Study of even-mass Ba nuclei by the (p, t) reaction

I

I.E.1 : 2.G

Nuclear Physics A341 (1980) 206 - 218; @ ~Ortk-Hoi~and P~iishi~g

Co., Ammta%m

Not to be reproduced by photoprint or microfilm without written permission from the publisher

STUDY OF EVEN-MASS Ba NUCLEI BY THE (p, t) REACTION

H. KUSAKARI Faculty of Edueafion, Chiba University, Chibu, Japan K. KITAO and S. KONO Narional Instime of Radiological Sciences, Chiba, Japan and Y. ISHIZAKI Institute for Nuclear Study, University of Tokyo, Tanushi, Japan Received 27 August 1979 (Revised 12 November 1979) Abstract: The (p, t) reaction on the nuclei ‘34x136,13*$a has been studied at a bombarding energy of 52 MeV. Angular distributions of emitted tritons were obtained between 6” and 60“. The following six negative-parity states were strongly excited by the (p. t) reaction: s-(2.121 MeV) and 7-(2.482 MeV) in 13*Ba, 5-(1.998 MeV) and 7-(2.274 MeV) in ‘34Ba, and Y(2.139 MeV) and 7-(2.031 MeV) in lJ6Ba. DWBA calculations using the code DWUCK successfully reproduce these angular distributions. The Of assignment to the 1.761 MeV level in lJ4Ba is confirmed. Intensities of the (p, t) reaction for low-lying states are discussed.

E

I

NUCLEAR REACTIONS ‘34*1J6,‘38Ba(p, t), E = 52 MeV; measured@, E,). ‘3z+134*i3aBa deduced levels, J, z, transition strength. DWBA analysis. Enriched targets.

I

1. Infliction The Xe-Ba region is a typical transitional nucleus region ‘). Neutron-deficient Ba nuclei have small j&deformation and are unstable for y-deformation ‘), where the parameters /I and y are the shape parameters used in the Bohr model 2). With increasing neutron number, the shapes of the Ba nuclei become more spherical, and then the neutron shell is closed in 13*Ba. Most of previous work on the nuclear structures of Ba nuclei was done by means of y-ray and electron spectroscopy. There have been few available data on transfer reactions on Ba isotopes. Our investigation of low-lying states of even-mass Ba nuclei has been done by using the (p, t) reaction on Ba isotopes (A = 134, 136 and 138). The (p, t) reaction is a powerful tool for the study of structure in even-even nuclei. The present study is complementary to the 206

H. Kusakari et al. / (p, r)

207

previous ones which were done by means of y-ray and electron spectroscopy. This paper reports the result of spin-parity assignments and discusses the intensities of the (p, t) reaction for low-lying states of the nuclei 132,134*136Ba. Previous experiments on 132Ba were done by means of in-beam y-ray spectroscopy [refs. 1*3-s)] as well as the radioactive decays of ‘j2Cs [refs. “,‘)I and 132La [refs. s-lo)]. The quasi-ground band up to lO+ and the quasi-gamma band up to 4+ were observed 1*4,s). Th e reduced electric-quadrupole transition probability B(E2; 0: + 2:) was determined by means of Coulomb excitation 3). The spins and parities of 5- and 7- were assigned to the 2.1199 MeV and 2.4830 MeV levels, respectively ‘95). Previous data on 134Ba were obtained by using the decays of 134Cs [refs. l1 - ‘“)I and 134La [refs. ‘3 “-“)]. Many reports on 134Ba were presented. However, the data obtained on 134Ba were limited to low-spin (J 6 4) states because of the low spins of parent nuclei and a low Qs value in the decay of 134Cs. The reduced transition probability B(E2; 0: --t 2:) was determined with the procedure of the Coulomb excitation 24-26). Previous investigations of 136Ba were made with the decays of 13%s [refs. “-“)I and 136La [refs. “*“)I, and also by means of the ’ 35Ba(n, y) reaction 33). Positive parity states with spins up to 6 were observed lgp 2’ - 33). The reduced transition probability B(E2; 0: + 2:) was determined by means of Coulomb excitation 24*25). Spins and parities of 5- and 7- were assigned to the 2.1396 MeV and 2.0300 MeV levels, respectively 28). A preliminary report of this work was presented at the 1977 International Conference on Nuclear Structure held in Tokyo 34). 2. Experimental procedure The (p, t) reaction on Ba isotopes has been investigated with a 52 MeV proton beam from the INS synchrocyclotron. Beam currents ranged from 15 nA for measurements at forward angles to 150 nA for those at backward angles. Targets were prepared by depositing Ba,CO, powder onto thin Mylar films (0.5 mg/cm2). The thicknesses of the 134*135,136*138Batargets were 2.00, 2.00, 2.71 and 0.80 mg/cm2, respectively. The 134,13%13%138Ba targets were’ isotopically enriched to 74 %, 94 %, 93 % and 99 %, respectively. Emitted tritons were analyzed by a broad-range magnetic spectrometer with a proportional-counter array in its focal plane. The solid angle for the broad-range magnetic spectrometer was previously calibrated 35) using the 56Fe(p, to) reaction, whose precise cross section is known 36). Triton spectra were stored in a PDP-9 computer, and were recorded subsequently on a magnetic tape. Angular distributions of differential cross sections for the ’ 34*’ 36v’ 38Ba(p, t) reactions were obtained at 2.5O intervals between 6O and 60”. The main isotopic impurities in the 134Ba target were as follows: “‘Ba (15 %),

H. Kusakari et al. / (p, t)

208

136Ba (4 %) and 13’Ba (5 ‘A)_For numerical subtractions of these contributions, triton spectra from the 135,136*138Ba(p,t) reactions were obtained at angles of 6” to 60”. These me~urements were done in the same magnetic field as the measurement for the ‘34Ba(p, t) reaction. The numerical subtractions of the isotopic impurity components were done by an off-line process using a OKITAC-4300 computer. The 134Ba target could be effectively enriched to 97 y0 by this procedure.

3. Experimentai data and analyses 3.1. ANALYSES

A typical triton spectrum in the ‘36Ba(p, t) reaction is shown in fig. 1. The excitation energies of the residual nuclei 132,134*136Ba were determined by self-~libration using the positions of the O:, 2: and 2; peaks, and also by kinematic calculations.

a

I

I

5

4

3

2 EXCITATION

1 ENERGY

0 f MtV f

Fig. 1. Energy spectrum of tritons from the lJ6Ba(p, t) reaction at E,, = 52 MeV.

Errors of energy determinations are estimated to be less than 10 keV. The present results are summarized in table 1 together with previous data obtained from y-ray spectroscopy. Differential cross sections of the (p, t) reaction were obtained for states of the

H. Kusakari et al. / (p, t)

209

TABLE1 Excitation energies and spin-parity assignments Nucleus “‘Ba

’ 34Ba

Energy (MeV) 0 0.465 1.032 1.129 1.685 1.948 2.121 2.384 2.482 2.660 2.768 3.228 3.420 3.697 3.904 4.083

0+

0.4646 “) 1.0321 ‘) 1.1280 “) 1.685 b, 2.1199 “)

(L)

0+

0 0.819 1.551 1.866 2.031 2.139 2.562 2.646 2.838 3.019 3.262 3.501 3.703 4.075

Errors in the present energy determinations ‘) Ref. I). “) Ref. lo). ‘) Ref. s).

2+ 2+ 4+ 2+ (4+) s-

2.4830 ‘)

0

0.605 1.168 1.402 1.761 1.998 2.274 2.479 2.740 2.836 3.079 3.241 3.416 3.754 4.019 ‘36Ba

J”

0.6047 d) 1.1679 d, 1.4006 d) 1.7605 d,

2+ 2+ 4+ 0+ 574+

4+

0.8186 ‘) 1.5505 ‘) 1.8663 ‘) 2.0300 ‘) 2.1396 “)

are estimated to be less than 10 keV. ‘) Ref. ‘l). d, Ref. “).

0+ 2+ 2+ 4+ 75-

4+ (4+)

H. Kusakari et al. 1 (p, t)

210

residual nuclei ’ “* ’ 34*’ 36Ba. Th e angular distributions of triton groups are shown in figs. 2 to 5. As is well known, spins and parities of even-even nuclei produced by the (p, t) reaction are restricted to J = L and 71= (-)‘-, respectively, where L is the transferred orbital angular momentum. Spin-parity assignments were carried out on the basis of shapes of angular distributions. The solid curves in figs. 2 to 5 are the results of distorted-wave Born approximation (DWBA) calculations using the code DWUCK 37). The shapes of the theoretical angular distributions with the same L-value were similar to each other and almost independent of the variety of transfer configurations presented in table 3. The twonucleon transfer option of the code DWUCK is based on the procedure of ref. 38) and was explained in detail in the appendix of ref. 39).The calculations were performed with a TOSBAC-3400 computer at INS. The proton optical-model parameters were taken from the average set of Becchetti and Greenlees 40), and the triton opticalmodel parameters from the average set of Flynn et al. 41). They are listed in table 2. The experimental cross section for the (p, t) reaction is related to the output of

TABLE2 Optical-model parameters used in DWBA calculations Proton ‘) A = 134

136

138

(fm)

45.71 I.17 0.75

45.98 1.17 0.75

46.25 I.17 0.75

V, WV)

8.72

8.72

8.72

1.32 0.625 0.80 6.2 I.01 0.75 1.25

I .32 0.634 0.94 6.2 I.01 0.75 1.25

1.32 0.642 1.09 6.2 I.01 0.75 1.25

VR WV (fm)

rR

aR

rI

(fm)

aI

(fm)

W, Vs rs as rc

WW

(MW (fm) (fm) W

Triton “)

Neutron

all A

all A

166.7 I.16 0.752 18.20 (A = 132) 16.58 (A = 134) 15.02 (A = 136) 1.498 0.817

(adj.) ‘) 1.25 0.65

(1 = 25)d) 1.25 0.65 1.25

The parameters are defined by the formula: U(r) = - VRf(rRI aa) - iCV, -4W,(dldr)lf(r,,

+ (h/m,42(V&)(dldr)f(rs,41

a,)

u + V,,

where f(r’, a’) = [I +exp((r-r’A”‘)/a’)]-’ and V, is the Coulomb potential of a uniformly charged sphere of the radius rcA’13. *) Ref. 40). b, Ref. *‘). ‘) Adjusted to give the neutron the binding energy of half the value of the two-neutron separation energy. d, I is the coeffkient of the Thomas term.

H. Kusakari et al. / (p, 1)

211

the code DWUCK. It is expressed as

d&3

cm c-3

=

pixwT --

2L+-1

exp

EB2a

nw”CK(@~

[refs. “‘*“‘)], where L is the transferred orbital angular momentum, and anwvck(f3) is the reduced DWBA cross section calculated by the code DWUCK for the transition of a pair of neutrons. The parameter 0; is the overall normalization factor which arises in making the zero-range approximation. The parameters A, E and B2 are the rms radius of the triton, the enhancement factor and the two-neutron spectroscopic factor, respectively. The values of A = 1.7 fm and O,$ = 22, which had been reported in ref. 42), were employed in the present analysis. Values for cB2 were obtained assuming the transfer configurations presented in table 3. Theoretical values of the spectroscopic factors B’([J~~],, --f [J;I - 21,) and B’([J”,IJ”,‘],+ by’- ‘I;‘- ‘1 J, where j is an angular momentum and n the number of neutrons on the j-shell, were given in

1

Ep = 52McV 50

L

=o

-i

3 t $

100

5o

2 j 0

100: 50-

10:

A

*136

5-

1:

0.5 -

Fig. 2. Angular distributions of the triton groups observed in the ‘M* ‘36*‘%a(~, t) reactions. Error bars shown represent statistical uncertainties only. DWBA predictions for the transitions to the ground states and the first 2+ states are shown with solid curves.

H. Kusakari et al. 1 (p, t)

212

refs. 42*43).If the neutron shell of the target nucleus is completely filled, these spectroscopic factors are equal to 25+ 1. In the present analysis of the data on the ’ 38Ba(p, t) reaction, the value of B2 = 25 + 1 was assumed, and enhancement factors E were obtained. The results are summarized in the sixth column of table 3. 3.2. SPIN-PARITY

ASSIGNMENTS

The observed angular distribution for the 1.761 MeV level in ’ 34Ba is shown at the bottom left of fig. 2. The shape of this angular distribution belongs to the type of L = 0 transfer and is similar to the shapes of angular distributions for the groundstate transitions. Therefore, the spin and parity of O+ are assigned to the 1.761 MeV level. The present result confirms the previous assignment 20-22) proposed from y-ray and electron spectroscopy. Angular distributions of the L = 5 and L = 7 transitions are shown in figs. 3 and 4, respectively. In 132Ba, the 2.121 MeV level is determined to be the 5- state, and the 2.482 MeV level to be the 7- state. The present results confirm the previous assignments of the 5- state lss) and the 7- state ‘) proposed from in-beam y-ray spectroscopy. In 134Ba, the 1.998 MeV level is assigned the spin and parity of 5-, and the 2.274 MeV level is assigned the spin and parity of 7-. DWBA predictions agree

0'

20'

LO.

60'

e

0' cm.

Fig. 3. Angular distributions for L = 5 transitions in the 1a*.136*138Ba(p, t) reactions. Error bars shown represent statistical uncertainties only. DWBA predictions are shown with solid curves.

20'

40'

6d

6c.m.

Fig. 4. Angular distributions for L = 7 transitions in the ‘J4*136*138Ba(p, t) reactions. (See caption of fig. 3.)

H. Kusakari et al. / (p, t)

213

very well with the observed angular distributions for these levels in 134Ba, as shown in figs. 3 and 4. In 136Ba, the 2.031 MeV and 2.139 MeV levels were strongly excited. The former level has been established as the 7- isomeric state 28,2g). The latter level is assigned the spin and parity of 5-, and the present result confirms the previous assignment **) proposed from y-ray and electron spectroscopy. The 2.479 MeV and 3.079 MeV levels in 134Ba and the 3.019 MeV level in 136Ba are assigned the spin and parity of 4+. The angular distributions for these levels are similar to those for the first 4+ states as shown in fig. 5. The 1.948 MeV and 2.660 MeV levels in i3’Ba and the 3.501 MeV level in ‘36Ba also seem to be 4+ states. c *‘*na (p,t 1

*Ba Ep=

52MeV

.

-

100:

f

50-

b\ P

_

l*

-‘I .

lo_

*

.

l.

*

. .’

5-

’ t

+

*

1.966

'*

4:

+

l-

=**

*

~=136 3.019 4.

A.136

*

+

t ‘4 A.134 1.402 4:

50

l.

.

I \ 100 P

..

A ~132 1.129

l*

4;

**

‘tt+’

*

.

t

**

‘t ++++ t t+‘+*

t 10 -

9:

“t

t

50-

A-132 1.948 (4')

+++t

**t*t+

+t

t +l+++ A=132

‘it”:.

I

t t

I-

t

‘1 t

Fig. 5. Angular distributions

A81%

3.079 4.

t

A-136 3.5ol (4.1

for f. = 4 transitions in the ‘W la6* 13sBa(p, t) reactions. (See caption of fig. 3.)

H. Kusakari et al. 1 (p, t)

214

4. Discussion

In the case of a small deformation, described as

and conclusion

the quadrupole

deformation

parameter

/I2 is

/I2 = 4z{B(E2; 0: + 2:)}*/3ZeR& [ref. “‘)I, where the value of R, = 1.2A* fm is employed and Ze is the charge of the nucleus. The values of /I2 = 0.170, 0.165 and 0.128 for 132*134*136Ba,respectively, are deduced using the experimental data 3*24-26) on the transition probabilities B(E2; 0: + 2:). The deformation parameters /I2 in light Ba nuclei increase monotonically with decreasing neutron number. The first 4+ state in 13’Ba was very weakly excited by the (p, t) reaction, but the one in ’ 36Ba was strongly excited. The cross sections for the first 4+ states drastically

4 -21.7

-22.6

-3l.4

,10.4

,250

37.3

4’

-29.7

,n.i

-35.0 4.

3 40.3

-26.0

7-N

:_

-23.9 -20.2

4‘ -23.4

__

W

-.

--.___

5‘r?______ 2

--_

(4.) 45.6

.

76.4 .* -.._

-7-m

__.-

4.9

136 9 .

4.26.4

2.3 **

, 3.j _ _ _- - - - -

114.9 :“C-t"7-m

66.1 5-___.--

0.1

6.3

82.3 -17.9

'43-32;*;

z I

36.6

(4.) m

.-

19.3:-

*-

.17.4

___--

i-

_.--

2.z.$_ - --

;*~8~3____-------

1

103.5

_ 2-B 43.5 2'-_--

0

i

___-----

67.1 _------

-2.m

96.1 o*~--------O*~________O'~ 132 56 Ba76

67.9

94.6

134 56 Ba76

136 66

Ba

60

Fig. 6. Low-lying levels observed in the ‘34*‘36.‘38Ba(p, t) reactions at IT, = 52 MeV. Experimental cross sections which are integrated between 6’ and 60” are presented numerically in pb, and also shown graphically with the lengths of the thick solid lines.

H. Kusakari et al. / (p, t)

215

vary with neutron number (see fig. 6). The shapes of the angular distributions for the first 4+ states of 13** 134p’ 36Ba are very similar to each other (see fig. 5). The present DWBA predictions do not agree very well with the observed angular distributions for the first 4+ states of 13**134*136Ba. For the ratio B(E2; 4: + 2:)/B(E2; 2: + 0:) in lJ4Ba, the value of 1.53 f0.16 was reported 26). This value roughly agrees with the rotational-model prediction (1.43) and/or the vibrational-model prediction (2.0). The spin-parity assignments of 5- and 7- in 134Ba are confirmed in agreement with the systematic trends of the 5- and 7- levels in even Ba nuclei. The energy gaps 24 in 132*134*136Baare estimated to be 2.28,2.22 and 2.13 MeV, respectively, on the basis of the neutron separation energies. The excitation energies of the 5- and 7states are nearly equal to the energy gap 24 of each Ba nucleus. These 5- and 7states are considered to be the lowest two-quasiparticle states. The order of the 5and 7- levels changes between 134Ba and 136Ba. This phenomenon corresponds to the fact that the order of the lowest-lying $’ and 3’ levels in odd Ba nuclei changes

Ba

-

isotopes

MeV

8’ , : 3/2+----.. .' *. .._ ' _....XC---- 1/2+A = 132

134

136

A =

131

133

135

Fig. 7. A comparison between the systematics of the 5- and 7- levels in even Ba and the one of the f ’ and 3’ levels in odd Ba. The change of the order of levels in even Ba corresponds to that in odd Ba.

between 133Ba and 135Ba (see fig. 7). This change of the order of levels in the even Ba nuclei can be understood in connection with the behaviors of the 3s+ and 2d, neutrons. In table 3, the products of the enhancement factors E and the spectroscopic factors B* are given for the transfer configurations made of the 3~ 2d,, lh, and 2d, neutrons. In the low-lying states of the Ba nuclei, the 3~ 2d and lh, neutrons are the most important components. The 5- and 7- states in l3 dBa were most strongly excited by the (p, t) reaction as shown in fig. 6. However, the obtained enhancement factor E for the 7- state is less than one. On the other hand, if the 5- state in 136Ba has a mixture of the configurations v(h+s+) and v(h,d+) with the same amplitudes, the enhancement factor E for this state can approach one (see table 3). It was reported that the g-factor of -0.38f0.04 for the 5- state preferred the configuration of

H. Kusakari er al. 1 [p, f j

216

TABLE3 Enhancement factors E and spectroscopic factors B’(j,j, ; J) for the two-neutron pick-up reaction Assumed transfer con~guration

‘34Ba(p, t) EB’

‘Y3a(p, t) ___~ EB’

zB2

E

(3s,$ (lh,,,,)2 (2d,,#

6.18 3.27 28.94 2.61

6.40 3.52 29.13 2.81

4.05 2.19 18.29 1.81

4.05 2.19 18.29 1.81

1 1 I I

(2d,,# (lh,,j$ (2d,/,2d,,,) (2d,,J*

8.17 39.08 7.88 3.24

14.56 68.25 14.29 5.86

19.80 89.66 19.29 7.86

3.96 19.93 3.86 I .57

5 5

2:

(2d,,,)* Uh, ,,J2 (2d,,z2ds,J (2d,,,)’

1.27 6.25 1.22 0.51

1.42 6.61 1.36 0.56

3.22 15.09 3.12 1.31

0.64 3.02 0.62 0.26

5 5 5 5

4:

(th,,,# (2d,,#

2.30 0.22

13.49 1.21

37.41 3.85

4.16 0.43

9 9

0:

(2d,,,)’ (3% ,z (fh,,,# (2d,,#

0.12 0.06 0.53 0.05

.5-

(fh,,,z3s,/2) (Ih , ,,&,d

(Ih I ,,A,A

1.12 5.72 2.01

2.19 11.44 4.10

3.38 17.57 6.29

0.31 1.60 0.57

if 11 II

Uh,,,,%,) Oh , u24,z)

0.98 2.22

I .76 4.00

2.86 6.47

0.19 0.43

15 15

Level

0,’

2;

7-

(2d,,d’

-

r3’Ba(p, t) assumed BZ

5 5

Values of d = 1.7fm and Dz = 22 are assumed,

v(hyd+) [ref. “r)]. This remark is different from ours. The ratio of cross sections for the 5- states of 132*134*‘36Ba is 2:4:7, and that for the 7- states in I329134*‘36Ba is also approximately 2:4:7. Therefore, the enhancement factors E for the 5- and 7states of 132P‘j4Ba seem to be more reduced than those of ‘36Ba. It is probable that the 5- and 7- states of 132*134Ba deviate from the pure two-quasiparticle states and possess a certain amount of the collective nature of rotational band. It should be noted that the first 2+ state in l 36Ba is excited more strongly than the ground state. The enhancement factors E for the ground O+ and first 2’ states of ’ 36Ba are greater than one. This means that the assumed wave functions of the target nucleus 138Ba and the residual nucleus ‘36Ba are not correct enough to predict the cross sections. Concluding remarks are made as follows: (i) The first excited O+ state in ‘j4Ba is confirmed by this experiment.

H. Kusakari et al. / (p, t)

217

(ii) The cross sections of the (p, t) reaction for the first 4+ states of 13**134*136Ba drastically vary with neutron number. (iii) The 5- and 7- states were observed systematically in i3**134,136Ba. It seems that the 5- state in 136Ba has the mixture of configurations v(h& and v(hydt). The change of the order of the 5- and 7- levels in the even Ba nuclei can be understood in connection with the behaviors of the 3s+ and 2d.+ neutrons. The authors would like to thank the staff of the INS synchrocyclotron kind assistance.

for their

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