Study of the level scheme of 117In via proton transfer reactions

Nuclear Physics Al83 (1972) 161-172; Not to be reproduced

by photoprint

@ North-Holland

or microfilm without

written permission

STUDY OF THE LEVEL SCHEME VL4 PROTON

Publishing

Co., Amsterdam from the publisher

OF “‘In

TRANSFER REACTIONS

S. HARAR t and R. N. HOROSHKO Nuclear Structure

Research Laboratory,

University

of Rochester,

Received 16 November

Rochester,

New York tt

1971

Abstract: The (3He, d) and (a, t) reactions on ii6Cd have been used to study levels in ii% up to 2.8 MeV excitation. The measurements were performed at the 3He and a-particle bombarding energies of 27 and 25.5 MeV, respectively, using a magnetic spectrograph. Deuteron angular distributions were compared with the distorted-wave Born approximation predictions to obtain angular momentum transfer and spectroscopic factors. Tritons were recorded at only three angles. Present results show significant configuration mixing of the proton wave function in the ‘i6Cd ground state. The low-lying positive-parity levels of “‘In are discussed in the framework of the particle core coupling model and the rotational model. E

NUCLEAR REACTION 116Cd(3He, d), E = 27 MeV; “%d(a, t), E = 25.5 MeV; measured u(E,, O), a(E,). “‘In deduced levels, J, rr, l,, . Spectroscopic factors. Enriched l16Cd taraet.

1. Introduction According to the simplest model, the nucleus I1 ‘In has one proton hole in the Z = 50 closed shell coupled to the ‘$n core. The ground state (e’) and the states at 315 keV ($-) and 588(3-) keV have been identified from previous studies ‘*‘) as proton hole states and their structure is represented mainly by a single hole in the lg,, 2p, or the 2p+ orbitals, respectively. Other investigations 3-5) have revealed the existence of positive-parity states in I1 ‘In at low excitation energies. From their radioactivity studies of ” ‘Cd, Backlin et al. “) have suggested that the levels at 660 keV (4’) and 748 keV (+’ or 4’) might be the start of the K = +’ [431] rotational band. Later, Pandharipande et al. “) have further suggested that the levels at 881 keV ($‘, +‘), 1249 keV (q+, 3’) and 1715 keV (s’, J$‘) might be other members of this band. The present (3He, d) and (a, t) investigations were undertaken to study in more detail the proton particle states in “‘In , to test the rotational band hypothesis noted above, and to identify the ground state configurations in the target nucleus, ‘16Cd. 2. Experimental procedure The (3He, d) measurement was performed at 27 MeV using the University of Rochester model MP Tandem accelerator. Isotopically enriched targets (97.2 % ” %d) 7 Permanent address: CEN Saclay, DPh-N/BE, France. tt Work supported by the National Science Foundation. 161

162

S. BARAR

AND R. N. NOROSHKO

163

“‘In LEVEL SCHEME

of 40 &g/cm2 thickness were prepared on 20 ~gl~rn’ carbon backings by vacuum evaporation techniques. Outgoing deuterons were momentum analyzed in the Enge split-pole spectrograph and recorded in 50 pm thick Kodak NTB emulsions which were covered with aluminium absorbers to eliminate triton tracks. Points on the angular distributions were measured at 11 angles from 7” to 50” lab. Normahzation was obtained from the elastic deuteron group observed with a thin NaI counter mounted in the scattering chamber at 45” to the beam. Absolute (3He, d) cross Optical-model

3He d P

170 101 “)

1.14 1.15 1.25

TABLE1 parameters used in the (3He, d) analysis

0.723 0.81 0.65

20 0 0

1.14 1.15 1.25

The optical potentials used have the form

u(r) = -W+e”)-l--i

[

W-W

$

1

(t+eX’)-I+

20 66.5 0

0 6

1.6 1.34

2 (pn,cJ rdr A!_

v,+,. i _d (1 +e”f-li*

0.81 0.68

0

where: x = (r-roA+)/a, 6 = 2Sjfi

x’ = (r-fOA+)/a’,

for spin 4,

6’ = S/n for spin 1. “) In a11cases, the depth of the well is adjusted for a bindingenergyequal to the experimental separation energy. The proton bound state wave function was calculated in a well of the form:

with a(l) = I

= -(1+-l)

for J = Z+* for J = I-*,

&,,. = 25 (coefficient of spin-orbit well).

sections were obtained by comparing the inelastic and elastic 3He cross sections at 24” lab. For this comparison, the deuterons and the 3He ions were detected simultaneously in the focal plane of the spectrograph using a position-sensitive detector (PSD) and a nuclear emulsion plate, respectively. At 24” a,,(DWBA) = 0.98 ~,i (Rutherford). Due mainly to the statistical errors in the inelastic evens and some uncertainty of the relative solid angles subtended by the plate and the PSD, the total uncert~nties in the absolute (3He, d) cross sections are believed to be about 20 %. A typical deuteron spectrum from the 116Cd(3He, d) reaction is shown in fig. 1A. Excitation energies are indicated for groups up to 2.8 MeV. The observed energy resolution was 20 keV FWHM. The “‘In level structure was also studied via the

S. HARAR AND R. N. HOROSHKO

I64

“%Zd(a, t)“‘In reaction at 25.5 MeV (fig. IB) with an energy resolution of 14 keV. Measurements of both (3He, d) and (CI,t) cross sections often provide complementary information on Z-transfers. ““Cd (3He,dlr’71n E=27 MeV

? 2

-3 32

5+ g ii7 zz= + + c

.-

33 -_

IO

1

I

t

I

I

I

I

IO

20

30

40

50

60

6,.,,

(degrees)

Fig. 2. DWBA predictions for transitions involving major orbits in the region 51 1 Z i 82. Calculations are for the 1’6Cd(3He, d) 1171nreactions at E3ac = 27 MeV, Q = 0.5 MeV and an excitation energy of 1.5 MeV.

3. The DWBA analysis The DWBA calculations were performed with the code DWUCK, using local and zero-range approximations. The optical-model parameters and the form of the potential for the “6Cd(3He, d) “‘In are shown in table 1. The present 3He parameters are those used by Conjeaud et al. “) in their analysis of the 18 MeV Sn(3He, d) data, and are slightly different from those used by Auble et al. ‘) in the analysis of the 25 MeV (3He, d) data on the Sn and Te isotopes, and in the ‘He elastic scattering of Gibson et al. “) at 37.7 and 43.7 MeV over a wide mass region. Variations of + 10 % in the 3He parameters were found to change the calculated absolute cross sections up to 20 % depending on the angular momentum transfer, however, the predicted an-

“‘In

LEVEL SCHEME

165

gular distributions changed only slightly. The deuteron optical model parameters were taken from Perey and Perey ‘). The wave functions of the transferred proton were calculated with a WoodsSaxon potential (table 1) with the depth adjusted to yield the proton binding energy equal to the experimental separation energy. It was found that a change in the bound state parameter r,, of + 10 % changed the magnitudes of all cross sections by about a factor of 2, but the relative cross sections changed by only 20 %. The shapes of the angular distributions were found to be insensitive to this parameter change. The theoretical angular distributions for the l1 6Cd(3He, d)“‘In reaction involving transitions to the major shells in this mass region, i.e., ~(1 = 0), d&l = 2), gi. (I = 4) and h,(l = 5) are shown in fig. 2. The cross sections corresponding to 1 = 4 transitions are much weaker than those for 1 = 0 or 2. Thus, a 5’ state lying within 30 keV of the $+, 3’ or 3’ states can easily be missed in the present (3He, d) measurement. To check further the possible existence of such doublets, the l1 %d (~1,t)i171n measurement was performed which favors high angular momentum transfers. This can be seen by comparing the yield to the ground state (I = 4) relative to the yield to the first two excited states (I = 1) in both the (3He, d) and (~1,t) reactions. Theoretical cross sections for the (CI,t) reaction were calculated at a few angles. Optical-model parameters for the a-particles were taken from McFadden and Satchler ’ “) and for the tritons, from Hafele et al. “). 4. Results 4.1. ANGULAR

MOMENTUM

TRANSFERS - SPINS AND PARITY ASSIGNMENTS

Angular distributions for the 22 deuteron groups observed up to 2.8 MeV excitation in the (3He, d) spectra are shown in fig. 3. Groups labelled 20(2.372 MeV), 21 (2.481 MeV) and 24(2.642 MeV) exhibit no identifiable angular distributions, presumably because they are not simple. Above 2.8 MeV excitation, the level density is too high to allow any detailed study with the present energy resolution. We now discuss the angular momentum transfer assignments suggested by the present results. Some spin and parity assignments are attempted where comparison with previous results is possible. 4.1.1. Levels l(g.s.), 2(0.315 MeV) and 3(0.588 MeV) have been previously assigned spins $+, _t- and +-, respectively, from the y-ray and the “sSn(d, 3He)‘1 71n measurements ‘, “). The present (3He, d) angular distributions for these states are reasonably well fitted with I = 4 and I = 1 transfers. 4.1.2. Level 4(0.655 MeV) has been assigned 3’ from the b-7 measurements 3s“). The angular distribution obtained for this level from the present investigation is in agreement with a d, proton transfer. 4.1.3. Group 5(0.746 MeV) was previously reported 3*“) as 3’ or 3’. The measured angular distribution exhibits a strong I = 0 dependence so a definite assignment of 3’ can be given. However, a comparison of the (3He, d) and (a, t) cross sections suggests

166

S. HARAR AND R. N. HOROSHKO “6Cd(3He.d)“71n E=27 MeV IOOE

ri/l,, 1.603 I:2

MeV

20 P = I

3/2

-

IO

I

200 50

/“+$r,,*

I

20

50

,A

1

100

10

50 ___r

!

19,

I696

Me” P:2

t 1

tq

e=0+4 20 /

IO

1

l,/ty, 1.774 I:2

:

i

MeV \

t-

100 50 20 1 IO’

J

100

20

I’

53 20 1

0

10

20 8,

30 ,.,.

40

50

(degrees)

60

!/

-5kTe-ce 0 8,,,(degrees)

-

0

IO

20 &,,

30

40

50

60

(degrees)

Fig. 3. Angular distributions of the observed “6Cd(3He, d)“‘In transitions. Error bars represent only statistical uncertainties and the curves are the DWBA fits.

‘171n LEVEL SCHEME

167

this group is a doublet. The second member should correspond to a high angular momentum (I = 4 or 5) and is probably J” = 3’ as suggested by the shell-model considerations. The separation energy of these two levels is less than 10 keV. The present f3He, d) angular distribution for the doublet has been fitted by a mixture of E = 0 (one part) and I = 4 (three parts) which gives a good agreement between experimental and theoretical results. Moreover the ratio of the (3He, d) cross section for this group relative to the (c(, t) cross section is consistent with the DWBA calculations if this I-mixture is used. 4.1.4. The y-ray decay scheme of li71n obtained from the 8-y measurements 3- “) revealed a possible 860-881 keV doublet and suggested a J” value of 3’ or 3” for the 881 keV member. In the present (3He, d) measurement, the angular distribution for level 6(0.877 MeV) is well fitted with an 1 = 2 transfer; so a J” = 3’ assignment is consistent with the y-ray measurements. Fig. 1B shows that within the experimental resolution of 14 keV obtained with the (g, t) reaction, no additional state is excited. 4.1.5. Level 13(1.883 MeV) shows 1 = 0 angular distribution, and is unambiguously assigned spin J” = $’ . 4.1.6. Level 19(2.308 MeV) has an I = 4 angular distribution. The spin can be 7 + 2 or 8+, however, since this state is not excited by “‘*Sn(d, 3He) reaction “) it is tentatively assigned 4’. 4.1.7. Croup 22(2.525 MeV) is fairly well fitted with an I = 0 transfer indicative of a +f level. Nevertheless the large strength observed in the (~1,t) reaction for this group suggests the existence of a second level with a high spin value (5’ or Js-). 4.1.8. Most other observed levels up to 2.75 MeV excitation have I = 2 angular distributions which restrict the spin values to either 3’ or 3’. No further restrictions are possible from other published data. 4.2. SPECTROSCOPIC

FACTORS

Extraction of absolute spectroscopic factors is very hazardous because of uncertain ties in the absolute cross sections and also due to the fact that the theoretical cross sections are subject to large uncertainties arising principally from unce~ainties in the optical model and in the bound state well parameters, discussed in sect. 3. Relative spectroscopic factors are much less sensitive to these uncertainties. In stripping reaction, the sum of all the spectroscopic factor strengths for a particular orbital provides a measure of the non-occupation probability of that orbital in the target ground state. If we assume that, for the low-lying states, i16Cd may be represented as two proton holes in the Z = 50 core distributed in the lg,, 2p,, 2pt and If+ orbitals, then for the 1”6Cd(3He, d) reaction, the sum-rule limit is

where Si are the spectroscopic factors and index n labels each state with spin j corresponding to the above orbitals. In the present (3He, d) measurement, only three

168

S. HARAR AND R. N. HOROSHKO TABLE 2 Summary of results obtained from the 116Cd(3He, d)“‘In

Level number

Excitation energy (MeV) “)

$

(B,,, = 24”) ‘)

I

reaction

J” ‘)

(2j-Fl)C’S

@b/sr) 0

0.315 0.588 0.655 0.746 6 I 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

0.877 1.048 1.360 1.603 1.653 1.696 1.774 1.883 2.005 2.047 2.159 2.223 2.255 2.308 2.372 2.481 2.525 2.560 2.642 2.755

48 15 35 77 165

4 1 1 2 0+4

I .05 &* + 0.28

320 20 15 160 20 17 9 40 68 27 20 40 24 54

2 2 2 2 2 2 2 0 2 2 2 2 2 4

3” + 3.40 2.76 0.26,0.18 0.21, 0.16 2.30, 1.70 0.30,0.22 0.21,0.16 0.18,0.14 0.21 1.0, 0.76 0.31, 0.24 0.31.0.24 0.48,0.36 0*30,0.22 2.10

44 42

0+(4,5) 2

72

1.37 0.29 0.34

P+, Q’

g+ + < 0.12 0.64,0.47

rH+.P’

0.80,0.71

il*+G$” or -9-l

2

“) Estimated errors in the excitation energies are 115 keV. “) Uncertainties on absolute value of cross sections are about 20 %. “) Spin assignments are discussed in sect. 4. TABLE

Summed strength (2j+l)C2S

s. p. level

“) See discussion in subsect. 4.2.

3

for levels in 11% up to 2.8 MeV excitation Experimental strengths “)

Sum-rule limit

1.37 0.28 0.35

2

9.3 or 11

10

0.61 5.5

2 8 12

“‘In

LEVEL SCHEME

169

TABLET

Shell-model components

A, in the l16Cd ground state wave function

Configuration

IA,1

(lgq);:

0.83

(2Pt_)Ol

0.37

(2P&f

0.42

3.0

2.5

5

2.0

S 6 & 5 .-: z .:: w

3/2*.5/2*-

2.755

-

2.642

3/2*.5/2+112*+v/z++,OR ,,,2-,-

2.560 2.525 2.481

7/z* 3/z* 5/z* 3/2*:5/2*3/2*.5/z*-

2.372 2.308 2.253 2.223 2.159

3/2*5/Z* 3/2':5/2*-

2.047 2.005

l/2'-

1.883

3/2'.5/2'-

1.774

3/2*5/Z+ 3/2*,5/2*3/2':5/2*-

1.696 1.653 1.603

3/2+.5/2*-

1.360

-

2.457 2.400

13/Z-.5/2-) =

2.310

-

2.094

-

1.996 1.972

l/2*.3/2*-

1.890

11/2*.9/2* -

1.715

1.5

1’/2’.9/2’

3/2*.5/2+-

3/2*,5/z*

I.048

i/2++

-

0.877

7/z* ~

-

I.249

f (13/Z I -

1.0

0.746

‘l/2*-

1.430

9/t*

-

1.069 1.056

7/2*.5/2*-

0.950 0.88, 0.860

112:3/z+ -

0.748

3/2*.5/2*3% -

0.655 0.588

3/2'-

0.660

3/2- -

0.905

3/z- -

0.587

1/z- -

0.315

1/z--

0.325

1/z--

0.3I5

9/Z'-

0

9/z*-

0

9/z*-

0

1.44

-

I.22

13/P's/z* -

1.04 1.02

7/z+ -

0.82

0.5

0

“%dt3He,d)“‘ln

“*Sn(d

,3He)“71n

Levels the

(a)

(b)

Observed

Decoy

(cl

of

in

Theory

‘17Cd

(d)

Fig. 4. Level scheme of “‘In observed via (a) the present 1’6Cd(3He, d)“‘In reaction, (b) the “*Sn(d, 3He)1171n reaction 2), (c) deduced from the y-ray decay of “‘In [refs. 5-5)] and (d) calculated 13) in the weak coupling approximation.

170

S. HARAR

AND

R. N. HOROSHKO

such states, i.e. proton hole states, were observed in a region up to 2.8 MeV excitation. These states are the ground state (e”), the 315 keV (p-) and the 588 keV ($-) levels. This result is consistent with the “*Sn(d, 3He)1’71n measurement where also only these three hole states were observed “)_ The extracted spectroscopic factors for the 116Cd(3He d) reaction are summarized in table 2. Values shown were normalized using relation (1). To be consistent, no sum-rule limit should exceed (2j+ 1) for each of the other higher-lying orbitals, i.e. 2d,, 2d,, Ig+ 3s, and Ih,. This is actually the case as shown in table 3. For the I = 2 transitions it is impossible to distinguish between the 2d, and the 2d, orbitals and consequently no unique I = 2 sum rule value can be given. However, limits can be obtained by assuming that, in the region from 1 to 2.8 MeV excitation energy, all 1 = 2 states are alternately either 3’ or 3’. This procedure yields a lower limit of 9.3 and an upper limit of 11.0 for the sum rule, which is in a good agreement with the theoretical value of 10. 5. The ground state wave function of ‘16Cd Considering the 48 protons of the r16Cd nucleus as 2 holes in the closed 2 = 50 proton core, the proton part of the r1 %YJdground state wave function may be written as: d,G.S. = A&lg&! -I-A,(2p,),;2 +A,(2p&. The fact that experimentally we observe (3He, d) transitions to the lgg, 2p, and 2p, orbitals, supports this shell-model picture. The coefficients Aj are related to the spectroscopic factors by lAjl = Ji< are given in table 4 and indicate that the proton Fermi surface is not sharp.

Values

6. Discussion The level’schemes of li ‘In based on the present and previous measurements are presented in fig. 4. The nucleus ‘“‘In has one proton hole and a number of neutrons outside the N = 50 core. One may expect that the low-lying excited states should be the proton hole states and should be well described by the spherical shell model. This is apparently the case for the ground state (f’), the 315 keV (4-) and the 588 keV (SW) states which are the only levels observed with the “*Sn(d, 3He)‘17.1n reaction ‘) (fig. 4B). Since ri6Cd has two proton holes in the Z = 50 shell the (3He, d) reaction on this nucleus may also be expected to excite levels in “‘In with 2h-lp configurations. Positive-parity states are observed in the (3He, d) reaction at 655 keV (j+), 746 keV (+’ and lz_‘) and at 877 keV (s’). The corresponding strengths are, respectively, 25 %, 14 %, 42 % and 46 % of the single-particle intensities (table 2) indicating that these states are only in part 2h-lp states. Mixing may occur with configurations obtained by coupling one particle in the lg,, 2d,, 2d,, 3s+ or 1% orbital with one-

“‘In

LEVEL SCHEME

171

or two-phonon states of the l1 %d core, which are at 513 keV and 1.220 MeV, respectively. The core-particle coupling is probably strong since the d,, d, and s+ strengths are spread out over 18 levels up to 2.8 MeV excitation energy, most of then having only few percent of the total single-particle intensities. Table 3 shows the summed strengths (2.Z+ l)C’S, with the normalization described in subsect. 4.2. The d, and d, single-particle intensities are found to be in good agreement with the sum rule limit value of 10. The s+ strength amounts to approximately one third of the expected total strength. Most of the lgz strength is observed up to 2.8 MeV excitation energy. Only a small percentage of the lh, strength might be located below 2.8 MeV excitation. Comparison

of experimental

spectroscopic

TABLE5 factors and the C,,2 coefficients of the Nilsson model 16)

Excitation energy (MeV)

(C,,2h! normalized

B =O.l

/3 = 0.2

0.655 0.746 0.746 0.877 not observed

0.14 0.037 0.45 0.37 0 0.997

0.084 0.038 0.66 0.20 0.01 0.982

0.20 0.14 0.36 0.25 0.05 0.950

3+

sum

(c,,2h.or

The (jHe, d) reaction on 1’8Sn which has the same number of neutrons as ll’%d and in addition has a closed proion core, shows that the strength for each of the d,, g;, h,, d, and s+ orbitals is concentrated mostly in one level 6*12). The spectrum observed in “‘In is quite different; strengths are spread out over many levels. This indicates clearly the importance of the residual interaction in r16Cd due to the two proton holes. BHcklin et al. “) found a strong B(E2) transition (100 single-particle units) for the 746 (+‘) -+ 655 (3’) y-ray transition. They suggested that these states might represent the start of the K = t_’ [431] rotational band. Using the experimental B(E2) value to deduce a deformation parameter p = 0.2, assuming that the inertial parameter h2/2Z is 28 keV and that the decoupling parameter a is equal to -2.2. Pandharipande et al. “) have calculated the spin sequence of this band to be 3’ (660 keV), 4’ (760 keV), s’ (872 keV), 3’ (1108 keV) and $+ (1670 keV). Pandharipande et al. “) observed a level at 881 keV with J” = f’ or 2’ and in order to support the rotational band hypothesis, they have assumed that this level is the 3’ state. However, the present measurements show that the 881 keV level is either a 3’ or 3’ and definitely not s’ . The J” value of 5 + is in agreement with both measurements. Moreover, the lowest 3’ state has been located at 0.746 MeV by Gregory and Johns who have calculated’ “) the excitation energies of the +’ [431] band members using 14 keV for the inertial parameter and -2.7 for the decoupling parameter. They found the following ex-

172

S. HARAR AND R. N. HOROSHKO

citation energies: 660 keV (s’), 752 keV (g’), 731 keV (+‘), 919 keV (5’). A good test of the existence of a rotational band can be made by comparing the experimental spectroscopic factors and the Nilsson coefficients, CT. Such comparison is made in table 5 and shows fairly good agreement for a deformation fi = 0.1. Similar results have been obtained by Thuriere ’ “) in the study of the l1 4Cd(3He, d) ” sin reaction. Nevertheless, more sophisticated calculations are necessary to explain the present data. States at 860, 950, 1053, 1068, 1249 (y’ or $‘) and 1430 keV were observed in the radioactivity studies 4, “) an d were found to decay primarily to the ground state. A tentative interpretation of these states as members of a multiplet arising from coupling of the 2+ phonon state of “*Sn to the ge proton hole has been made by Pandharipande 4*i ‘). In th e p resent (3He, d) measurement these states are not excited, or at most very weakly for the 1048 keV level, which is consistent and lends support to the weak coupling interpretation noted above. References 1) V. R. Pandharipande 2) 3) 4) 5)

6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16)

et aZ., Phys. Rev. 143 (1966) 740 M. Conjeaud, S. Harar and E. Thuriere, Nucl. Phys. Al29 (1969) 10 A. Backlin, B. Fogelberg and S. G. Malmskog, Nucl. Phys. A96 (1967) 539 V. R. Pandharipande et al., Nucl. Phys. A109 (1968) 81 R. P. Sharma, K. P. Gopinathan and S. R. Amety, Phys. Rev. 134 (1964) B730; R. V. Mancuso and R. G. Arns, Nucl. Phys. 68 (1965) 504; R. Moret, J. de Phys. 30 (1969) 501 M. Conjeaud, S. Harar and Y. Cassagnou, Nucl. Phys. All7 (1968) 449 R. L. Auble, J. B. Ball and C. B. Fulmer, Phys. Rev. 169 (1968) 955 E. F. Gibson et al., Phys. Rev. 155 (1967) 1194 C. M. Perey and F. G. Perey, Phys. Rev. 132 (1963) 755 L. McFadden and G. R. Satchler, Nucl. Phys. A84 (1966) 177 J. C. Hafele, E. R. Flynn and A. G. Blair, Phys. Rev. 155 (1967) 1238 T. Ishimatsu er al., Nucl. Phys. A104 (1967) 481 V. R. Pandharipande, Nucl. Phys. Al00 (1967) 449 P. R. Gregory and M. W. Johns, private communication E. Thuriere, Thesis, Saclay, 1970 A. Faessler et al., Phys. Rev. 148 (1966) 1003