction at accelerator and the tandem the McM aster University "'Pr('2NC, 4n) reaction at the Oak Ridge Isochronous Cyclotwo large NaI tron. IA the Oak Ridge measurement, counters werc used as a total energy filter and 7 Gc detectoIS counted thc pllmaly y-y colncldcncc data. TI'lplc coln-
cidences between the Gc detectors were accumulated and subsequently analyzed to give approximately 240 million yy pairs in coincidence with the total energy range which emphasized the ' 9Tm reaction product. Angular distribution data and angu18r coI'Iclatlon data werc analyzed to assign spins and extract multiple mixing ratios. Two distinct rotational structures, composed of stretched E2 and crossover E2/Ml transitions, were assigned based upon the coincidence and angular distribution data. The structure on the left in Fig. 1 is yrast based upon the larger population intensity, and has been assigned previously 5 as The a band b«lt upon the ~[5231 Niisson configuration. spins and parities of the other band in Fig. 1 are determined largely by the stretched dipole nature of the 717.5 and 790.8 and 2 levels, respectivekeV transitions feeding the 2 ly, of the ~ [523] band. A further argument against negative parity for the band on the right is that the two = 2 bandheads should have negative parity and bc split by only 36 keV with little apparent mixing. This band is evidently built upon the 2 [404j Nilsson orbital. Possible low energy
I
' transitions from the backbends to an I = —, ground state have not been observed. Parts of this level scheme have been reported previously. Shal p backbcnds occu1 ln both thc /l 1 1/2 8nd g 7/2 stI'ucturcs, where the i l, y2 neutron alignment results in the crossbands by three-quasiparticle ing of the one-quasiparticle Below the backbcnd, in the bands of greater alignment. hIII2 band (I & —, ), a large energy difference between the OI984 Tile AHlerlcaIl Physical Soc&et/
SHAPE EFFECTS IN h))p AND gp(2 BANDS IN two
signatures
is clearly present. The unfavored band i.e. , n = + z in the notation of Refs. 1 —3
(I = —,, z, . . . ,
and 8) lies at least 100 keV above the favored structure (n = —2 ). After the backbend (I energy 2 ), the
)
difference between the two signatures is less than 10 keV. In contrast, the g7g2 band shows essentially no splitting before or after the backbend. The very different degree of signature splitting in these two E = 2 bands below the back-
1935
Tm
bend is rather remarkable and likely indicates that the nucleus has different shapes in these two modes. The observed behavior of the E = —, bands in "Tm is consistent with the predicted' influence of these quasiparticle orbits on the degree of the core triaxiality y. In the case of the ~[523] band, the chemical potential X, for protons is in the middle of the h~~~~ shell. Calculations using the cranked shell model (CSM) show that for this value of k, the n = —~ signature of the ~ [523] quasiparticle state has —50' a well-defined minimum at co=0.3 MeV/h and y while the n= +~ signature is less y driving with a fairly —70', this produces a rather large shallow minimum at y splitting. The observation of a large signature splitting indicates that the nucleus does indeed follow the driving influence of the hl]~2 orbital. Adding the y dependence of these quasiparticle orbits to the expected hydrodynamical behavior of the core (V„cos3y)' gives equilibrium values of —25' (n= —~) and y —14' (a= + ) at co =0.3 y MeV/A. The value of V~, = —0.89 MeV is chosen to reproduce the signature splitting seen in the 2 [523] band. After the backbend, two i]q~2 quasineutrons are added. At W 90 the A. for neutrons is at the beginning of the i~3/p shell, which leads to an orbit driving the core towards small positive y, where the signature splitting in the h~I~2 band disappears. The neutrons have a stronger driving force than
=
960 59/2
=
907
I
I
434 55/2
=
833.4 437 1[
53/2
763.2 403.2
49/2
=
—
395.4 799.5
51/2
359.5 725.2
47/2
685.4 365.6
45/2
320.0 643.8 I I
43/2
599.7 323.5
I
'IF
I
41/2
43/2
722
41/2
I
'277
39/2
552.8
276
511
1[ 'l[
37/2
35/2 33/2
871.1
]I
486.3„208.7
430.0
277
31/2 29/2
$ lSZ. B
248
lr
3&/2
)l544 5p9 439.5] [174.8
27/2 25/2
493.0
264.1 573.6
293.5 583.6
l7/2
461.7
35/2 13/2
100.0
27).3 526 4
330.7
234.5 445.2
230.9 28).0
)I
7/2
vz [5zs]
&59
7/2
69Trr]90
FIG. 1. Level scheme for
Tm.
I7/2 +
&3/2
11/2 +
403.9, 2'I0. 3
9/2
21/2
15/2
489.6 255.0
345.2 445.2
V
,
7~
25/2
)9/2
560.5 289.5
116.2
19/2
29/2 +
1
433.1 549.5
558.3
—
23/2
.2 603. 309.3
61
$25.2
23/2 21/2
I1/2
.9
ft&7. Z
629.7
33/2
455
361.6 208
1f
496.9 6
649.7
35/2
244
491 1[
37/2
575
234.5 443.0 I[
193.8
[404]
7/2
1936
A.
J. LARABEE
the protons and thus the combined influence of these three quasiparticles on the core yields equilibrium values of y 0 for both signatures, which is consistent with the observed disappearance of the signature splitting. This y flip-flop has already been observed in '5 Ho (Ref. 9) and 8'Kr (Ref. 10) and has been discussed in detail in the former case in Ref.
well-aligned bands. The observed increase in the Ml/E2 ratio in ' Tm is quite dramatic and consistent in the two —1 observed bands. Measured mixing ratios of the transitions in the Atty band also show an Ml/E2 enhancement after the backbend, averaging 5=0.30+0.07 before the backbend and 0.03 +0.03 after. Classically, M1 radiation is generated by the timedependent (perpendicular) component of magnetic vector as it precesses about the rotation axis. In a cranking approach, it is assumed that the rotational axis is perpendicular to the symmetry axis (I, ) and thus the alignment of i ~3iq neutrons along this rotation axis (I„) would not obviously influence the M1 rates between the two signatures of the h~]/~ or g7/g bands. ' However, the recent approach of Donau and Frauendorf' takes account of the fact that the total angular momentum I is the rotational axis of the system, and is different from I for high-K bands. The angular momentum along I„, coming from the aligned i]y~ neutrons, can then be resolved into a component along the axis and a comThe perpendicular component can ponent perpendicular. contribute to the Ml transition probabilities. Using such a geometrical approach, I3onau and Frauendorf' show that particles aligning during the backbending process are able to contribute coherently to the timedependent component of the magnetic vector. If the g factor (gt —ga) for the one-quasiparticle state below the backbend (with aligned angular momentum i~) and the g factor (gq —gs) for the two quasiparticles aligning at the backbend (with iq) have opposite signs, then the time-dependent component of the magnetic moment is increased, giving rise to an enhancement of the M1 rate. This can clearly be seen in the expression for the 8(Ml)/8(E2) ratio
—
I
1. In the case of the —, [404] band, the A. for protons is at the top of the gyq shell. Such orbits, with along the symmetry axis, do not drive the core to triaxial shapes. In the CSM calculations, the quasiparticle energy is constant for —30' & y 30' and the equilibrium shape simply corre—90 sponds to the hydrodynamical shape of the core, y =0. at cv 23 MeV/A. The two i ~yq particles again provide the dominant driving force in the three-quasiparticle band and 0' results. The CSM calculations predict no signature y splitting in this region of the calculated y deformation and indeed no splitting is observed immediately before or after the backbend in this band. The transition matrix elements within these bands can be of the observed signature used to test this interpretation Branching and mixing ratios for many of the splittings. transitions in both bands have been extracted, which can give a detailed comparison of Ml/E2 ratios of matrix elements before and after the backbends. The 8 (Ml; —2) values for many of the states I I —1)/B(E2;I in the h~i~q and g7p bands are extracted from measured branching ratios and displayed in Fig. 2. Hagemann et al. have reported an enhancement of this 8 (M (E2) ratio in the crossing region of the backbend in '"Ho, but here we emphasize extraction of ratios for states not involved in the backbend in order to probe the quasiparticle influence in
j
(
et al.
—
—
I
I
I
"
1)/8
2. l
2.4
"59Tm
7' [523]
59T
o
0—
N
0 ~Q= + ~r, -O=- ~r,
5'&
/2
3'2+
~
Xw
AFTER BB
12
27
2
~
——TH EORY
II
CQ
BEFORE B B
D
CU
~
[404]
Q= —&/2~@ = + &r2 Q=
2.
&.
7y,
08
lXl
0.4—
0.1
3
5'
2
2
2'+ 2
I-y-Q-— m--$ —
$ 29'/2 I
I
I
0.2
0.5
0.4
I
0.1
0.2
l
0.4
%cu (MeV)
FIG. 2. Ratio of the stretched M1 to stretched E2 reduced transition probabilities for members of the & [523] band (left) and the [404] band (right) in 5 Tm. Experimental values come from observed branching ratios, the theoretical values from Donau and Frauen~ dorf (Ref. 3). Theoretical parameters used were: (g] —g~) =0.92, i] =4t (h]]~q protons); (g& —gz) =0.42, i, =2h, y= —9 (g7/z protons); (g~ —g&) = —0.52, i~=9.5h, y=0' (i~3/p neutrons); and Q0=5 eb. For the —[523] band, signature-averaged values were used below the backbend, where y = —25' (o. = —& ) and y = —14' (n = + & ).
SHAPF. aFFECTS 1N
8 (M1;I
I »„AND
g„, m
NDS 1N "sTm
I —1)
8(E2;I- I-2)
~
~
This cxpl'csslon h8s bccn modif lcd fl om that of Rcf. 3 to include the effect on the E2 rate of the nonzero y. A substantial increase in the 8(M1)/8(E2) ratio is evident in Fig. 2. In the theory, this results not only from an increase of the 8 (Ml) rate arising from the g factor of the two aligned ii@2 neutrons but also from a decrease in the 8(E2) due to the loss in collectivity as the 7 shifts from negative values to near 0, Recent Hartree-Pock-Bogoluibov calculations by the Lund group" indicate that only a small decrease ((10'/o) in e2 is expected after the backbend, which affects the calculated ratios only slightly. The calculations presented here have assumed 8 constant e2 deformation throughout the structure. The results of the calculation based on Eq. (1) are illustrated by the dashed lines in Fig. 2. The y values used are those extracted from a fit to the observed signature splittings in the bands, as described above. There is a qualitative agreement with the experimental values for the 2 [404] band and above the backbend in the —, [523] band. However, below the backbend in the latter the experimental points arc enhanced for the a = —2 to + 2 transitions and depressed for the e = 2 to —~ transitions, This effect was explained in Ref. 3 as resulting from a (1@6,e'/rtcu) factor in Eq. (1), which depends on the energy of the signature splitting. Since we have postulated that the signature splitting in the h11~2 band results both from a transition to the rotation-allgAcd coupling scheme and from dlffclcnt y deformations for the two signatures, this expression has not been used. The increase in the 8(Ml)/8(E2) ratio after the backbend predicted by the theory for the —, [523] band ls ln f8111y good qUaAtltatlvc agrccmcnt with thc experimentally observed increase, if at a given frequency the signature averaged experimental ratio below the backbend is cornpared with the experimental ratio above. For the ~[404] band the theoretical increase in the ratio after the backbend falls somewhat short of the observed increase. However, thc gcncral qUalltativc agrcclTlcnt strcngthcrls thc conclusions concerning the shape change. IA conclUslon, 8 change ln thc slgnatUrc spllttlng ln thc
energies and ln the 8 (Ml;I I 1)/8 (E2;I I 2) values is observed in the 611~2 proton band through the neutron backbend, and this change is attributed to the differing driving influences of these quasiparticles to triaxial shapes. In the g7g2 proton band no splitting is observed before or after the backbcn. d since that orbit always has an axial shape. EqullibrlUID p valUcs arc extracted by coIDparlson of the energy splittings to the cranked shell model. In addition, a large increase in B(M1;I I —1)/8(E2;I I —2) values arc observed in both bands after the backbend. These increases are explained as a result of both a decrease in the E2 transition rates after the backbend (7 becomes positive) and an increase in the Ml rates (the gx —grt of the aligned I~y 2neutrons contributes). These observations thus demonstrate in some detail the differing influences of various quasiparticlc orbits in the rather soft N =90 shapes. There are separate measurements of the changes in the E2 and in the M1 transition rates due to the alignment of quasiparticles in a backbend, In ' Yb, Fewell et ai. ' have observed a decrease in 8(E2) values after the backbend, suggesting a movement to positive values of y as discussed here. In 8'Kr, Funke et al. '0 directly measured an increase ln 8 (M 1 ) values after the gsr 2 proton backbend, and explained it using the model of Ref. 3. Both effects are needed to explain the observed 8(M1)/8 (E2) changes induced thc /13/2 Acutron backbcnd ln TID. An lIDportant fU" ture measurement would be a lifetime experiment on ' Tm, in order to directly extract the 8 (E2) values before and after the backbend. This would bring even more understanding to quasiparticle-dependent shape effects in the X = 90 transition region.
Permanent address: Central Institute for Nuclear Research, Rossendorf 8051, Dresden PB 19, German Democratic Republic. ~Present address: Department of Nuclear Physics, Australian National University, Canberra, Australian Capitol Territory 2601, Australia, rs. Frauendorf and F. R. May, Phys. Lett. 128B, 245 (1983). G. A. Leander, S. Frauendorf, and F. R. May, ln ProceedIngs of tAe Conference on High Angular Movrenturn Properties of Nuctei, Oak Ridge, 1982, edited by N. R. Johnson (Harwood Academic, New York, 1983), p. 281. 3P. Donau and S. Frauendorf, Ref. 2, p. 143. 4A. J. Larabee and J. C. Waddington, Phys. Rev. C 24, 2367 (1981). 5R. Holzmann, J. Kuzminski, M. Loiselet, M. A. Van Hove, and J. Vervier, Ref. 2, Vol. 1; Phys, Rev. Lett. 50, 1834 (1983). 6C. Ekstrom, M. Olsmats, and B. Wannbcrg, Nucl. Phys. A170, 649 (1971). ~L. L. Riedinger, L. H. Courtney, A. J. Larabee, J. C. Waddington, M. P. Fewell, N. R. Johnson, I. Y. Lee, and F. K. McGowan,
Ref. 2, Vol. 1. SR. Bengtsson and S. Frauendorf, Nucl. Phys. A327, 139 (1979). 9M. D. Devous and T. T. Sugihara, Z. Phys. A 288, 79 (1978); C. Foin, S. Andre, D. Barneoud, J. Boutet, G. Bastin, M. G. Desthuilliers, and J. P. Thibaud, Nucl. Phys. A324, 182 (1979). 'OL. Funke, F. Donau, J. Doring, P. Kemnitz, E. Will, G. Winter, L. Hildingsson, A. Johnson, and Th. Lindblad, Phys. Lett. 1208, 301 (1983). G. B. Hagemann, J. D. Garrett, B. Herskind, G. Slctten, P. 0, Tjom, A. Henriques, F. Ingebretsen, J. Rekstad, G. Lovhoiden, and T. F. Thorsteinsen, Phys. Rev. C 25, 3224 (1982). '2I. Hamamoto, Phys. Lett. 1028, 225 (1981); 1068, 281 (1981). R. Bengtsson, Y. S. Chen, J. Y. Zhang, and S. Abcrg, Nucl. Phys. A405, 221 (1983). '4M. P. Fewcll, C. Baktash, M. %. Guidry, J. S. Hattula, N. R. Johnson, I. Y. Lee, P. K. McGowan, H. Ower, S. C. Pancholi, L. L. Ricdinger, and J. C. %'elis, Ref. 2, p. 69.
The
wish to express our appreciation to foI' his coIDIDcnts and partlclpatlon ln dlscUsResearch at the University of Tennessee is supported
authors
G. Lcandcr
sions. by the U. S. Bepartment of Energy under Contract No. BEAS05-76ER0-4936. At Oak Ridge National Laboratory, the work is supported by the Department of Energy under Contract No. %-7405-eng-26 with the Union Carbide CorporatiOA.
