Level structure of 124Ba

Nuclear

Physics A496 (1989)

North-Holland,

605-620

Amsterdam

LEVEL STRUCTURE T. KOMATSUBARA,

T. HOSODA,

H. SAKAMOTO’,

of’ Pl~,wics, Uniwrsity

Inri,u,e

of Tsukuha,

Received (Revised Abstract:

states of “‘Ra

Excited

reactions of “‘Cd(“O,3n) been studied

by y-ray

spectroscopy.

NUCLEAR E

measured

REACTIONS E,,

I,,

I,(A),

K. FURUNO

Japan

1988)

by means of in-beam

The high-spin

y-ray spectroscopy

oia

states have been observed

up to J” = 18’.

band have been newly established.

Systematic

band and the band crossing in barium isotopes are discussed.

“‘Cd(‘“0,

3n),

E =65

lzJBa deduced

yy-coin.

Enriched RADIOACTIVITY

30-5 Iharaki,

and

4n). The decay of lzJLa to the levels in ““Ba has also

a quasi-y-vibrational

of the quasi-~-vibrational

T. AOKI

19 July 1988

15 December

have been investigated and ‘“Cd(“O,

Several side bands including hehaviours

OF “‘Ba

MeV,

and “‘Cd(“‘O,4n),

levels .I, CT, Routhian.

E = 85 MeV;

Boson expansion,

target, Nat crystal array.

lzJLa [from “‘Mo(“CI,

2pn)];

measured

ET, I,,

T,,?.

Enriched

target.

1. Introduction The nuclei in the region of the neutron number N < 82 and the proton number Z > 50 are interesting targets for the investigation of the interplay between singleparticle and collective motion. The study of the nuclear structure in this region has recently been extended towards the more neutron-de~cient side and to higher-spin states. The softness of the y-deformation is a remarkable property in this region of nuclei. Since Wilets and Jean ‘) discussed the surface oscillation with deformed potentials independent of the shape parameter Y, the quasi-y-vibrational bands found in Xe and Ba nuclei have been investigated from the point of view that the quasi-~-vibrational band might be a strong indication of the ~-instability of the nuclear deformation ‘*‘) {we call hereafter the quasi-y-vibrational band simply as y-band). Barium isotopes appear to be the most interesting nuclei. Backbends have been ““Ba [ref. “)I, reported in “‘Ba [ref. ‘)I and ““Ba [ref. “)] at the spin of J” = IO’. In some cases, two super-bands have been observed, and interpreted to arise from the particle aligned states involving protons or neutrons in the hlijz orbit. In addition to high-spin phenomena, y-bands have been assigned. A remarkable feature is the strong staggering of the excitation energies. The level spacings between 3; and 4: states, 5: and 6: states and so on are very narrow. Zolnowski and Sugihara ‘) discussed this narrowing as being due to the y-instability in “‘Ba, using the boson expansion theory. ’

Present address: Faculty of Engineering,

0375-9474!89/$03.50 (North-Holland

0

Gifu

University,

Elsevier Science Publishers B.V.

Physics Publishing

Division)

Yanagido,

Gifu 501-l

1, Japan.

T. ~~mat.~ubara

606

Prior to our investigation [ref. “)]. Recently,

Martin

et al. ,/ “4Ba

of 12’Ba, Conrad et al. have

et al. reported

extended

yrast states up to J” = 12+

the yrast

states

up to _I” -22+

and several side bands. Further[refs. 95’o)]. They have reported two super-bands more, Gizon et al. have measured y-rays from the P-decay of lz4La with the ISOL and/or He-jet system ‘O,“). Only a few levels of the y-band, however, were observed. The present in-beam spectroscopic study is aimed at the search for higher-spin members of the level structure in ‘24Ba, the systematics of experimental evidence of the level staggering in the y-bands, and the investigation of the y-instability over a wide range of barium isotopes. In the following sections, experimental methods and results will be presented. The systematical behaviour of backbends in the yrast states is discussed on the basis of experimental routhians. In the final section, an analysis based upon the boson expansion theory will be given in regard to the y-instability. A preliminary report of our experimental results has been published in ref. 12).

2. Experimental

method

In order to populate the excited states in ‘24Ba, two reactions of “2Cd(160, 4n) and 1”Cd(‘60, 3n) were employed. For investigation of high-spin states, we used the “2Cd(‘60, 4n) reaction. The “‘Cd(‘60, 3n) reaction populated many levels in side bands with rather low spins. The ‘(‘0 ions were accelerated by the 12 UD tandem accelerator at the University of Tsukuba. The targets were metallic foils 4 mg/cm’ thick. The enrichment was higher than 90%. Measurements of singles y-ray spectra, excitation functions, yy-coincidences, and y-ray angular distributions were carried out to establish the level scheme. The y-rays were measured by four Ge detectors and a NaI sum-energy spectrometer. The absolute efficiencies of the Ge detectors were lo- 18% in reference to a 7.6x7.6 cm NaI(T1) detector. The energy resolutions were 1.8-3.0 keV (FWHM) at 1333 keV. The relative efficiences were calibrated with an ls2Eu source at several energies. The Nal sum-energy spectrometer consists of an array of crystals; two cylindrical elements 15 cm tall and 20 cm in diameter are placed above and below the target together with 5 additional sectorial elements. The Ge detectors were inserted into this NaI array. The distances from the target to the Ge detectors were about 7.5 cm. Lead shields were placed between these Ge detectors to suppress the cross talk due to Compton scattering. The y-rays from activities were reduced by means of the sum-energy signals.

2.1. yy-COINCIDENCE MEASUREMENTS The coincidence measurements were carried out at 65 MeV for the “‘Cd(“O,3n) reaction, and at 85 MeV for the ‘12Cd( 160, 4n) reaction. Typical singles-counting rates were about 8 kc/s for the Ge detectors and 60 kc/s for the NaI detector array

T Komatsubara

et al. / ‘-‘Ba

607

with a beam intensity of 1.6 particle nA. The coincidence rate was about 1.1 kc/s. The data were accumulated event by event in list mode on magnetic tapes through the CAMAC interface, VAX11/750, and VAX11/780 mini-computers. The total numbers of 2-fold coincidence events were 1.3 x 10’ for the “‘Cd(‘(‘0, 3n)‘24Ba reaction

and 1.5 x 10’ for the “‘Cd(‘hO,

were sorted into to the gain shift. The with the subtraction displayed in fig. la. y-ray are presented

2.2.

ANGULAR

4n)‘24Ba reaction,

a 2048 x 2048 2-dimensional gated spectra were obtained of Compton background. Examples of coincidence cuts in fig. lb-d.

respectively.

The list data

matrix with careful correction of from the 2-dimensional spectrum A typical projection spectrum is gated by the 451,565, and 690 keV

DISTRIBUTIONS

The angular distributions were measured at 90”, 105”, 125” and 157” with respect to the beam axis. The Ce detector was placed at a distance of 18 cm from the target. Another Ge detector was kept at 45” angle for the normalization of photo-peak intensities. The integrated beam current was used for secondary monitor. The experimental data were fitted to Legendre polynomials defined by W( 0) = A,,( 1 + A,P2(cos

17)+ A,P,(cos

0)) .

Assuming tentative spins of initial and final states for a certain calculated ,$ values as a function of arctan 6 with the coefficients quantity 6 is the mixing ratio defined as 6

=

(AA

(1) y-transition, we A2 and A,. The

Ilji)

(jf-IIA‘llji) . Fig. 2 shows an example of the angular-distribution measurements for the 673 keV y-rays. The solid line indicates the least-square fitting. The values of x2 are drawn in fig. 3. From these results, the 673 keV transition can be assigned to the mixedmultipole radiation 4+ 4 with arctan 6 = -0.37 + 0.03. The confidence level was set lower than x2 = 1 for all transitions assigned in the present mental results of A, and A, are listed in table 1.

2.3.

BETA-DELAYED

experiment.

The experi-

y-RAYS

The activity of ‘24La was produced by the “Mo(~“CI, 2pn)‘14La reaction. The 35C1 ions provided by the tandem accelerator were injected into a post-accelerator in order to increase the energy from 110 to 137 MeV. The post accelerator generates an accelerating voltage of -2 MV per charge 13). The beam was chopped by a simple beam deflecting magnet. The duration of the irradiation was 41 s. After the irradiation delayed y-rays were measured in a period of 41 s in the multispectrum analysis

T. Komatsubara

608

et al. / 12’Ba

451keV gote

7i E tr 1T y VI

2000 1000 5000

-E 8

4000

o

3000

565keV gate

690keV gate

"

200

400

600

800

1000 1200

Channel 3~) reaction at 6$ MeV [a). The photo of the coincidence matrix for the “‘Cd(‘hO, y-rays has been greatly reduced by the Nal sum-energy filter. Coincidence cuts gated by the 451, 565, and 690 keV transitions (b-d). The Compton background is subtracted.

Fig. 1. Projection

peakoftheannihilation

T Komatsuhara

609

/ “JBa

673 keV

13-

h

et al.

12-

08 07

A,= 0 146?0028 A4=-0.114f0.042

06 05L

I 30

0

I 60

I 120

I 90

I 150

180

0 Ideal Fig.

105

2. Angular

of the 673 keV

y-ray

673 keV

t

IO-Z-

distribution

’

-15

I -10

I -05

I

I

0.0

05

I 10

15

arc1an 6 Fig.

mode. counting

3. ,y’ plots

The irradiations statistics.

for the angular

distribution

and the measurements

The half-life

of the ground

of the 673 keV

were repeated

transition.

to obtain

sufficient

state of ‘14La is 29 s [ref. ‘“)I.

3. Results are The properties of y-transitions of ‘24Ba observed in the present experiments summarized in table 1. A total of 47 transitions and 34 levels have been identified. All of the y-rays, except for the 847 and 873 keV lines emitted from states with higher spin, have been observed in the “‘Cd(“O,3n) reaction.

T. Komatsuhara

610

et al. / “‘Ba

TABLE

Energies,

intensities,

angular distribution

4 193.2kO.l 215.710.1 229.9 * O.l** 325.8kO.l 345.5 * 0.1 349.0 f 0.3 421.5*0.1** 446.5 i 0.2 451.710.1 451.5*0.2 459.8k0.1 510.0*0.1 533.4*0.1 565.3 i 0.1 576.9*0.1** 599.5 f 0.1 612.7iO.2 615.8+0.1 620.9 f 0.1 629.7kO.l 643.4kO.l 673.1 *O.l*” 681.310.1 689.8 i 0.1 689.8 zt 0.2 695.1 *O.l** 717.8i0.2 748.8 * 0.2 764.6 * 0.2 767.6 zt 0.5 781.8k0.2 793.6 f 0.2 798.4 i 0.2 847.9 * 0.3* 873.2 i 0.4* 873.3 i 0.3 932.8 + 0.2 942.4 f 0.2 1003.8+0.3 1020.8 * 0.2 1033.3 *0.1** 1057.0 * 0.2 1094.5 * 0.3 1130.9 * 0.2 1260.6 f 0.3** 1381.6i0.3 1614.5 i 0.8

4.9 I 0.6 3.5 * 0.5 100*2 1.4kO.2 4.8 k 0.3 0.4 f 0.2 94*2 2.8i 1.3 5.0*0.5

coefficients,

1

and assignments

4 -0.3895 * -0.6393 f 0.2533 * 0.381+ 0.280 i

of the y-transitions

Assignment

A‘l 0.0036 0.0028 0.0023 0.065 0.027

0.3211 f 0.0030 -0.500 * 0.043 0.333 * 0.010

0.0024 i 0.07 15 * -0.0380 i -0.163 f -0.093 f

0.0053 0.0040 0.0035 0.096 0.039

-0.0503 * 0.0044 0.082 i 0.063 -0.025 f 0.016

5.5* 1.0

0.325 i 0.018

0.003 i 0.027

3.0~0.2 8.6kO.6 70*3 2.8 * 0.6 2.810.5 41 zko.5 3.6kO.5 3.2 zt 0.6 1.6ztO.5 6.4+ 1.0 5.2zkO.5 7.0 * 0.7

0.151*0.030 0.288*0.015 0.3144*0.0027 0.296 * 0.042 0.808 It 0.077

-0.079 i 0.046 -0.064ztO.022 -0.071 * 0.004 0.088 f 0.063 -0.09*0.11

-0.01610.035 0.003 * 0.050 0.146*0.028 0.194+0.025 0.423 f 0.026

0.085 *0.053 -0.128*0.075 -0.114iO.042 -0.110*0.037 -0.048 i 0.038

45*3 1.6;tO.6 1614 27*4 2.4 f 0.4 3.3io.9 3.ozto.4 8.3* 1.3

0.7 f 0.3 5.012.3 2.1*0.3 0.5 f 0.2 2.4 i 0.5 9.21 1.2 1.3 * 0.2 0.5 f 0.2 4.0* 1.0 4.1 kO.6 1.8 f 0.2 1.2 * 0.4

0.2797 * 0.0057

-0.0641

of lZ4Ba

f 0.0085

2++0+ (6)+ (4) (8) + (6) 4++2+ (6)+5” (IO)+(g) 9”+7’-’ 6++4+ 1,“+9’-’ 6++4+ 1 l’_‘+ 10+ 7++5+

6++6+ (2+)+2+ 4++4+ (W)*ll” 14+ * 12+ 8+*6’ 12+ + 10+ 10+ + 8+

0.27110.014 0.2954 * 0.0098

-0.070*0.021 -0.108*0.015

0.222 * 0.033 0.220*0.034 -0.203 f 0.014

-0.101 io.049 0.081 i 0.050 0.037 * 0.021

0.063 * 0.048 0.151 iO.026 -0.095 * 0.071

-0.044 i 0.072 0.019*0.039 -0.11*0.11

0.537 f 0.060 -0.238 i 0.019 0.217* 0.087

0.189*0.085 0.029 f 0.028 0.2OiO.13

5++4+ 7’-‘+6+

0.25 1 f 0.040 -0.191 iO.042 0.347 f 0.088

0.029 f 0.060 0.063 i 0.062 0.09io.13

(6)+6+ 5(-‘-4+ (4) + 4+

(m;’

+

7++6+

The intensities and the angular distribution coefficients have been deduced through in-beam experiments by using the “‘Cd(“0,3n) reaction. Two y-transitions (*) have been observed through the “2Cd(‘h0, 4n) reaction. The p delayed y-rays have been observed (**) from the activity of ““La.

T. Komatsuhara

3.1. LEVELS

SCHEME

OF

et al. / ““Ba

611

““Ba

from the yy-coincidence measurements is The level scheme of ‘24Ba constructed proposed in fig. 4. The excited states can be classified into 7 band structures. The ground-state

band (g.s.b.) is indicated by D. A super-band C crosses with the g.s.b. at the spin J” = lo+, and is built up to the 5767.4 keV level. In our previous report 12), the 767 keV transition in the band C was not assigned. Since the 767 keV transition forms a doublet in our coincidence spectrum together with the 764 keV transition in the band D, we have performed a more careful analysis of the coincidence spectrum for this energy region. It turned out that the two y-rays could be reasonably resolved if we gated on the 764 and 690 keV y-rays shown in fig. 5. The placement of the 767 keV transition into band C was supported by the intensity balance. Because of counting statistics, the doublet could not be resolved with narrower gates. The 451 keV transition is a doublet and assigned to members of the bands B and F. The 690 keV transition in the bands A and C is also a doublet. The 510 keV y-ray in the band A forms a doublet with annihilation y-rays. The placement of these doublets into the corresponding bands consistent with the cascade relation and the

‘24Ba Fig. 4. Proposed level scheme of lzJBa constructed from 4n) reactions. The intensities “‘Cd(‘hO, 3n) and “‘Cd(‘“0, “‘Cd(“O,3n) reaction.

coincidence measurements of y-transitions are taken

with from

the the

612

iY Komarsubara

et al. J “‘Ba

1800 1600 1400 1200 1000 800 = E 0

400

600

e

200

2Lo 9002 "

aoo -

690keV

(b)

gate

700 600 500 400 300 200 100

u A

730

740

760

750

770

780

790

Channel

Fig. 5. Coincidence cuts gated by the 764 and 690 keV transitions. Since the 767 keV transitions forms a doublet with the 764 keV line, this doublet can be seen in the self-gated spectrum (a). The 767 keV peak creates a shoulder (b). intensity

in the level scheme. Our level scheme is in good agreement by Martin et al.yX’O)with respect to the bands C, D, E and F.

balance

that reported 3.2. SPIN-PARITY

with

ASSIGNMENTS

The 799, 1033, and 1261 keV transitions

were found

to have A = 1 character

of

multipole radiation. The band E can be assigned to be an odd-spin band which is quite similar to the odd-spin negative-parity bands observed in ‘26Ba [ref. “)I and ‘28Ba [ref. ‘)I. Gizon et al. have reported a state with the spin-parity of 5- at 1912 keV in their P-decay study I’). The parity of this band can be assigned to be negative. The band F is a good candidate for an even-spin negative-parity band which has been reported in 12’Ba [ref. “)I and 12’Ba [ref. ‘)I. The 446 keV y-ray which decays into the 5- 1912 keV level is due to a 6+ 5 or 4+ 5 transition from the analysis of the angular distribution. The 1131 keV y-ray feeding the 6+ 1228.3 keV level is a 6 + 6 or 5 + 6 transition in the similar manner. From these analyses, the most probable spin of the 2358.8 keV level would be 6h. These spin-assignments are in a good agreement with those of Martin et al. 9,‘0) and Gizon et al. ‘I). The spin-parity of the 873.3 keV level, which is the band head of the band B, has been tentatively assigned to be 2+ due to the weak intensity of the transitions. The 1324.6 keV level was assigned as 4+ state from the analysis of the 673 keV transition shown in figs. 2 and 3. The band B, therefore, has been assigned to be the even-spin part of the y-band. Excited states in band A were assigned to be the odd spin

T. Knmatsuhara

members

of the y-band

from the analyses

et al. / “-‘Au

613

of the 933, 1021 and 1057 keV transitions.

There is a discrepancy

in transition energy between our result and those by Martin et al. and Gizon et al. ‘0,“) in the odd-spin part of the y-band. The 510 keV transition in the band A in our level scheme was reported as 577 keV. In our experiment the

annihilation y-ray was suppressed by the NaI sum-energy filter, and the 510 keV transition was clearly observed. The higher transitions in the band A were well confirmed by the cascade relations. 3.3. RADIOACTIVITY

RESULTS

From

analysis of decay curves, 9 transitions have been assigned to P-delayed transitions of ‘14Ba. Fig. 6 shows the decay scheme of lZ4Ba where cascade relationships and spin assignments are deduced from in-beam measurements. A remarkable feature is that the p-decay populates the 8+ state of the yrast band, 5 and 7- states of the side band, and 6+ state of y-band. These results are in good agreement with those reported by Gizon et al. ‘I). Since the selection rule of P-decay is AJ = 0 or 1, some of these states might be not populated directly. The ground-state spin of ‘24La is expected to be 7 or Sk 4. Discussion 4.1.

EXPERIMENTAL

ROUTHIAN

In order to investigate the interplay between intrinsic structure and collective rotational motion, we have deduced the excitation energies in the rotating frame 29s /-

Fig. 6. Partial

level scheme

of “‘Ba

populated

by P-decay

lZ4L a

of ““La.

614

T. Komatsubara

et al. / lz4Ba

(routhian) and the gains of spin alignment with respect to the ground-state band. The detailed prescription of this transformation is given by Bengtsson and Frauendorf 15). The experimental routhians and alignments for ‘24Ba are shown in fig. 7 as a function of the rotational frequency determined so as to give zero alignments

w. The Harris parameters 16), which are for the g.s.b., are JO= 12.2 h’/MeV and

J, = 83.3 h4/MeV3. The super-band crosses with the g.s.b. at a rotational frequency of 0.365 MeV/h. From fig. 7b, the alignment of the first crossing is estimated to be 6h. This suggests that the configuration of the s-band is (r or vh,,,2)2 of twoquasiparticle structure. The routhians of the bands E and F have approximately the same declinations as that of the super-band, so that these side bands would also be of two-quasiparticle nature. Routhians and alignments for the y-band are also shown in fig. 7. We have tentatively assumed that the K quantum number of this band is 2. The intrinsic energy of the y-band exhibits a quite different declination from those of the 3.0 25

-

z 3 -0,

2.0 -

_j

1.5 -

g 2

1.0 -

I (a)

ln4Ba

Jo= 12.2ih.W

_

J, = 83 3h4/MeV3 F\x ?

B,+&l .\

g 05‘C x Lzoo-0 -05

60

c

‘A -0

-

-

-

-

0.I

0.3

0.2 ”

04

0.5

06

[MN/*]

Fig. 7. Experimental routhians (a) and alignments (b) of ““Ba. Harris parameters are J,= 12.2 h’/MeV and J, = 83.3 h4/MeV3. The routhians and alignments for each band are labeled by the same letters as in fig. 4. Even- and odd-spin bands are drawn by solid and dashed lines, respectively. The ground-state band crosses with the super-band at a rotational frequency w = 0.365 MeV/ h. The alignment of the band crossing is estimated to be 6h.

T Komatsuhara

super-band

and the two-quasiparticle

et

al. /

side bands.

615

‘-‘“Ba

The signature

splitting

between

even- and odd-spin parts was observed. Systematical behavior of the band crossing of even-even barium isotopes is shown in fig. 8. For the heavier isotopes of ‘16Ba, “*Ba and ““Ba the experimental data are taken from refs. 4--6).The first crossing frequency

decreases

as the neutron

number

decreases (see little arrows). An interpretation of the systematics is complicated because not only neutrons but also protons in the h,,,2 orbit can be aligned by Coriolis and centrifugal force. Indeed, two super-bands have been reported in the nuclei ““Ba, lzaBa and “‘OBa [refs. “-“)I. In the case of the proton crossing the isotope dependence of the crossing frequency is attributed only to deformation of nuclei. When deformation increases (the neutron number decreases), a moment of inertia increases and the a[5SO]$ orbit drops close to the Fermi surface located near the bottom of the shelt, then the crossing frequency decreases. On the other hand, the neutron crossing strongly depends on the location of the Fermi surface in Nilsson orbits where the candidates for the crossing orbit are v[532]$ and v[.523]$. When the neutron number decreases from 74 to 68, the Fermi surface drops and the aligned angular momentum of the h t ,,2 orbit increases, and the crossing frequency decreases. According to Wyss ef al. 17) the backbend is observed in “‘Ba at w = 0.37 MeV/ #i. The neutron alignment is blocked; the backbend is due to the proton alignment. Since the crossing frequency of lz4Ba is very similar to that of “?Ba, it is more suggestable that the backbend in lz4Ba could be attributed to the proton alignment. A similar crossing frequency for ‘““Ba has been reported by Martin et al. “‘).

Fig. 8. Systematics of the experimental rout&ins for the yrast states of lzJBa, ““Ba. ““Ba, and ““Da. The open squares show the ground-state bands (g.s.b). The first super-band (closed squares) crosses with g.s.b. at rotational frequencies indicated by little arrows. The second super-band observed in the “fiBa, “*‘Ba and ““Ba is shown by triangles.

T. Komatsubara et al. / lz4Ba

616 4.2. SYSTEMATICS

OF THE

QUASI-y-VIBRATIONAL

The quasi-y-vibrational y-deformation. isotopes. vibration

band

provides

BANDS

a sensitive

Fig. 9 shows the excitation

energies

test of the instability of the y-band

for the

of the barium

These bands deviate strongly from the prediction of the simple rotationcoupling model. The level spacings between 3: and 4;, 5: and 6;, . . .

states are much narrower than those between 2; and 3:, 4: and S:, and so on. In 12’Ba the spacings become narrowest and the orders of even and odd-spin states reverse above 7; state.

MeV 5

,

I

0 I

68

70

72

74

76 N

Fig. 9. Excited states of the y band of lz4Ba, “‘Ba, lz8Ba, and “’ Ba. The even-spin states are plotted by open circles; the odd-spin states by closed circles. The experimental data are taken from refs. 4.5.h,‘X).

To investigate this phenomenon, we have carried out a microscopic calculation in terms of a normal-ordered linked-cluster boson expansion theory ‘9,20). The most important guiding principle in this calculation is the concept of the nuclear saturation and the self-consistency between a nuclear density and an average potential. The theoretical framework is based on the paring + (QQ) model. However, the usual QQ interaction breaks the nuclear saturation and the self-consistency when we go to the deformed system. In order to overcome this difficulty, self-consistent higher-order effective interactions have been derived. The hamiltonian is given by H=H,,+(H”_pair-hpNp-h”N”)+H2_pair+

vC2’+ vC3)+ v’4’

(3)

where the H,, stands for the spherical limit of the Nilsson hamiltonian; HO-pair and H7_pair are the monopole and the quadrupole paring hamiltonian, respectively. The interaction Vc2) is the effective two-body interaction which corresponds to the QQ interaction. The interactions V”’ and Vc4’ are the effective three- and four-body interactions introduced to recover the saturation and the self-consistency 20).

T. Komatsubara

The

strengths

of the

monopole

et al. / “‘Ba

paring

interaction

617

have

been

fixed

so as to

reproduce the gap parameters A,, and A, which are taken from experimental values of separation energies for the proton and the neutron *I). The values are comparable with (12/a) MeV. In our calculation there are two adjustable parameters; the strengths of the quadrupole paring (g,) and of the effective interactions V”‘, V’3’ and V’4’ (fi =.f; =fJ, which have been adjusted in the range from 0.8 to 1.2. The values of gz and ,fi should be 1.0 for the pure self-consistent case. Comparison between results from the calculation and the experimental data for ‘24Ba is illustrated in fig. 10. The theoretical spectrum (middle) was obtained from the fitting with the data, using only two parameters f2=0.93 and g, =0.95. The energies of the g.s.b. and staggering of the y-band are successfully reproduced by calculation, whereas the level energy of the band head of the y-band is too low. In barium isotopes only two valence protons occupy the lowest h,,,, orbit, therefore, the collective motion with respect to y-degree of freedom might be quite sensitive to the high-j orbit. We have raised the single-particle energy of the nhll12 orbit by 1 MeV. This modified calculation is shown as “adjusted fit”. The experimental spectrum below spin J s 8 in the y-band and the g.s.b. are qualitatively reproduced by the modified calculation, although the band head is still low. Potential energy surface corresponding to the “adjusted fit” is shown in fig. 11 as a function of the shape parameter p. The energy of the zero-point oscillation is

‘24Ba

MeV 3-

8-

8-

7-

2-

8-

I -

8-

8-

E-

6-

43-

65-

43-

63--

24-

O-

7-

65-

6-

87-

4-

2-

4-

2-

2-

2-

O-

O-

Q-

experiment

theory

2-

adjusted fit

Fig. 10. Comparison of the experiment with the boson expansion theory for the low-lying collective states in “4Ba. The calculation with two parameters off? and g, of effective interaction is shown in the middle column (“theory”). The “adjusted fit” is a modified calculation discussed in the text.

T. Komatsuhara

618

et al. / “‘Ba

43 -

‘24Ba

I

2I I -0.4

I

I

I

I

I 0.4

P

-4L Fig. 11. Potential energy surface resulting from the boson “adjusted fit”. The energy of zero-point oscillation

expansion calculation corresponding is indicated by dashed lines.

to

drawn by dashed lines. This potential surface has two minia on both sides of positive and negative p; the minimum in the prolate side is slightly lower than that in the oblate side. However the difference in depth on both sides is much smaller than the energy of the zero-point oscillation. This feature of the potential surface implies the instability for y-deformation.

MeV 3

1

I

I

I-

,‘,-

adjusted fit

,- ‘----------:,’ ,,m_.

,,_,’

8+ _,+-~’ 7+-s’

6+ -;;&. 5+3+

__--

2+ --__----

I

68 spectra

,:-

__.---_~_;‘,*

4+z;$-_z_---~-~~-

,‘,‘,*-

_rr*----__*,, _--__ --I _;z_--

2

Fig. 12. Energy

I

Z = 56 -

I

I

I

of y-bands

70 in even A barium expansion

I

72 isotopes theory.

I

74 obtained

I

I

76

N

from “adjusted

fit” in the boson

T. Komatsubara

et al. / “‘Ba

619

TABLE 2 Parameters

used in boson

expansion

calculations

A,, WV1

1.22

1.32

1.47

1.33

A, [Mevl

1.22

1.33

1.41

1.33

1.23

.f, Lf ?“I

0.90

0.92

0.95

0.92

0.90

0.98

0.97

0.96

0.95

0.88

gz

lg’z’“l

1.37

The experimental data of the y-band of barium isotopes (fig. 9) exhibit distinct systematic behaviour. We performed the boson expansion calculation as a function of the neutron number shown in fig. 12. The calculation is the “adjusted fit” mentioned above. The parameters used are summarized in table 2. The staggerings of the y-band are qualitatively consistent with the experiments. However, the by the narrowest spacing between 3: and 4: state in “‘Ba cannot be reproduced present

calculation.

5. Conclusions in detail on In this paper, the level structure of ‘24Ba has been investigated high-spin phenomena and also on low-spin states with collective nature. The yrast states have been constructed up to J” = 18+. A backbend observed at w = 0.365 MeV/h can be ascribed to the proton alignment of h,,,? orbit from the comparison with ‘“‘Ba and ‘*‘Ba. The odd-spin part of the y-band has been observed for the first time, and the even-spin part has been extended up to J” = 8+. The y-band exhibits strong staggering. Distinct systematical features of the y-bands in the even-even barium isotopes have been revealed. The spacing of the 3; and 4; states, for instance, reaches a minimum at 12*Ba, and then this spacing gradually becomes wide when the neutron decreases further towards ‘24Ba. Through the analysis with the boson expansion theory, it turned out that the staggering of the y-band was partly due to the instability with respect to the y-deformation. However, the present calculation cannot clarify that the nucleus “*Ba is the most y-unstable. Further theoretical studies are necessary for understanding of the relation between the behaviour of the y-band and y-softness. We are deeply indebted to Dr. K. Shiffer at the Niels Bohr Institute for beneficial discussions. Thanks are due to Mr. I. Sugai at the Institute for Nuclear Study, Tokyo, for target preparation. We would like to express our sincere thanks to Drs. T. Kishimoto, W. Galster, and Y. Shimizu for fruitful suggestions and discussions. Profs. H. Morinaga and T. Mikumo are acknowledged for warm encouragement during this work. We would like to thank the technical staff and faculty members

T. Komarsuhara

620

at the Tandem

Accelerator

Center

et al. / “‘Ba

of the University

of Tsukuba

for assistance

in

the experiment.

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