Nuclear Physics A250 (1975) 211--220; ( ~ North.Holland Publishing Co., Amsterdam

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

YRAST CASCADE IN e°Ni

H. J. KIM

Oak Ridge National Laboratory t, Oak Ridge, Tennessee 37830 and

CEN Saclay

and

R. BALLINI, B. DELAUNAY, J. DELAUNAY, J. P. F O U A N and M. PICHEVAR tt

Ddpartement de Physique Nucl~aire, CEN Saclay, BP 2, 91190, Gif-sur-Yvette, France

Received 1 April 1975

AlWtraet: Yrast levels of eONi were investigated via the study of in-beam y-rays induced by 15-25 MeV u-particles on SSNi, 26--48 MeV 12C ions on S°Cr and 30-60 MeV l e o ions on 4eTi. The compound nucleus formed by these target-projectile combinations is e2Zn, and its decay by two-proton emission populates yrast levels of e°Ni. The ordering and decay modes of the yrast levels were determined from the analyses of in-beam y-ray angular distribution and Y'7 coincidence measurements. The new levels established are at 4.262, 5.345 and 6.807 MeV. These together with the known 2x+(1.332 MeV) and 41+(2.505 MeV) levels constitute the yrast cascade. The spin assignments based on the present study are 6, 7, 9 for the 4.262, 5.345 and 6.807 MeV levels, respectively. The excitation functions for the yrast y-rays from the S°Cr(12C, 2p)e°Ni reaction show peaks near 33 MeV incident energy.

NUCLEAR REACTIONS SSNi(% 2py), E = 15-25 MeV; 4eTi(xeO, 2p7), E = 30-60 MeV; measured ~(E,E~,), 77-coin. SOCr(t2C, 21D,), E = 26--48 MeV;

measured or(E, Ey, O) 79,-coin. 6eNi deduced levels, J.

1. Introduction

Even with the restriction that the four extra-core neutrons outside the 5eNi core be confined to p , , p~ and f , shell-model orbits, one expects relatively low-lying J -- 6 states in 6°Ni [ref. 1)]. Although more than one hundred states below 7 MeV excita- tion have been reported 2) for this interesting nucleus, the highest spin value thus far established is J ffi 4. Furthermore, many shell configurations can yield low-spin states, but possible configurations for high-spin states are very much restricted. For example, to have J ~ 7 it is necessary to include the g~ orbit or open the core. These considera- tions make a search for high-spin states very interesting.

A very expedient experimental method for populating high-spin states is the study of in-beam 7-rays induced by heavy-ion compound-nuclear reactions. This method offers the following interesting features for studying high-spin states 3):

t Operated by Union Carbide Corporation for the ERDA. tt On leave from Nuclear Institute (Teheran).

211

212 H.J. K:IM et aL

(a) high selectivity of specific residual nucleus (~°Ni for the present case) at appropriate bombarding energy for properly selected target plus projectile combina- tion;

(b) the large amount of angular momentum brought in by heavy ions makes populating high-spin states possible;

(c) the high degree of nuclear spin alignment for the residual states, resulting from the compound-nuclear process, would be manifested in the characteristic angular distributions of y-rays from these residual states.

We investigated high-spin states in 6°Ni via the 5SNi(~, 2py)6°Ni, 5°Cr(t2C, 2py) 6°Ni and 46Ti(160, 2py)6°Ni reactions. A preliminary account of this investigation was given previously 4).

2. Experimental details sad results

A self-supporting 58Ni target (~ I mg/cm 2) and thin targets ( ~ 250/~g/cm 2) of 5°Cr and 4#Ti evaporated on thick Ta (0.2 ram) backings were bombarded by 15-25 MeV ~-particles, 26-48 MeV 12C ions and 30-60 MeV 1~O ions, respectively, accelerated by the Saclay FN tandem. All targets wese isotopically enriched (_~ 99 ~o). Two coaxial G-e(Li) detectors (40 and 80 cm3), having ~ 2.7 keV resolution at 1.33 MeV, and standard electronics were used for the y-ray spectroscopy, singles and y-y coincidences.

Relatively high Coulomb barriers for the 50Cr~ t. 12 C and "6Ti + ~ sO combinations allowed the use of the Ta backed targets (Ta backing being the beam stop) which in turn facilitated 0 - -0 ° measurements relative to the beam direction, but for the 58Ni + ~ combination the need for more involved beam-dump and associated shielding did not allow 0 = 0 ° measurements. The energy and efficiency calibrations were effected by S~Co, 6°Co and l~2Eu sources. The known y-rays from the in-beam production of 6°Cu and the Coulomb excitation of ~S~Ta were also useful. The computer codes SAMPO 5) and TIZZY 6) were extensively used to obtain the energy and intensity of relevant y-rays. The estimated precision of our energy measure- ments is+ 1 keV.

2.1. CHOICE OF REACTION AND BOMBARDING ENERGY

The selective production of 6ONi nuclei, as ascertained by the yield of the 1173 keV (47 -* 2 +) y-rays, in preference to the others and experimental convenience were the main considerations for choosing the target-projectile combination and energy for performing the extensive singles and Y-7 coincidence measurements. Excitation func- tions taken for this purpose (in 2 MeV steps) indicated that the selectivity is the best for the SSNi + • combination. However, the need for the 0 ° measurements, which are very important as explained later, dictated that we choose the S°Cr+ 12C combina- tion, the second best. A typical singles spectrum is shown in fig. 1. The excitation function for the 1173 keV y-ray from the 5°Cr(lZC, 2py)6°Ni reaction is shown in

YRAST CASCADE IN 6°Ni 213

E (key) lOOO.

* , J , . ,

s ~ ® ,", $ , •

' ~ i i

~5

g o ° 2 .

1 0 3 " aCPlUC~2PlmNI ' I l 1 3 3 N O V ~ = : 5 ~ 1.

gO0. lttO0. CHANNELS

~ 1 0 0 .

!

1800.

Fig. I. In-beam )'-ray singles spectrum for 33 MeV 12C ion bombardment of a thin 5°Cr target. Gamma rays from the 5eCr(12C, 2pT)eONi reactions are identified by their energies (in keV) and those from the SOCr(12C, 2pny)SgNi reactions are identified by plus symbols. The peaks labeled

~eCr and 2ONe are from the inelastic and 12C(~2C, e,y) reactions, respectively.

> . I X

t~ z t,J

~100

. J

50Cp(12Co2p~)60Ni

g (MeV) Fig. 2. Excitation function for the 1172 keY, 41 + -* 2s + ),-ray from the S°Cr(12C, 2pT)e°Ni reac- tions. The incident energy corresponding to the Coulomb barrier is indicated by an arrow marked Bc.

fig. 2. The yield is the best near 33 MeV incident energy, and the main body of our data were obtained via the S°Cr(12C, 2p?)e°Ni reaction at 33 MeV.

214 H . J . KIM e t al.

2.2. TWO-PARAMETER 7"Y COINCIDENCE MEASUREMENTS

Having settled on the choice of reaction and energy, we performed 7-3' coincidence measurements using the two detectors. Two distinct purposes for these measurements were firstly to construct the level and decay scheme and secondly to obtain limited (two-angle) triple-angular-correlation data. The latter purpose dictated that the detectors be at asymmetric angles (0 # 0') and sufficient distances from the target so that the attenuations caused by the detector size be not too severe. They were placed at 0 = 0 °, 0' -- 90 ° and about 8 cm away from the target.

Coincidences between the two detectors were acquired event by event and a two

•10! 1172 gate 1462 (9--7)

1083 1 3 3 2 1 7 5 7

00 . . . . 'aa~dt~Jl-.~r- -

1172 I '1332 gate t083(746) I

I I ~ 757

~ • , . . . . i . . . . i . . . . i . . . . ' 1 . . . . i . . . . i . . . . • . . . .

o. 0075 ~ , ,

117'2 9ate 1 332(2 + O~s ) I] o e27 I

015C I ~ - - -

C H A N N E L

Fig. 3. Coincidence spectra for the yrast cascade y-rays, where E== c -~ 33 MeY, and the reaction is socr(tZC, 21yf)eONi. See text for details.

YRAST CASCADE IN e°Ni 215

4; 3

41 2~

9

o*

6.807

5.345

4.262

5.119

2,626 2.505

2,159

t .332

0.0

6ON|

Fig. 4. Summary of the e°Ni level scheme presently observed. The widths of the transitions shown correspond to the relative 7-ray intensities as observed via the S°Cr(Z=C, 2pT)6°Ni reaction for Et= c = 33 MeV and 0 = 55 °. The spins for the three new states above 4 MeV excitation are from

the present study.

parameter matrix was obtained from them after having subtracted time-random coincidences. Representative coincidence spectra obtained from the matrix by inte- grating the area under the peaks (and removing underlying continua) along one axis, say the X-axis, and projecting in the other axis, the Y-axis, are shown in fig. 3. Revers- ing the role of the axes yielded similar but complementary coincidence spectra. Besides providing crucial but familiar bases for constructing the level and decay scheme, these and their complementary coincidence spectra enabled us to obtain DCO ratios for relevant 7-ray pairs. As defined by Krane et aL 7) the DCO ratio Ryl • (0 , 0 ' ) = I [? t (O) - - y z (O ' ) ] / I [ y l (O ' ) -?2 (O)] , where I[~1(O)--y2(O')] is the coin- cidence intensity for detecting ?t at 0 and 72 at 0' and 1171(0')-72(0)] is the comple- mentary intensity, and as demonstrated by Grau et al. e) such ratios for heavy-ion induced y-ray cascades constitute very useful experimental measurements for ascer- taining the nature (such as spins and multipolarities) of the cascades. The DCO ratios for relevant y-ray pairs, which were deduced from the y-7 coincidence matrix, are given in table 1.

216 H. J. KIM et al.

TAeLB 1

R~,t~2(90, 0) for the SOCr(tZC, 21D,)e°Ni reaction for Et2 c = 33 MeV

Y~t~ 1332(2+ "-* 0+) 1172(4+ ~ 2+) 1757 1083

1172 1.~4-0.03 1757 0.98~0.05 1.034-0.06 1083 2.10±0.15 1.9 ±0.2 2.2~0.3 1 / 6 2 0 . 9 2 ± 0 . ~ 0 .96!0.13 0.9±0.1 0.54-0.1

The level and decay scheme constructed from the 7-Y and singles results are shown in fig. 4. The widths shown correspond to the relative 7-ray intensities for E,~c ffi 33 MeV. The three levels above 4 MeV are new, and the spins shown for these result from the present study as described later.

2.3. G A M M A - R A Y SINGLES A N G U L A R DISTRIBUTION MEASUREMENTS

Both detectors were also used for 7-ray angular distribution measurements: the smaller detector served as a monitor and the larger one as a movable counter. Gamma- ray yields at the five angles 0 ffi 0 °, 30 °, 55 °, 75 ° and 90 ° with respect to the 33 MeV incident 12C beam were measured. After having been corrected for the dead-time and detector-size effects these results were least-square analyzed using the usual expression W(O) ~- 1 +~',A,P,(O), where P,(0) is the vth order Legendre polynomial. No angular distribution required the inclusion of terms with v > 4. The angular distribu- tion results are summarized in table 2.

TABLE 2

Summary of y-ray angular distributions from the S°Cr(lZC, 21y),)eoNi reaction for E12 c ~ 33 MeV

E 7 (keY) El (MeV) F-a (MeV) A2 A,

1172 2.505 1.332 0.304-0.01 --0.06-t-0.01 1757 4.262 2.505 0.28-t-0.04 --0.09 4-0.05 1083 5.345 4.262 -- 0.28 4-0.02 0.08 4-0.03 1462 6.807 5.345 0.484-0.14 --0.I 4-0.1

3. Spin assignments

The spin assignments for the newly established states at 6.807, 5.343 and 4.262 MeV which together with the 47 and 27 states constitute the main de-excitation cascade for the high-spin states presently populated, are considered in this section. Since measured angular distributions do not warrant them (recall that Az and A4 were sufficient) and since exceptions are not found in this mass region, transitions higher than quadrupole transitions between these states were excluded from the analyses. Thus, five spin possibilities for each of the above three new states were considered in the analyses. For example, J ffi 2-6 were the spin possibilities for the 4.262 MeV

YRAST CASCADE IN 6°Ni

TABLE 3

Summary o f z 2 analysis

217

Ex (MeV) J¢ ./'t ~z ~ ~ ") Z z probability (e/~)

4.262 4 6 0.61 0.31 pure L ----- 2 ~> 70 4 0.90 0.24 1.6 ~, 10 5 0.59 0.0 0.43 ~ 2

J.345 6 7 0.70 0.16 --5.0 > 80 5 0.61 0.30 8.2 > 70 6 0.75 0.0 --2.5 ~ 2

6.807 7 9 1.0 1.0 pure L ~ 2 :> 80 7 1.0 1.0 0.55 ~ 10 8 0.6 0.0 1.1 ~ 2

") The values of ~ sensitively depend on small clumges in the values of ~'z and ~ which, however, do not appreciably affect the Z 2 probability. The % and 6 are as defined in ref. 7).

state which decays exclusively to the 4 7 state via the 1757 keV y-ray. Combined experimental results, angular distributions plus DCO ratios, were compared to calculated results to determine the most probable spin values by applying the mini- mum Z 2 deviation criterion. Details of the Xz analysis are given in the appendix, and the results are summarized in table 3. Only the results for those spin possibilities having greater than I ~ g 2 probabilities are shown in this table. As commonly done in similar situations, we assumed that the spin of the cascade-member states decreases as the decay proceeds downward toward the ground state in making the spin assign- ments, discussed below individually.

3.1. THE 4.262 MeV STATE

A total of seven experimental measurements were included in the X 2 analysis: five from the 4.262 MeV --, 2.505 MeV (Jr -- 4+), 1757 keV y-ray angular distribution measurements and RlTsT.1172(0, 90) and R17s7.1332(0 , 90). The most probable spin is J -- 6 (see table 3), and we assign Y -- 6. This is consistent with the absence of y- ray branches to the lower J -- 2 and 3 states and implies that the 1757 keV y-ray results from a stretched-spin quadrupole transition, 6 L~.2 4.

3.2. THE 5.345 MeV STATE

The angular distribution results and three DCO ratios (see table 1) were included in the Z2 analysis. As noted in table 3, we utilized the J -- 6 assignment for the 4.262 MeV state. The most probable spins are J = 5 and 7, but we assign J :- 7 in acx~ordance with the earlier stated assumption. The absence of y-ray branches to the lower J -- 2, 3 and 4 states is consistent with this assignment. The X z probabilities for J ffi 8 and 4 (stretched-spin quadrupole cases) are less than 1 ~o and are not given in table 3.

218 H . J . KIM et al.

3.3. THE 6.807 MeV STATE

The angular distribution results and four DCO ratios, given in table 1, were included for the Z2 analysis performed utilizing the J -- 7 assignment for the 5.345 MeV state and the J = 6 assi~,nment for the 4.262 MeV state (the spin of the 5.345 MeV state only enters for calculating angular distributions but both spins enter for DCO ratios). The most probable spin is J = 9. The absence of y-ray branches to the lower J = 2, 3, 4 and 6 is consistent with this assignment.

4. Comparison with theory

The energy of the Y = 6 state established in this work agrees well with that of the lowest-lying 6 + state predicted by Glaudeman's shell-model calculation 1) but not with that of Parikh's band-mixing calculation 9). Also, J = 7 and 9 states are missing in this band-mixing model 6°Ni spectrum although a number of J -- 6, 8 and l0 states are present. It would be interesting to see whether realistic shell-model calcula- tions which include high-spin states can explain the present results.

5. Summary and conclusion

The results of the heavy-ion induced in-beam y-ray study, presented in fig. 4, clearly show the selectivity of high-spin states. The existence of a well developed yrast cascade in 6°Ni is also apparent from this figure. Simple calculations show that more than 12 ~ of angular momentum is available for 6°Ni residual states populated by the 5°Cr(lZC, 2p) reactions for E12c = 33 MeV, but the highest observed spin is 9 h. This implies that the reason for not having been able to observe higher-spin states is not to be found in the particular reactions adopted. Perhaps it is due to the structure of a°Ni.

The yrast spin sequence implied by the predicted 9) band-mixing theoretical spec- trum of 6°Ni is l0 -~ 8 ~ 6 ~ 4 - , 2 ~ 0 whereas the observed sequence is 9 ~ 7 -~ 6 ~ 4 - , 2 -~ 0. This disagreement may mean that the band-mixing model is not valid for 6°Ni insofar as high-spin (J > 6) states are concerned.

Appendix

Although y-rays emitted from such highly spin aligned states as those populated in the present heavy-ion reactions have characteristic angular distributions which depend on spin changes £ ~ Jr, the inference of unique spin changes is usually not possible solely from observed angular distributions 1o). Consider the case of the 4.262 MeV state as an example. The measured angular distribution of the 1757 keV T-ray from this state to the 2.505 MeV, 4 + state is very similar to that of the 1172 keV, 4~ -~ 2+ stretched-spin quadrupole y-ray (see ,4, values given in table 2) which sug- gests a similar stretched-spin (6 -~ 4) nature of the 1757 keV y-ray. In fact, the X z

YRAST CASCADE IN e°Ni 219

probability, which is based on the angular distribution alone, exceeds the 90 confidence level for J = 6 and confirms this suggestion. The values of spin alignment parameters e,(J), which specify the spin afignment of the 4.262 MeV state, as described by Yamazaki 11), and which are implied by the % 2 analysis are 0e2(J = 6) = 0.61 and ce4(J = 6) -- 0.31. These values fall in the ranges of ce, values commonly observed for stretched-spin transitions lo). However the same angular distribution can be represented by an admixed dipole-quadrupole transition from a similarly aligned J = 4 state with a comparably high probability if the admixture is specified by 6 ~ 1.6 [the mixing ratio 6 is as defined in ref. 7)]. Clearly, we need an independent measurement of 6 to remove this particular ambiguity.

That the DCO ratios, R175~.x172(90, 0) and R1757.t3az(90, 0) for the T-ray pairs from the ~/'1757A+• "~1 117Z~+• ~1 1332n+~.,, cascade can provide the needed additional measure- ments is demonstrated: the theoretical ratios for both T-ray pairs are P-th(J) ---- 1 for J = 6, which is the universal value s) for such stretched-spin cascades as 6 --, 4 --, 2 --, 0, independent of the values of ~, whereas the calculated ratios for J = 4 with the ~, and 6 values specified by the angular distribution analysis are Rth(4) = 0.82. The measured ratios (R1757-1172 (90, 0) = 1.03 ±0.06 and R1757-1332(90, 0) -- 0.98 ±0.05; see table 1) definitely favour J = 6.

In determining the most probable spin value for each of the three new states we minimize the quantity Qe(j), where

0.2(~)

In this expression W~ and A W~ are measured angie-dependent T-ray yield and error at 0~, RT.y J and ARj are the measured DCO ratio and error for the Y-T~ pair and W(~2, ~4, 6, 0t) and R~(e2, ~4, 6) are analogous theoretical values. Using the formalism and results given in ref. 7) a computer code was prepared for minimizing Qe(j), and the results obtained are summarized in table 3. In order to expedite the X 2 analysis, the e, were restricted by the conditions 0.4 < ~2 < 1, 0~4 < ~2 and ~6 and higher terms ignored. The first of these conditions may be justified on the ground that the value of ~2 for the 4 + state, as determined from the 1172 key T-ray angular distribution, is e2 = 0.59 and the e2 values for higher states should be similar to this value, while the latter two conditions are compatible with the statistical nature of the heavy-ion induced high-spin state decay 11) assumed for the present cases. Delta values ranging from 10-3-103 were considered in these analyses.

One of us (HJK) gratefully acknowledges the hospitality provided by Mme. Farraggi and Mr. Cotton while at CEN, Saclay. We are thankful to Prof. Glaudemans for the shell-model calculation and useful discussions.

220 H . J . KIM et aL

R e f m

1) P. W. M. Olaudemans, private commumcation 2) S. Raman, Nuci. Data B2 (1968) 5-41 3) 3. O. Newton, Prog. Nucl. Phys. 11 (1970) 53 4) H. J. Kim, R. Ballini, B. Delaunay, J. Delaunay, J. P. Fouan and M. Pichevar, Proc. Int. Conf.

on reactions between complex nuclei, Nashville, vol. 1 (North-Holland, Amsterdam, 1974) p. 145 5) J. T. Routti and S. G. Prussin, Nucl. Instr. 72 (1969) 125 6) W. T. Milner, unpublished 7) K. S. Krane, R. M. Steffen and R. M. Wheeler, Nucl. Data A l l (1973) l 8) J. A. Grau, Z. W. Grabowski, F. A. Rickey, P. C. Simms and R. M. Steffen, Phys. Rev. Lett.

32 (1974) 677 9) J. K. Parikh, Phys. gev. C10 (1974) 2568

10) J. A. Grau, F. A. Rickey, G. J. Smith, P. C. Simms and J. R. Tesmer, Nucl. Phys. A229 (1974) 346

11) T. Yamazaki, Nucl. Data A3 (1967) 1