A comparative study of proton states in 121,123,125,127,129,131I excited by (α, t) and (3He, d) reactions

Nuclear Physics A320 (1979) 309-334; ©North-Holland Publishing Co ., Amsterdam Not to be reproduced by photoprint or micaofllm without written permiaion from the publish-

A COMPARATIVE STUDY OF PROTON STATES IN 121,123.129 .127,129,1311 EXCITED BY (a, t) AND (3He, d) REACTIONS A. SZANTO DE TOLEDO 1, H. HAFNER 11 and H. V. KLAPDOR - Kernphysik, 6900 Heidelberg, Germany Max-Planck-Institutjsv Received 6 November 1978

Abstract : Proton states in 121,`23,125,"',129,1311 were investigated by means of Tc(a, t)I and Te(3He, d)I reactions at 36 MeV bombarding energy using a Q3D magnetic spectrograph . Angular distributions were measured for transitions to' 21 1. From ratios of cross sections of transitions in the reactions (3He, d) and (a, t) to final states in 125-1311, the transfered orbital angular moments and relative spectroscopy factors are extracted. New levels are observed including J+ and - singleparticle strength fragments. The results are interpreted using the three-particle-cluster-phonon coupling model.

u

E

NUCLEAR REACTIONS 120-130Te(3He, d), 124-13oTe(a, t), E = 36 MeV, measured a(Ed, 0), .1311 deduced levels, l, J, n, S,,, . DR'BA analysis, three.123,125,127,129 .121 a(Et, t,0) particle-cluster-phonon coupling model calculations for 1211 .

1. Introdaction

The transitional nuclei around Z > 50 are known to be rather "soft", and changes in nuclear shapes can be expected for neighbouring nuclei. Proton states in the odd 123-1311 isotopes 1-3) were investigated by means of (3 He, d) reactions. In these experiments, mainly low angular momentum states were populated (3sj, 2d . and 2d t orbits) and only one fragment of the 1g ., and and Ih,,, strength was observed in each iodine isotope. The fact, however, that these investigations were done at different bombarding energies and analysed with different sets of optical-model parameters allowed only a limited comparison of experiment to a systematic theoretical description of these nuclei 4). In the present work, proton states in 121,123,125 .127,129,1311 were systematically investigated by means of the Te(a, t) and Te( 3 He, d) reactions. The (3 He, d) and (a, t) reactions have proved to be complementary tools for investigating the proton orbitals in the Z > 50 region 5-9). The former reaction mainly favours the transfer of a few units of angular momentum, in contrast to the (a, t) reactions which, due to the angular momentum mismatch between the entrance and exit channels, f On leave of absence from Instituto de Fisica da Universidade de Sao Paulo, Brazil . Fellow of the Alexander-von-Humboldt Stiftung. Present address : Instituto de Fisica da Universidade de Sa6 Paulo, Caixa Postal 20516, Sah Paulo, Brasil. 11 Present address: BBC, Mannheim .

310

A. SZANTO DE TOLEDO et ai.

will preferentially transfer a larger amount of angular momentum and select transitions to the 1 gi, lh., and l i* orbitals . Consequently, a comparative study of these two stripping reactions can be used to locate the total particle strength in the Z > 50 region . The ratio of cross sections for ('He, d) and (a, t) reactions for a given final state is strongly dependent on the transfered angular momentum and represents further information for spin determination that can, in some cases, substitute the measurement of complete angular distributions. 1I no information on the single-particle For the neutron-deficient isotope "'I strength distribution existed. Information on the level scheme of this nucleus has so far been based on studies of the ß + decay of "1Xe [refs. 10-12)] and of collective states in the `Sb(3He, ny) and (7Li, xny) reactions 13 .1 a). For this isotope, which lies almost in the middle of the neutron shells N = 50 and 82, strong configuration mixing with a pronounced collective character is expected 1 s -1a). For the heavier isotopes, for which information can be found in refs. 19-22), some new levels were identified, including fragments of the J+ and J-- single-particle strength . The experimental procedure and analysis of this work are presented in sects. 2 and 3. Results on "1 I are discussed in subsect. 4.1 . The comparison between the (3 He, d) and(a, t) reactions is discussed and confronted with the systematic behaviour of the odd-iodine nuclei in subsect. 4.2. In sect. 5 we interpret the data within the framework of the three-particle-cluster - phonon coupling model. 2. Experimental procedure

The experiments have been performed at the MP Tandem Van de Graaff accelerator of the MPI Heidelberg with a 36 MeV 3He (a) beam. Tellurium targets of ., 100 jug/cm 2 thickness on 15 l,Ig/cm2 carbon backing were used. The reaction products were analysed and detected by means of a three-wire (AE, E, veto) position-sensitive proportional counter (140 cm long) located at the focal plane of a Q3D magnetic spectrograph . Four-parameter event-mode data (AE, E and two position signals) were accumulated in a E2 on-line computer. All combinations of one and two parameters could be displayed to control the experiment. Exposures were taken for the 120Te(3He, d)1211 reaction at 25 angles covering the interval from 3° to 32°. Spectra for the 122-130Te(3He, d) 123-1311 and 122-130Te(a, 1) 123-131 1 reactions were taken at 12° and 15°. An overall energy resolution AEIE x 3oó0 was achieved, i.e. 13 keV FWHM in the (3He, d) spectra and 8 keV FWHM in the (a, t) spectra. Typical spectra are shown in figs. 1-6. The total amount of exposure varied between 0.8 mC (for forward angle exposures) and 1 .5 mC (for backward angles). Solid angles varying between 0.5 and 8 msr were used depending on the behaviour of the predicted angular distributions (see sect. 3). A solid state monitor detector placed at 0,,b = 45° in the target chamber

PROTON STATES IN IODINE 6

UN

120 Te (3He,d)'1211 ELab = GLab = 29P 1

28

36.0

il

11

MeV

e

1111

15 il

u

13 1

10

12

n

s

1 I

a

.s

12"

25 22 19 ' 22 20 17 k

26 27

311

~

~9110 U)"

n

W CHANNEL 200 300 400 500 600 Fig. 1 . Energy spectrum of the 12°Te('He, d) 12 'í reaction . (The excitation energies are given in table 3.) ~ T arm ,

was used to observe the elastically scattered 'He particles, in order to obtain the relative normalization of the deuteron angular distributions, and to observe possible target deterioration. Short exposures of elastically scattered 3 He particles on 1Z °Te were also taken at the Q3D focal plane for the absolute normalization of cross sections. The elastic

122 Te (3He , d.)123I

800

C

EL = 36 MeV 0 L =12°

600 9

O

0 400

200

432

0

100

200

300

400

500 Channel

Fig. 2. Energy spectrum of the 122Te(- He, d) 123 1 reaction . (The excitation energies are given in table 4.)

100

200

300

400

500

600

700 Channel Fig. 3 . Energy spectrum of (a) the reaction 124Te( 3 He, d) 1251 and (b) the reaction 124Te(a, t)1251 . (The excitation energies are given in table 5 .)

scattering of 3He from a 12'Te target at 01,b = 15° was assumed to be 1 .07QR, where aR is the pure Coulomb cross section. The limited degree of enrichment of 120Te commercially available (51 .38 % 12'Te, 4 .76% 122Te, 1 .31 % 123Te, 3.71 % 124Te, 4.40 % 125 Te, 9.43 % 126Te, 11 .89 12'Te and 13.21 % 130Te) was exploited in order to have many calibration points in the spectrum . In this way, correction of Q-values and energies for different target thicknesses is also avoided. Spectra measured for the reactions 122-13oTe(3He, d)

313

PROTON STATES IN IODINE 1250 1000 2

c 750

0 U

500 250

100

200

300

400

500

600

700

Channel

1000 u) 750 C U

500 250

0

100

200

300

400

500

Fig. 4. Energy spectrum of the reaction (a) ' 26Te('He, d) 12 'í and (b) energies are given in table 6.)

600

700

Channel

116're(a, t)'2'í. (The excitation

under the same experimental conditions with targets enriched to > 95-99 % have been used to determine, after subtraction, lines originating from 1211 and lines from other 1-isotopes used in the calibration procedure 23) 3. Analysis

Angular distributions were obtained for 26 transitions in the t2°Te( 3He, d) 1211 reaction . DWBA calculations in the zero-range approximation were performed

314

A. SZANTO DE TOLEDO et al. 200E

c

0 U

150E

100~

Fig. 5. Energy spectrum of the reaction (a) "'Fe(- He . d)" 9 I and (b) '"Te(a, t)'=9 I . (The excitation energies are given in table 7.)

using the code DWUCK even target is

24) .

The cross section for stripping reactions on an even-

aWB) da(9) = N 2Jr + 1 CZS d1Z 2J,+ 1 2j+ 1 ' where the reduced cross section 4w(B) is the single particle cross section predicted by DWBA calculations, and J,, Jr andj represent the total angular momenta of the

PROTON STATES IN IODINE

315

Channel Fig. 6 . Energy spectrum of the reactions (a) 130Te(3He, d)13'I and (b) 130Te(a, t)' 3 'I. (The excitation energies are given in table 8 .)

target nucleus, residual nucleus and transfered proton, respectively. The constant C represents the isospin coupling coefficient and N the normalization factor. For the (3He, d) reaction the well-established 2s) value N = 4.42 was used ; for the (a, t) reactions big discrepancies exist in the literature, with values varying from N = 46 to 250 [refs.'-9 .26-29)] . The shell model predicts that the proton captured by the Z = 52 Te target should occupy the lg4, 2dj, 241, 3s, or lh V orbits, corresponding to the transfer of 4, 2, 0 or 5 units of angular momentum, respectively. Thus, only for lp = 2 does there

31 6

A. SZANTO DE TOLEDO et al. TABLE 1

Optical-model parameters used in the DWBA analyses Parameter v set (MeV) s, ')

133.3 170.5 101.0 99.0

TZ b)

d, ') d 2 0) p,

0) 1)

P2

218.6 189.1 149.6 166.3

a, d) 2 2 d) t, d) t2 d)

ro (fm)

(fm)

1 .24 1 .14 1 .15 1.12 1 .20 1 .14 1.373 1.309 1.24 1.16

0.667 0.723 0.81 0.82 0.65 0.65 0.553 0.62 0.706 0.752

a

W (MeV) 23 .07 17 .5

W (MeV)

ró (fm)

(fm)

r., (fm)

66 .5 63 .0

1 .46 1 .6 1 .34 1 .24

0.781 0.86 0.68 0.86

1 .25 1.25 1 .25 1 .25

1 .373 1 .435 1 .378 1 .498

0.553 0.62 0.903 0.817

1 .34 1 .40 1 .25 1 .25

29 .87 24 .2 21 .88 15 .2

a'

°

25 .0 25 .0

The optical potential used was of the form U(r) _

-V(1+e)- ' -d(W-W'&,)(1+e',)-1+

with x

= (r-roA'r3)a,

x' =

(r-róA113)/a

.,

2

(ne xc) V" A .

r, = ro .A1 1 3.

r dr (1+ex)_1l .a .

a=

2S/h for spin +} Slh for spin 1.

°) Ref. 2). ') Ref. ') . b) Ref. 30) . d) Ref. 31). °) The well depth for the transfered proton is adjusted to give a binding energy equal to theexperimental separation energy .

remain an ambiguity in the spin determination from the measured 1-value. The optical-model parameters used in the calculations are given in table 1 . It is known that the magnitude of the cross sections predicted by the DWBA calculations is very sensitive to the geometry of the bound state potential of the transfered particle, i.e. a variation of 5 % in the potential radius leads to changes of 30 % in the reaction cross section. Thus with the relative spectroscopic factors obtained in this work having an uncertainty estimated to be 10 % to 15 %, absolute spectroscopic factors may have uncertainties up to x 35 %. Fig. 7 shows the predicted angular distributions of the (a, t) reactions. While for the (3He, d) reactions, from the measurement of the angular distribution, one can determine the transfered 1-value, in the case of the (a, t) reaction almost no structure is expected in the angular distributions and therefore the (a, t) reactions are not very sensitive for spectroscopy by itself. Assuming that the transfer of the proton is localized at the surface of the nuclei, it is seen in the grazing collision picture 32) (fig. 8) that the (3He, d) reaction is well matched for the transfer of very low angular momentum (1 = 0, 1, 2) where ki R-k.R x 0. In the case of the (a, t) reaction for low excitation energies the angular momentum mismatch between the entrance and exit channels, due mainly to the very negative Q-value, Q(a, to ) x -14 MeV, will favour the transfer of 1= 4, 5, 6 and, consequently, the

PROTON STATES IN IODINE

-Con

317

ió-2

a

E

. -.

" k~ 2d W

\

1 9712 1

0

% 'v 10

-

' 3ay4 20

30

40

ee.m.

Fig. 7. Predicted DWBA angular distributions for the reactions i"Te(a, t) 12 'í using the optical-model parameter set (a  t, . pl).

cross section for low spin states will be inhibited. This selectivity of the (a, t) reactions for higher "Ip" compared to ('He, d) reactions can be exploited by measuring the ratio ofthe cross sections for a given final state when populated by the two reactions. The ratio ofDWBA cross sections shown in fig. 9 displays the strong 1-dependence .

25 20

w

15 10

(a,t )

5 i IA i i i 1 , , . if I Fig. 8. Grazing collision : vertical lines represent the entrance grazing angular momentum (1) and the parabolae the grazing angular momentum in the exit channel as a function of the excitation energy E* of the residual nucleus (and Q-value of the reaction).

31 8

A. SZANTO DE TOLEDO et ai .

10 b

v

v x

43 11

0.01 Q8

t0

t5

20

2.5 E,x (MeV)

Fig. 9. Ratio of DWBA cross sections for ('He, d) and (a, t) reactions at 0 = 12° for different sets of optical-model parameters . Ratios were normalized to unity for (1 = 2, Eá = 0) . The dashed lines correspond to the use of the parameters (r d l , p,) and (a  t p l ) ; the solid lines to (r2, d2, P 2 ) and (a 2 , t2, P2); the dotted lines to (s  d2, P2) and (a  t P,) ; thedash-dotted lines to (s  d2, P2) and (a2, t2 , P0 "

Several sets of parameters were used in the calculations (see table 1), and the relative values of this ratio shown to be independent of the choice of optical-model parameters. Thus, if the spin of at least one state is known, relative cross sections can be used for !-determination.

4.1 . THE

I

11 re('He, d) 12 '1 REACTION

4. Results

Figs. 10 and 11 show the experimental angular distributions obtained for the reaction 120Te(3He, d) 121j, the solid lines representing DWBA fits when using the set i1, dl, p1 of, optical-model parameters . Table 2 presents the excitation energies corresponding to the observed transitions (mean values from the spectra obtained at B,,b = 3°, 5°, 10.5°, 12° and 15°), the maximum experimental cross sections (for lp = 0 transitions, (dtr/dáa). corresponds to the second maximum at 0 14°), the transfered angular momenta 1p, assigned spins I, experimental spectroscopic factors C2S, and, for low-lying levels, the spectroscopic factors for the (3He, d) reaction calculated on the basis of the cluster-phonon coupling scheme (see sect . 5). In the present experiment, a strong 1 = 2 transition has been observed for the 1211 ground state, in agreement with the previous assignment 10-13) ,x = j+ and with the systemactics of the 123-125,1271 isotopes . The first and second excited

PROTON STATES IN IODINE TABLE

31 9

2

Summary of results obtained for "'I Level no .

E.') (MeV)

du b) _ dß

1 2 3 4 5 6

0 .000 0 .096 0 .133 0 .176 0.812 0.931

1 .87 0 .46 0 .28 0 .22 0 .45 1 .53

7

0 .959

1 .72

8 9 10 11 12 13 14 15 16

1 .005 1 .035 1 .113 1 .140 1 .270 1 .385 1 .466 1 .557 1 .607

0 .19 0 .22 0 .09 0 .31 0 .13 0 .08 0 .43 0 .40 0 .44

17

1 .749

0 .32

18 19 20 21 22 23 24 25 26 27 28 29

1 .775 1 .802 1 .852 1 .885 1 .919 1 .957 2 .039 2.080 2.350 2.375 2.471 2 .762

0 .14 0.16 0.15 0 .31 0 .19 0 .06 0 .05 0 .28 0 .09 0 .08 0 .07 0 .12

.

v

2 0 4 2 5 2 0 + 2 2 2 (2) 2 2 2 0 0 2 0 + 12 2 2 2 0 2 2 2 0 2 2 2 0

i d)

C3 `S. P °)

1 1

0.30 0.12 0.54 0.07 0.51 0.24, 0 .49 0.20

} } ;1

}, 4 }

1, 1

}, } }, } (}, }) }, } }, } ,} } }1

1,

}

}, } }, }

1, 1

}, } }

1, 1 ,} }, }

111 ,I }

0.30, 0 .16 0 .06, 0 .03 0.07, 0 .03 0.03, 0 .02 0.10, 0 .05 0.04, 0 .02 0.03, 0 .0l 0.12 0.11 0.14, 0 .07 0.05

.

0 .28 0 .09 0 .32 0 .08 0 .39 0 .07 0 .10 0 .14

0.04, 0 .02 0 .04, 0 .03 0.05, 0 .03 0 .04, 0.03 0.08 0.06, 0 .03 0.02, 0 .01 0 .02, 0 .0l 0.09 0.03, 0 .02 0.03, 0 .02 0.03, 0 .0l 0.03

') Excitation energies in MeV obtained in the present wpyk . Uncertainties are estimated to be x 4 keV for states up to 1 MeV excitation, . 6 keV up to E+ x 1 .8 MeV and x 8 keV for E+ x 1 .8 MeV . % Absolute cross sections (mb/sr) at the first maximum of the angular distribution . °) Transferred angular momentum attributed. d) Total angular momentum attributed according . t o IP . ') Absolute spectroscopic factors obtained using eq . (1), presented in the same order as 1.

states observed at 0.096 MeV and 0.133 MeV correspond to 1 = 0 and 1 = 4 transitions, respectively . This indicates an inversion of the levels with respect to 1 Z 3 I which follows the systematic behaviour observed in the odd-iodine isotopes (fig . 12). A state populated by a /P = 2 transition was observed at 0.176 MeV in agreement with the J+ level proposed in ref. 16) . A strong -U- (1P = 5) state, also

A. SZANTO DE TOLEDO et al.

32 0

VI 11

E

áv

0

0

10 20 30 0,.

0 10 20 30 6-

0 10 20 30 6t.

Fig. 10 . Experimental angular distributions of the reaction '"Te('He, d)1] 11. The solid lines correspond to DWBA fits .

observed in the other iodine isotopes, has been identified in 121 1 at 0.812 MeV. Twenty other IP = 2 transitions were observed, but most of the . 2d t and 2d., single-particle strength is concentrated essentially . in four levels at 0.931 MeV, 123,1251 . Seven 1 = 0 0.959 MeV, 1 .140 MeV and 1 .607 MeV, as is the case in transitions leading to states with spin I + were observed above 0.8 MeV. t)125-13 1 1 REACTIONS 4.2. THE 1s=-13o-re(3He, d) 1=' -131 1 AND 134-130Te(a,

In this section we will only focus on the new systematic features observed in the structure of these 1-isotopes . The results obtained in the present work are summarized in tables 3-7 and figs. 13-16. Relative spectroscopic factors and relative ratios of cross sections R = da(3He, d)/da(a, t) were computed with reference to the values for the first strong 11 state (ground state for 121,123,125,1261) which have been normalized to unity.

PROTON STATES IN IODINE

OA1 P 0

32 1

. I .- I . . . . I . . . . I . . . . i .l 0D1 L . . .i . . . . i . . . . i ' ., 1, 10 20 30 81-m 0 10 20 30 km 0 V 20 30 km Fig. 11 . Same as fig . 10.

As predicted by semi-microscopic calculations °), the spectroscopic factor S.í , for the lowest I, state (13 '1 and 1291 ground states) shows a slight systematic decrease with respect to S,, with decreasing mass of the isotope. On the other hand, the relative single-particle strength of the J, state is constant, revealing a similar degree of admixture as in the 1, state. Besides the rapid decrease of excitation energy of the 1, state, the relative spectroscopic factor is conserved. A 42 state has been identified in most of the nuclei : 0.539 MeV in 1251, 0.629 MeV in 1271 and 0 .766 MeV in 1291 ; in 1311 this state is hidden by contaminants . These j states were mainly observed by the (a, t) reaction, and the spectroscopic strength is of the order of 0.04S,í,. Two strong l = 2 transitions are observed in every iodine isotope. The systematic behaviour of spectroscopic factors allows the conclusion that the I state identified by y-decay studies 2° .2') at 1 .143 MeV in 1311 corresponds to the state 1 .112 MeV in 1291, 1 .097 MeV in 1271, 1 .065 MeV in 1251, 1 .152 MeV in 1231 and 0.931 MeV in 12 '1. A further strong l = 2 transition leads to the 1 .294 MeV state in 1311 identified 20,2 ') as being a I+ state, corresponding to the state at

A. SZANTO DE TOLEDO et ai.

322 2.0

11n-

~` :1v2-

-

an "

.In. ''

.5 0

'. 312*

.0 0

W, 1331

. . .~. . . %2+

. . . . . . . .W* 1311

_

1291

" 1271

.112* + 5/2 1251

3n "

312 " tsn+

-__ 5n "

1211

1231

and -V- in the odd

Fig. 12 . Systematic behaviour of the lowest-lying level with spins iodine isotopes . TAet.E

3

Summary of results obtained for 1131 Level no . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Energy') (MeV)

Energy 9) (MeV)

Present work) energy (MeV)

1 -)

0 0.138 0.148 0.178 0.330 0.94 1.01 1.05 1.15 1.24 1.31

0 0.144 0.144 0.176 0.332 0.942 1.010 1.046 1.152 1.240 1.307 1.338 1.368 1.394 1.493 1.583 1.629 1 .653

0 0.138 0.149 0.175 0.327 0.941 1.010 1.046 1.152 1.241 1.307 1.334 1 .370 1.394 1.493 1.582 1.635 1.658

2 4 0 2

1.37 1.49 1.57 1.63

5 2 0 2 0 2 0 2 0 2

J

S.Vt . h)

} } }, } } }, }

1

}, } } }, } }

2

See table 2. From ref. ') . From ref. 3 ) . h) Relative spectroscopic values normalized to S,,z, (ground state of order as J.

1 .0 1 .31 0.34 0.17 1 .24 0.65, 1 .30 0.48 0.78, 0.39 0.11 0.116, 0.058 0.010 0.086, 0.(43 0.168, 0.088, 0.044 0.068

a. c, °)

121-1271)

presented in the same

PROTON STATES IN IODINE

32 3

TAau 4 Summary of results obtained for '"I

Level no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Energy') ( Me 0 (2) 0.111 (4) 0.187 (2) 0.243 (0) 0.371 (2) 0.536 (}*)') 0.596 (1*) 0.935 Q+) 1 .005 (2) 1 .066 (2) 0) 1 .087 + ~5) 1 .198 (2) 1 .254 1 .337 (2) 1 .381(0+2) 1 .439 (2) 1 .580 1 .610 1.663 (2) 1.690 (0) 1.735 1.779 (0) 1.827 (2) 1 .916 (0) 1 .939 (2) 1 .978 (2) 2.031 (2) 2.069 (0) 2.142 (0) 2.183 (0) 2.231 (2) 2.302 (2)

Energy 11) (Meh 0 (2) 0.114(4) 0.188(2) 0.243(0) 0.372(2)

Present work 8) (3He, d)

0 0.113 0.188 0.241 0.373

')

(a, t) 0 0.113 0.188 0.244 0.371 0.539 0.625 0.930 1 .006

') 1.01 (0) 1.09 (2)

1.006 1 .065

1 .09 (5)

1 .087

1 .087

1.21 (2) 1.26 (2) 1.36 (2)

1 .199 1 .254 1 .338

1.39 (2) 1.44 (2)

1 .383 1 .440 1 .578 1 .609 1.666 1.691 1.732 1.781 1.827 1.915 1 .937 1.969 2.035 2.068 2.141 2.182 2 .230 2.301

1 :195 1 .249 1 .336 1 .365 1 .392 1 .441

1.60 1 .70 (2) 1.82 (0) 1.95 (0)

2.19 (0) 2.22«0»

R daeHe, dy) da(a, t)

1 .662 1 .729 1 .777 1 .827 1 .936

1

ÎP

C)

1 .00 ±0 .2 0.043±0 .003 1 .24 +-0.1+ 6.69 ±0 .90 1 .02 ±0 .13 0.066±0 .027 (0.39 ±0 .14) (0.28 ±0 .11) 1.78 ±0.14

2 4 2 0 2 4 (2,4) (4,2) 2

unresolved peaks

(5) + (0) 2 4 2

2.20 ±0.26 0.079±0.015 2.28 ±0.25 2.66 ±0.28 2.99 ±0.52 > 5.3 > 10.3 1 .84 ±0 .21 18.41±5.9 0.11 ±0 .02 2.50 ±0 .47 0.262±0.027 > 15 .7 3.17 ±0.34 >5 .5 >6.7 > 1 .9 > 10.4 > 12.3 > 15 .4 > 5.2

(2)

2+(0) 2+(0) (0) (0) 2 (0) 4 2 4+(2) 0 2

j d)

1

} }

1 1 1

(He, d)

Sroi h) (a, t)

1 .00 1 .71 0.17 0.60 0.060

1 .00 1 .79 0.14 0.41 0.069 0.04

S , h)

1,4 (1,4)

0.66, 0.33 0.47, 0.94 1.47

(1)

0.15 0.14, 0.28 0.30 0.14, 0.28

(V)

1,1

}

1,1

1+(1) 1+(1) (1) (1)

1,1 1 1 1,4

< 0.21 < 0.080 0.03 0.02 0.07, 0.14 0.17 0.16 0.16, 0.32

0.70, 0.35 < 1.40 0.11 . 0.22 0.22 0.14, 0.28 0.18 0.06

0.24 0.16

.. C. d . r. ,) See tables 2 and 3. h) Relative spectroscopic factors from (3 He, d) and (a, t) reactions. From ref. ") . J) Ratios of cross section for given transition observed via (3He,. d) and (a, t) reactions. The ratios R were normalized to unity for the transition to the 1, state.

1 .050 MeV in 1291, 0.993 MeV in 127 1, 1 .006 MeV in 1251, 1.010 MeV in 1231 and 0.959 MeV in 1211 . These states carry most of the d., single-particle strength that increases with decreasing mass of the isotope. Like the 1, state, the 12 states decrease

A. SZANTO DE TOLEDO et al.

324

strongly in energy with A while the spectroscopic factor rises due to the increasing zero-phonon component. The lowest negative parity state with J = Z- does not show a strong decrease of spectroscopic factor in spite of the excitation energy and single particle energy TAat,E

5

Summary of results obtained fro "'1 Level no.

Energy m) (MeV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Energy') (MeV) present work (3 He, d)

(a, t)

0 (2) 0.058(4) 0.203(2)

0 0.057 0.204

0.375(0) 0.418(2)

0.378 0.420

0 0.058 0.204 0.295 0.378 0 .421 0.473 0.632 0.745 0.831 0.883 0.993 1 .046 1 .097 1 .127 1 .236 1 .274 1 .319 1 .342 1 .375 1 .402 1 .437

(0 .629x}) t) (0 .745x1+) t) 0.991 (2) 1 .044 1 .095(2) 1 .124(0) 1 .235(5) 1 .275

0.993 1 .045 1 .096 1 .122 1 .234 1 .274

(1 .350) (1 .362) 1 .401 (2) 1 .444(0) 1 .515 1 .554(2)

1 .401 1 .444 1 .507 1 .554

+l653 1 .658

1.657

1 .778 1.83 (0) 1 .868(2) 1 .89 (2) 1 .92 (0) 2.065 (0) 2.16 (2)

1.791 1.836 1.863 1.873 1 .885 1.913 1.978 2.060 2.143 2.166

R

- da(3He, d) ')

1 -)

jn

)

S,.

e

)

(He, d)

SI., ,, )

(cc, t)

1.00 ±0.02 0.045±0.004 1 .32 ±0.12

2 4 2

} } }

1.00 1.96 0.17

1 .00 1 .93 0.13

9.3 ±1 .8 1.14 ±0.08

0 2

} }

0.60 0.20

0.21 0.19

0.29 ±0.05 0.079±0.016

(4)

(})

1.53 ±0.06 0.053±0.010 1.46 ±0.03 7.06 ±2 .10 0.018±0.001 0.062±0.007 0.13 ±0.10 0.1 ±0.1

2 4 2 0 5 4 (4) (4)

1,1 }

1,1 }

u 1

(}) (})

(0 .04)

0.62, 0.31 0.26 0.55, 1 .10 0.20 1.68 0.43

0.62, 0.31 0.23 0.60, 1.20 0.24 1 .40 0.45 0.01 0.02

2 2+0 2 2+(0) 4 2

1,1 1+1 1 1+(1) 1 4,1

4.73 ±0.6

(0)

(1)

0.15

0.20

1 .865

3.80 ±0.71

(2)

(1,1)

0.07

0.05

1 .887 1.913

1.72 ±0.35 4.7

2 (0)

4,1

(1)

0.10 0.15

0.14

2.137 2.169 2.233 2.256

1.81 ±0.22 2.38 ±0.33

(2) (2)

(1,1) (1,1)

0.06 0.05

0.08 0.05

1 .555 1 .569 1 .656 1.696 1 .719 1 .793

1.57 3.76 1.40 2.55 0.10 1.12

±0.08 ±0.03 ±0.31 ±0.26 ±0.04 ±0.16

0.34, 0.17 0.38, 0.19 0.28+0.25 0.24 0.01 0.12+(0.23) 0.10 0.02 0.14

PROTON STATES IN IODINE TABLE

Level Energy no. ( Me 41 42 43 44 45 46 47 48 49

m)

2.50 (0)

'. °. d.

Energy a) (MeV) Level present work no . ('He d) 2.318 2.359 2.406 2.431 2.456 2.496 2.524 2.611 2.641

n. j) See table 4.

50 51 52 53 54 55 56 57 58

32 5

5 (continued)

Energy m) Energy') (MeV) Level Energy') Energy') (MeV) present work present work no. . (MeV) (Me V) ('He d) (He, d)

2.85 (0) (2 .93) (0)

') From ref. ") .

2.689 2.735 2.752 2.792 2.816 2.849 2.894 2.947 2.997

59 60 61 62 63 64 65 66

3.12 (0)

3.010 3.102 3 .126 3.218 3.283 3.335 3.372 3.404

') From ref. _) .

both decreasing with A . This fact, together with the difficulty of reproducing the decrease of excitation energy by the cluster-phonon coupling model, reflects a strong dependence of its structure on the cluster coupling to the 3 - state of the Sn core, the energy . of which decreases with A. States that were assigned 14, 19, 22) to have J = I + by y-decay studies were weakly observed by the (a, t) reaction, i.e. 0.596 MeV in 1251, 0.745 MeV in 127 1 and 0.845 E,,,

Fig. 13 . Experimental values for the ratios of cross sections to several states in "'I populated by means of the ('He, d) and (a, t) reactions. The solid lines correspond to DWBA predictions for the ratio R = (d,( 3 He, d))/(do(a, t)) when optical-model parameters (r  d p,) and (a  t p,) are used. The value R(J' = }+, E+ = 0 MeV) is noramized to unity.

326

A. SZANTO DE TOLEDO et al . TAaLE

6

Summary of results obtained for '29 1 Level no . 1 2 3 4 5

Energy) (MeV)

0 (4) 0.028(2) 0.279(2) 0.487(2) 0 .M0(0) 0.769(}) 6 0.845(}, l)'-7 7 1 .052(2) 8_ 1 .111(2) 9 1 .210(0) 10 1 .261(2) 11 1 .282(}) ') 12 1 .402(5) 13 1.483(0) 14 15 1.566(2) 16 1 .621(2) 17 18 1.741(0) 19 1.823(0) 20 1 .861(2) 21 22 23 1 .963 24 2.012(0) 25 26 27 2.073(2) 28 29 2 .208(0) 30 2.40 (0) 31 32 33 2.59 (0) 34 2.79 (0) 35 2 .85 (2) 36 2.95 (0) 37 3.20 (0)

Energy ') (MeV) present work R ('He, d)

(a, t)

0 0.029 0.280 0.491 0.562

0 0.028 0.280 0.489 0.560 (0 .766) 0.843 1 .050 1 .112 1 .208 1 .261 1 .283 1 .401

1 .049 1 .112 1 .210 1 .272 1 .400 1 .484 1 .567 1.620 1 .704 1 .743 1.821 1 .860 1 .959 2.016 2.072 2.208 2.401 2.450 2.511 2.595 2.753 2.854 2.938 3.170

1 .521 1.569 1.619

dor('He,d) J) "(a, t) a--

lo

~)

0 .189±0.016 1 .00 ±0.04 1 .106±0 .170 1 .220±0 .074 13 .0 ±1 .95

4 2 2 2 0

0.90 ±0.20 1 .09 ±0.07 1 .73 ±0 .06 9.72 ±1 .76 1 .45 ±0.46 0.085±0 .025 0 .070±0 .008 27 .4 ±5 .5

(4) 2 2 (0) 2 (4),(5) 5 0 (4,5) 2 2 (Ó) (4)+(0) (0) (2)

2.81 ±0 .84 3.16 ±0 .46

1 .743

1 .17 ±0 .17

1 .867 1.909 1 .940 1 .963 2.002 2.026 2.050 2.071 2.150

2.09 ±0 .29

d)

} } (j) } } (})

s..") ('He, d)

Snl h) (a, t)

1.76 1 .00 0.16 0.45 0.58

2.06 1 .00 0.19 0.44 0.43

1

0.73 0.48 0.04 0.10

1

1 .05 0.52

(}), (V)

u

1,1

}, } (}) (})+(}) (})

a,1

0.09, 0.0.4 0.12, 0.06 0.05 0.08 0.25 0.22, 0.11

0.04 0.96 0.50 0.07 0.12 (0 .28), (0 .10) 1 .31 0.40 0.08, 0.04 0.11, 0.06 0.17 0.25, 0.12

.. e . d . n. l . t . ') See table 5. ') From ref. _ 1) .

MeV in 1291, The observation of these states which are not expected to be populated by one-step direct transfer suggests that two-step processes occur, corresponding to the weak coupling of a 2dß. or I g4 proton to a 2' excited Te target .

PROTON STATES IN IODINE

327

0 f

a b v

v

So-2

01

ts=a

Lp=5

iL

L ~ 1llIiliI[[IIIIillitil

0.5

1D

1 .5

Fig. 14. Same as fig. 13 for 5. Description

the structure

of

2.0

2.5 Eex ~)

1211 .

within the thre0-particle-cluster-phonon Coo~ model

of 's'I

The general trend of the structure of 123-1311 isotopes has been quite well understood by the cluster-phonon coupling model °) . This model is thus applied . here to, the isotope 121 1. Since a detailed description of the model can be found in the literature a .33 .34) only the main ideas underlying the calculations are presented here . The model

129 1

..

f

F

10

i, .0

ä

t, .2

v 1.0 ift-4-1 s

x

M

n

04

1 P -4

0.1

1,-5

u ~ I

0.5

m i I m

t0

n 1 m n I m o

1.5

2A

Fig. 15 . Same as fig. 13 for 1291.

I

25

E,, (MeV)

328

A. SZANTO DE TOLEDO et al. TABLE 7 Summary of results obtained for "'I

Level no . 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Level no . 23 24 25 26 27 28 29 30

Energy') (MeV) present work

Energy m) (MeV) 0 (4) 0.150(2) 0 .492(2) 0.602(2) 0.877(0) 1 .098(2) 1 .147(2) 1 .298(2) 1 .346(0) 1 .427(2) 1 .500(2) 1 .638(5) 1 .677«0),(2» 1 .718(0) 1 .759 1 .797(2) 1 .801((2)) (1 r880) (1 .924) (1 .980) 2 .00 Energy m) (MCV)

R

-

da(3 He, d) J) ~) da(a, t) 1°

j d)

(3He, d)

(a, t)

0 0.151 0 .91 0.599 0.874 1 .096 1 .148 1 .294 1 .339 1 .429 1 .499 1 .643 1 .677 1 .718 1 .757

0 0 .150 0 .492 0 .601

0 .13 1 .00 1 .44 1 .17

±0 .02 ±0 .04 ±0 .25 ±0.06

4 2 2 2 0

1 .143 1 .294 1 .399 1 .424 1 .494 1 .639

0.94 ±0.1 1 .92 ±0.15

}, } J, }

2.07 ±0.41 2.32 ±0.28 0.103±0 .008

2 2 2 2 2 5

1 .718

10 .05 ±0.51

0

1 .802

2 .052

Sr.1 h) ('He, d)

s,. . ")

(a, t)

1 .83 1 .00 0.17 0.85 0.61

2 .04 1 .00 0 .16 0 .95

4,1 1,1

u

0 .32, 0.64 0 .62, 0.31 0 .11, 0.06 0 .10, 0.05 0 .24, 0.12 1 .23

0.46, 0 .92 0.62, 0 .31 0 .10, 0 .05 0 .08, 0 .04 0 .28, 0 .14 1 .50

}

0 .81

0.90

} } }

}, }

1 .790 1 .831 1 .875 1 .915 1 .985 2 .029

Energy') (M'V) present work ('He, d)

Level no.

Energy') (MOV)

Energy') (MCV) present work (3 He, d) .

Level no .

Energy') (MeV) present work ('He, d)

2 .134 2 .188 2 .329 2 .358 2 .435 2 .567 2 .595 2 .638

31 32 33 34 35 36 37 38

(2 .699) (2 .744) (2 .807)

2.694 2.737 2.780 2.854 2.894 2 .925 2.985 3 .090

39 40 41 42 43 44

3 .132 3 .183 3 .219 3 .284 3 .427 3 .760

(2.175)(0) 2 .332 2.346(0) (2.444)

.. . . d, h .1 . m) See table 5 .

Hamiltonian is H = H. +Hs .p.+H..+H,

where H.1 , describes the harmonic quadrupole vibrational field of the Sri core,

PROTON STATES IN IODINE 100

329

1

131

1 P .0

s'"

A

b v il 0 .1 71 gr

4

P

L .5

m I

Q5

w o

I

lA

wo

I

15

m l ~

2.0

Fig. 16. Same as fig. 13 for "' 1.

i

2.6 E  (M@1/)

H..P. describes the single-particle motion of the three valence protons, H,., represents the residual interaction between the three protons in the valence shell cluster, approximated in the present work by a pairing force, and Hi , describes  the interaction between the three-particle cluster and the vibrational field. The strength of the interaction is related to the effective deformation parameter ß of the core. The three active protons are distributed among the 184, 2dt, 2d}, 3sj and I h,,, single particle states coupled to zero, one or two phonons. The model parameters in the present calculations were extrapolated from the values used in ref. 4) for 123-1311 (see table 8) and the same configuration space was used . In the evaluation of the theoretical spectroscopic factors for the one-proton transfer reaction, the ground-state wave function of the 120Te target (table 9) has been calculated using the same Hamiltonian in the representation of two-particle cluster coupled to N quadrupole phonons. To situate in the systematics of the odd iodine nuclei we show in fig. 17a the 1211

TABLE 8

Parameters used in the present calculations a(g,i2) (MeV) a(d,n) (MeV) 48,/2) (MeV) e(d3/2) (MeV) £(h 1112) (MeV) &0

(MeV)

ß . G (pairing) (MeV)

0.00 0.15 0.80 1 .10 1 .00

1 .10 0.146 0.15

33 0

A . SZANTO DE TOLEDO . et al. TABLE 9

Calculated wave functions represented by I{V lj2) J12 , j3) J, NR> of low-lying states in +0 .4791{(8712) 20, ds/2)1 ; 00> +0 .2231{(97/2)% ; 12> -0 .2921{(87/2) 22, ds/2)1S ; 12> +0 .25711(87/2) 22 , ds/2)3 ; 00>

+0 .2481{(97/2)3)1 ; 00> - 0 .343 1{(B7,,)20, d3,,11 ; 12> -0 .2601{(S7/2)22, d,12)$ ; 12>

- 0 .5211{(87/2)20, ds12)1Q ; 12> +0.2311{(87/2)22 , ds/2)3 ; 24> +0.2751{(8712)2 2, s1/2)} ; 12> +0.2841((9,,7 1 2)3 )j ; 00>

-0.5161{(87/2)2 0, 8112)} ; 00> - 0.2051{(87/2)20, d3/2)1 ; 12> -0.239 1{(87/2) 22, ds12)1 ; 00>

+0 .5151{(g712)3Îj ; 00> -0 .2501{(g712) 3 }} ; 12> +0 .254l{(97/2) 22, d s/2 )i ; 00>

-0.2ó01{(87/2)3)1 ; 12> - 0.2761((97/2)22 , d3/2)i ; 00>

121 1

-0.2301{(d ,12) 2 0, 87/2)1 ; 00> -0.2641487/2)3}3~, 12> _ +0.2021{(8712) 0, ds12 11 , 12>

-0.3891{(8712)3)j ; 12> +0'2901((97/2)'0, d312)1 ; 00>

-0.6891{(87,,)20, h, 112)V ; 00> +0.3471{(87/2) 2 0, h, 1/2W ; 12> -0.3741{(8712)2 2, h11/2)331 ; 00> +0.3071{(87/2) 22, h,112W ; 12> +0.2711{(8712)2 2, h,112)'9 ; 12> -0.3611(8712)22 ; 12> +0 .40Ó1(d 512 ) 2 0 ; 00> +0.5801(97/2 ) 20 ; 00> -0.1821(h11/2)20 ; 00> + 0'281 1(9712 , d3/2)2;12> -0 .22Ó1(d5/2)22 ; 12> Only amplitudes larger than 4 % are listed .

dependence of the calculated positive parity levels on the cluster-field coupling strength . It is seen that a strong coupling strength (ß - 0.16) reproduces the systematic compression of the low-lying levels in the I-isotopes (see fig. 12) as well 1291 and 127 1. These two as the 1, and i t ground-state crossing observed between states, which have the highest spectroscopic factors in all I isotopes, are in zeroorder approximation described by the 1{(g .,) 2 0, d.,t ) 1, 00> and l{(g,)3)1, 00> vectors, respectively . On the other hand, the increasing coupling strength necessary to describe the lighter I-isotopes reflects the larger collective character leading to the stronger configuration mixing. This fact is illustrated by table 9 where some calculated 2t wave functions for the lowest-lying levels in t I are listed . In the 11 state the reduction of thezero-phonon I {(91)20, d.1 ) 1, 00> component and the increase of the amplitudes of the one-phonon and zero-phonon cluster states of seniority-three 1(g-1)22, d t} j,12> and 1{(g.,)22, d t) J, 00) components, compared to the heaviest I-isotopes, is in agreement with the observed reduction of the spectroscopic factor . A similar result is expected for the 11 state since the amplitude of the 1{(g t)3} 1, 00) component is strongly attenuated while the 1{(9.,)22, dat}j, 00) component is increased due to the reduced difference between the q and E., single-particle energies . A much more rapid decrease in excitation energy has been observed experimentally for the I t state than for the other states . This fact can be explained by the increasing amplitude ofthe I {(91)20, Si) 1, 00> component with respect to the I {(g i) 2 0, dt} j,12>

PROTON STATES IN IODINE

331

2.5 % 2A n w 1.5 z w z 0 á 1.0 F Û X W

0.5 0 0

0.04

0.08

0.12

0.16

0.20

0

2.0 -V2"

Xro 1.5 cn

_ . . - . . - . ._ . .- . .- . .i . .u .

W z

~

.

w 1 .0 z

0

á X Oä W

0.0

2.0

1.5 E1/2 (MOV)

1.3

Fig. 17. (a) Calculated lowest-lying levels ( .1' 5 }) (using the three-particle-cluster vibrational-field coupling model) in dependence on the coupling strength (p). (b) Dependence of excitation energy of lowest-lying levels on the 81,2 single-particle energy . Parameters used in this calculation correspond to those used in the generation of the space configuration, i .e. 8,,2 = 0.0 MeV, 8,,2 = 0.50 MeV, 63/2 = 1.80 MeV, 811/2 = 1.55 MeV, G = 0.15 MeV, 8w = 1 .15 MeV and ß = 0.08.

A. SZANTO DE TOLEDO et al.

33 2

component and by the very strong sensitivity of this state to the s. single-particle energy that decreases very rapidly with decreasing A. This fact, illustrated in fig. 17b, has also been observed in the light Sb isotopes as) . In the theoretical level scheme presented in fig. 18 the use of the same value of e-, as in ref. a) for the generation of the configuration space leads to a shift of the I+ strength to higher excitation . The single-particle strength removed from the 11 and 1 1 states in 121 1 is mainly shifted to the states around 1 MeV excitation which show increasing amplitudes of the zero-phonon configurations 1{g.,)20 , dt) 1, 00> and 1{(gí) 2 0, d.1 } J, 00>. The large spectroscopic factor observed for the u1 state, being the lowest negativeparity level, is well reproduced by the calculations and is due to a strong 1{(g1) 2 0, h,~t}-, 00) component. The low excitation energy is not reproduced, however ; probably due to the space truncation and non-inclusion of octupole vibration modes that must be very important in the description of this state in very light I-isotopes . EXPERIMENT 2 2 2

ao3 .o .01 .03,0101 0 0=02

0 2

0 .09 0.0 .0-1

3/2t5/2 " 3,2".5/2" 3/2".5/2*

--~-

v

v

2

CD W Z W Z 0 Q U X W

1D

THEORY

0.ÓdAA3 z 0.

1n' 3/r.512 " 3/2t

512"

ó~ ~~ 13/- Z-

" 512 "

1V2-

0 .14î07 .11

Y25/2' Y2 4

0 2

0.12 0.03o .01

112' 3/2~5/2"

2

0.04.0.02

3/2t512 "

3 2 5

ó:

R. 24,Q49 0.51

-5/2! 3/2"

n/2*

.15 912-0

=--
ZC

1V2-

0.54 0 .12 0.30

Sj

0.10

5/2'

Z 7/2' 712 "

là:

0,00

5/21

007 We 021

3/2V27/2-

028

5/2"

Fig. 18 . Experimental and calculated level schemes and spectroscopic amplitudes for "I .

PROTON STATES IN IODINE

333

The low-lying collective I + and + states in 121I calculated by this model (see fig. 18) are mainly built up by the {(gí)22, d,} and {(g.,)3} clusters which are energetically very close and thus strongly mixed. These levels, at excitation energies of about I MeV, are of vibrational nature, and probably none of them can be identified with the 0.434 MeV and 0.529 MeV states which are the basis of the Al = 1 and AI = 2 rotational bands, respectively, and which are possibly of lh-2p nature . It can be seen from fig. 18 that in spite of the three-particle-cluster vibrationalfield model being able to describe the single-particle structure of the low-lying levels (E+ x 1 MeV) of 1211, levels at higher excitation energies are only poorly reproduced. This is due to the fact that including only the degrees of freedom described by two harmonic quadrupole phonons and the anharmonicity introduced by the explicit description of the two active protons in the Te core is insufficient in describing the deformed light iodine nuclei . The description of the widely open neutron valence shell must take into account the correlations induced via the N-N interaction as well as the anharmonicity introduced in the core description. The lowering of the 3 - state in the ligher Te isotopes indicates that higher multipolarity modes must also be taken into account. 6. Conclusion

The investigation of proton states in nuclei with Z > 50 by means of(a, t) reactions is shown to be an important tool for spectroscopy of orbitals of high angular momentum. Good agreement is obtained between the values of the transfered angular momentum extracted from the ratio da(3He, d)/da(a, t) and established values . The high sensitivity of this ratio to the transfered /-value makes the comparative study of ('He, d) and (a, t) reactions a very powerful complement for spectroscopy of higher spins. The good energy resolution obtained in the present work allowed us to identify several new states in the odd iodine isotopes . A comparison of the trends in the experimental level schemes with the predictions by the cluster-phonon coupling model shows that the single-particle structure, being the main characteristic feature in the heavier I-isotopes, is diluted in favour of strongly collective behaviour in the lighter I-isotopes, which is more complex than a simple harmonic quadrupole vibrator . The authors are indebted to Dr. W. Saathoff and Mrs. E. M. Szanto for their participation in part of this work and Mr. H. Dias for his contribution to the theoretical calculations .

33 4

A. SZANTO DE TOLEDO et aJ.

References A. Szanto de Toledo, M. N. Rao, N. Ueta and O. Sala, Phys . Rev. C16 (1977) 438 R. L. Auble, J. B. Ball and C. B. Fulmer, Phys . Rev. 169 (1968) 955 J. R. Lien, J. Gard, C. Lunde Nilsen, G. Lovhoiden and P. B. Vold, Nucl . Phys . A281 (1977) 443 A. Szanto de Toledo, M. N. Rao, O. Sala and F. Krmpotic, Phys. Rev. C16 (1977) 438 R. H. Price, D. G. Burke and M. W. Johns, Nucl. Phys . A17ó (1971) 338 J. S. Boyno and J. R. Huizenga, Phys . Rev. C6 (1972) 1411 K. A. Erb and W. S. Gray, Phys . Rev. C8 (1973) 347 D. A. Lewis, A. S. Broad and W. S. Gray, Phys . Rev. C10 (1974) 2286 L. K. Wagner, D. G. Burke, H. C. Cheung, P. Kleinheinz and R. K. Sheline, Nucl . Phys. A24ó (1975) 43 10) D. J. Horen, Nucl . Data Bó .(1971) 75 11) H. Schrader, R. Stippler and F. M(Innich, Nucl . Phys. A151 (1970) 331 12) F. Mfmnich, H. Kugler, H. Schrader and R. Stippler, Nucl . Phys . A179 (1972) 205 13) D. M. Gordon, M. Gai, A. K. Gaigalas, R. E. Shroy and D. P. Fossan, Phys. Lett . ó7B (1977) 161 14) U. Hagemann et al., CERN report 76-13 (1976) 397 ; Int. Symp. high-spin states and nuclear structure, Dresden (1977) p. 16 ; Nucl . Phys. A299 (1977) 292 15) F. S. Stephens, Rev. Mod. Phys. 47 (1975) 43 16) J. Meyer-ter-Vehn, Nucl . Phys . A249 (1975) 111 17) H. Toki and A. Faessler, Nucl . Phys . A253 (1975) 231 18) G. Álaga and V. Paar, Phys. Lett. ó1B (1976) 129 19) B. W. Renwick, B. Byrne, D. A. Eastham, P. D. Forsyth and D. G. E. Martin, Nucl . Phys. A209 (1973) 574 20) G. Lhersonneau, J. de Raedt, H. van de Voorde, H. Ooms, R. Haroutunian, E. Schoeters, R. E. Silverans and L. Vanneste, Phys. Rev. C12 (1975) 609 21) S. V. Jackson, W. B. Walters and R. A. Meyer, Phys . Rev. C11 (1975) 1323 22) L. G. Mann, W. B. Walters and R. A. Meyer, Phys. Rev. C14 (1976) 1141 23) A. Szanto de Toledo, H. V. Klapdor, H. Hafner, W. Saathoff, E. M. Szanto and M. Schrader, Phys . Rev. C17 (1978) 2253 24) P. D. Kunz, Univ. of Colorado, 1967 (unpublished) 25) R. H. Bassel, Phys . Rev. 149 (1966) 791 26) W. R. Hering, H. Becker, C. A. Wiedner and W. J. Thompson, Nucl . Phys. A151 (1970) 33 27) R. G. Markham and H. W. Fulbright, Phys. Rev. C9 (1974), 1633 .28) M. Matoba, I. Kumabe and E. Tak-saki, Nucl . Phys. A17ó (1971) 178 29) G. Hauser, R. LBhken, G. Nowicki, H. Rebel, G. Schatz, G. Schweimer and J. Specht, Nucl . Phys . A182 (1972) 1 30) B. H. Wildenthal, E. Newman and R. L. Auble, Phys . Rev. C3 (1971) 1199 31) C. M. Perey and F. G. Perey, Nucl. Data Tables 10 (1972) 539 32) H. V. Klapdor, H. Reiss, G. Rosner and M. Schrader, Phys. Lett . 49B (1974) 431 33) V. Paar, Nucl . Phys . A211 (1973) 29 34) R. Almar, O. Civitarese and F. Krmpotic, Phys . Rev. C8 (1973) 1518 35) S. Sen and B. K. Sinha, Phys. Lett. 31B (1970) 509 1) 2) 3) 4) 5) 6) 7) 8) 9)