Level structure of 90Mo via the 92Mo(p, t)90Mo reaction

Nuclear Physics A192 (1972) 442-448;

@ North-Holland Publishing Co., Amsterdam

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

LEVEL STRUCTURE

OF 9oMo VIA THE 92Mo@, t)90Mo REACTION

D. H. YOUNGBLOOD and R. L. KOZUB Cyclotron Institute, Texas A & M University t, College Station, Texas 77843 Received 24 April 1972 Abstract: Twenty-two levels in gOMo were identified using the (p, t) reaction on g2M~ at 39 MeV bombarding energy. Angular distributions were obtained for 12 levels and are compared with distorted-wave Born approximation calculations. Definite spin-parity assignments were made for five previously unassigned levels. Only one very weak 0” excited state was observed. The results are compared to similar studies of *4Kr and 88Zr. E

NUCLEAR

REACTIONS g2Mo(p, t), E = 39 MeV; measured o(E,, 13). gOMo deduced levels, J, z, L.

1. Introduction

The structure of nuclei in the region around the closed N = 50 neutron shell has received extensive study. When this work began, however, no excited levels of the N = 48 nucleus “MO were known. Ball et al. ‘) had studied the “Zr(p, t)**Zr reaction and observed two excited O+ levels in 88Zr with strengths comparable to other excited states. The strong excitation of these levels was attributed to rearrangement of the proton configuration between the target and residual nuclei. Similar strengths for excited O+ levels have been observed in 84Kr with the (p, t) reaction ‘). Moalem et al. “) recently reported a study of the levels of “MO with the (p, t) reaction indicating one possible excited O+ state. We have studied the ‘*Mo(p, t)goMo reaction at 39 MeV bombarding energy, initially to locate the excited levels of ‘OMo and to look for excited Of states. We report here 5 new spin-parity assignments and excitation energies for 9 previously unobserved levels. 2. Experimental procedure and results

The experimental details are similar to those described earlier “). A 38.6 MeV proton beam from the Texas A & M cyclotron was used to bombard a 1.10 mg/cm* self-supporting MO foil enriched to 98.3 % in ‘*MO. The outgoing tritons were detected by two AE- E surface-barrier detector telescopes spaced at a constant angular interval of 10”. Each telescope consisted of a 500 pm AE, 2 mm E and a 1 mm detector in anti-coincidence with AE and E to block pulses due to elastically scattered protons. Proton elastic scattering data were also taken using a telescope containing silicon t Supported in part by the US Atomic Energy Commission and the National Science Foundation. 442

*OMo LEVELS

443

detectors of 8 mm combined thickness. A detector fixed at 30” was used to monitor the current integrator. Triton pulses were selected using power-law identifier circuits for each telescope, and the total energy (E+dE) pulses were routed into analog-to-digi~l converters interfaced to the IBM 7094 computer. The data were reduced on-line to absolute, c.m. cross sections with the aid of the display oscilloscope. A typical triton spectrum is shown in fig. 1. The overall resolution is approximately 45 keV FWHM. An energy 120

I

I

I

1

I

I

I

384

448

512

576

‘I

I

I

768

832

I

14

0

260 W F

ill&ii 120

192

256

320

CHANNEL

640

704

896

NUMBER

Fig. 1. Triton spectrum for the g2Mo(p, tjgoMo reaction taken at a lab angle of 25.1’.

calibration was obtained from the (p, t) reaction on ‘eNi, 66Zn, 13C, and 16G, and the energies of 22 levels in g*Mo were measured (table I). Angular distributions were measured for 14 levels for laboratory angles between 7.5” and 65” (figs. 2 and 3) with an absolute normalisation uncertainty of about 10 %. A Gaussian peak-fitting computer routine was used to separate closely spaced groups. The data were collected in three different experimental runs. Selected angles were repeated each time, and the cross sections were reproduced to within the statistical error in each case. 3. Analysis Distorted-wave Born appro~mation ~l~ulations were performed using the code DWIJCK {ref. ‘)I, which calculates the two-nucleon form factor by the method of Bayman and Kallio “). Since wave functions for “MO are not available, the cal-

D. H. YOUNGBLOOD

444

AND

R. L. KOZUB

TABLE 1 Results of the gzMo(p, t)goMo reaction compared with those of Moalem ef al.

No.

Moslem ef al. ‘)

Presentwork J”

%u *)

J=

640 x @xvucK (mb/sr) 0 1 2 3 4 5 6 I 8 9 10 11 12 13 14 15 16 17 18 19 20 21

0 950* 5 1890& 8 1997& 8 2437*10 2542-+10 2612flO 2858&10 3083f15 3169*15 3337*15 3521f15 3672flS 3741*20 3863&20 3966 f20 4058 &20 4259*15 4419f25 4548 &25 4621&25 4715*15

0+ 2+ (20;+) 34+ 2+ (F) 2+

0.040 0.25 0.16 0.11 0.12

(4+)

0.025

0.16

2+

0.025

0.15

‘) 15” unless indicated otherwise. ‘) Ref. 3).

b) 20”.

0 960 1900 2010 2450 2550 2620 2860 3100 3170 3320 3520

1 0.38 0.006

2.1 0.55 0.01 0.023 0.075 b) 0.074 0.025 0.052 ‘) 0.02 b) 0.015 0.007 0.012 0.008

‘) 34”.

o+

(& (2+, 4+) (23q+) (2+) 5-

4200

4+

*) Ground state normalised to unity.

TABLE 2 Potential parameters for DWBA

calculations

Particle

kc.. (ML)

P “) t b, n ‘) Ref. ‘).

(MC)

52.2 170.2

5.84 18.8

$2) 12.56

(f:)

(f:)

1.12 1.16 1.30

0.78 0.74 0.65

(f:) 1.32 1.52

(f:) 0.57 0.75

vI.s (MeV) 6.2

rrs (fm)

(z

0.98

0.75

25

b, Ref. s).

culations were made assuming that the even-parity levels were formed by picking up two lg+ neutrons and that the odd-parity levels were formed by picking up a l& and a 2pa neutron. The binding energy for each single-neutron orbit was taken to be one-half the two-neutron separation energy. Angular distributions calculated using the optical parameters listed in table 2 are shown with the data in figs. 2 and 3. The proton optical parameters are the r. = 1.12 set of Becchetti and Greenlees ‘),

90Mo LEVELS

445

obtained by extensive analysis of available elastic scattering and polarization data over a wide range of target nuclei and bombarding energies. Triton optical parameters obtained by Flynn “) for 20 MeV triton scattering from “Zr were used in the exit channel. (The triton energies were between 20 and 25 MeV.) Calculations were performed with bound-state radius parameters of 1.20, 1.25 and 1.30 fm, and the best fits to the data were obtained with the largest radius. DW3A calculations were also performed with the Fkcchetti and Greenlees r. = 1.22 proton parameter set and with parameters derived from our own elastic scattering data, but the quality of fits to the data were not improved. Also, several other sets of triton parameters were tried, in-

Fig. 2. Triton anpuIar distributions for gOMo levels below 2.9 MeV. The curves are DWBA predictions. The errors indicated are statistical only.

D. H. YOUNGBLOOD

446

AND

R. L. KOZUB

“Mo(pt)‘“Mo

-

mb

1

3169 MeV _

_

Bc.m.. (Deg.1 Fig. 3. Triton

angular

distributions for 9oMo levels above 2.9 MeV. The curves are DWBA predictions. The errors indicated are statistical only.

eluding a set of 3He parameters, but still no improvements in the fits were obtained. Our calculations at 39 MeV bombarding energy were more sensitive to proton optical parameters, in contrast to the results of Ball et ad.I), who found the ,angular distributions were quite sensitive to the triton parameters at 30 MeV proton energy. The angular distributions for the ground and 1.89 MeV states are best fit by an L = 0 DWBA curve (fig. 2). The fit for the 1.89 MeV level is poor for angles greater than 30”, but no other L-transfer would reproduce the rapid decrease in cross section between 20 and 30”. Moslem et al. “) gave a possible O+ assignment for this level, while Taketani et al. lo) do not report observing it in their search for excited Of levels in the MO isotopes. The 0.950, 2.612, 3.169 and 4.715 MeV levels all have similar angular distributions (figs. 2 and 3) and are assigned..P = 2”. The first two of these were likewise assigned by Moalem et al. “). In addition, the group at 1.997 MeV has a shape which might be explained by a sum of L = 2 and L = 4 transfers, in~cating the possibility of an unresolved doublet. The two levels would have to be separated by less than 20 keV, how-

90Mo LEVELS

447

ever, as this group was not noticeably broader than nearby groups. The fits to the 2+ levels are rather poor as there is considerably less structure in the data than in the calculations. A similar problem was encountered in the 38 MeV work of Ball et al. “) for the N = 50 “Zr target nucleus, although satisfactory L = 2 fits were obtained for the other Zr isotopes. The 2.542 MeV level appears to be a 4+ state, although the DWBA fit is not very good. The group at 4.259 MeV appears to contain contributions from other levels and, while it was assigned 4+ by Maolem et al. 3), our data (with better resolution) is not convincing. The 2.437 MeV level was best fit with L = 3 curve, in agreement with the 3- assignment of Moalem et al. “). An L = 5 curve reproduces the angular distribution very well for the 2.858 MeV level, which was assigned JR = 5- by ref. “). The distribution for the level at 3.080 MeV is shown with an L = 3 curve, but the poor quality of the data for this weak level prevents a definite assignment, and an L = 0 assignment cannot be ruled out. 4. Summary and conclusions The level structure of “MO is compared with those deduced from the (p, t) reaction to other doubly even, N = 48 nuclei in fig. 4. The 84Kr data is from ref. 2), and the **Zr data from ref. ‘). Also shown is the ratio of the experimental (p, t) cross section

‘($*;I; (5:2+) (\:-$I 223-1

0.12 4+

3.225 3.32 3.085 2.768 yoy

2.095

$gg

2.675 2.743

0.02ti'

2.570 2.446

8:;:2;

%$I

I.897 1.835

0.28

2*

I.0 o+

l 820 0.09

o+

1.517

0.34

2+

I.057

I.0

o+

0.0

0.882

0.0

0.122+ (3) 0.115'

3.337 3.169 3.083 2.612 2.658

0104 gj 24 3-

2.542 2.437

(2?4+) 0.006 O+

0.38

2+

Ix) o+

1.997 1.890

0.950

0.0

Fig. 4. A comparison of the level structure deduced with (p, t) reactions for doubly even N = 48 nuclei. The excitation energies are given in MeV, and spin-parityassignmentsare indicated. The ratios aer,,/%vBA (normalised to unity for ground states) are given at the left of each level. The *%r and * *Zr results are from refs. 2**), respectively.

448

D. H. YOUNGBLOOD

AND R. L. KOZUB

to the DWBA cross section normalised to unity for the ground state. Calculations were performed with DWUCK for the data of refs. 2S‘) with the same form-factor parameters used in the present work. The ratios b,,,&,, for the **Zr and 84Kr ground states were a factor of 1.7 and 3.7 larger, respectively, than for 90Mo. The only excited level with a definite O+ assignment is extremely weak, about &$h of the ground state strength, where as considerably more strength is observed in both 84Kr and **Zr. These effects can be interpreted in terms of differences in the ground state proton configurations of the N = 48 and N = 50 isotopes of a given element. It appears that the 90Mo and 92Mo ground states have essentially the same configuration, whereas larger differences exist between the 88Zr-90Zr and 84Kr-86Kr pairs, thereby causing more splitting of the O+ strength. It should be noted, however, that the (p, t) cross sections can be quite sensitive to admixtures of different neutron configurations, and more meaningful comparisons could be made if model wave functions were available for each of the nuclei. The relative strengths of the other levels observed are similar to corresponding levels in Kr and Zr, with no obvious systematic differences. References 1) J. B. Ball, R. L. Auble, R. M. Drisko and P. G. Roos, Phys. Rev. 177 (1969) 1699 2) 3) 4) 5) 6) 7) 8) 9) 10)

E. C. May and M. J. Levine, Bull. Am. Phys. Sot. 17 (1972) 50 A. Moalem, M. A. Moinester, J. Alster, Y. DuPont and M. Chabre, Phys. Lett. 34B (1971) 392 R. L. Kozub and D. H. Youngblood, Phys. Rev. C4 (1971) 535 P. D. Kunz, University of Colorado, unpublished B. F. Bayman and A. Kallio, Phys. Rev. 156 (1967) 1121 F. D. Becchetti, Jr., and G. W. Greenlees, Phys. Rev. 182 (1969) 1190 E. R. Flynn, D. D. Armstrong, J. G. Beery and A. G. Blair, Phys. Rev. 182 (1969) 1113 J. B. Ball, R. L. Auble and P. G. Roos, Phys. Rev. C4 (1971) 196 H. Taketani, M. Ada&i, M. Ogawa, K. Ashibe and T. Hattori, Phys. Rev. Lett. 27 (1971) 520