The E2-M1 mixing ratio for the 2+2 → 2+1 transition in 60,62Ni

)l.E.4:3.A 1

Nuclear Physics All8 (1972) 355-364; Not to be

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THE E2-Ml MIXING RATIO FOR THE 2:+2:

from the publisher

TRANSITION IN 60’62Ni

D. M. VAN PATTER, E. J. HOFFMAN, T. BECKER t and P. A. ASSIMAKOPOULOS tt Bartol Research Foundation of the Franklin Institute, Swarthmore, Pennsylvania 19081 ttt Received 8 September 1971 Abstract: The E2/Ml mixing ratio for the 2*+ + 21+ transition in 60*62Ni has been measured using a reaction-independent method involving ratios of the coefficients of the same or&r of Legendre polynomial from singles angular distribution data (accuracy 5 1 %) for the cascade and crossover y-ray transitions. Values of 6 = -0.6810.22 and -3.19f0.11 were obtained for 60Ni and “Ni, as well as branching ratios (crossovers/cascades) of 0.161 ho.008 and 1.242 kO.017 respectively. Weighted averages of available nuclear spectroscopic information yield values of 542f65 (58Ni), 315&60 (60Ni) and 25.7AO.4 (6zNi) for the ratio of the reduced E2 transition rates, B(E2: 22+ + 21+)/B(E2: 21+ + O1+). The trend of these values is not well reproduced by any of the various shell-model calculations employing exact configuration mixing or quasiparticles.

E

NUCLEAR REACTIONS 60.6zNi@, p’y), Ep = 4.8-7.0 MeV; measured Z , u(/$, e,), 60*62Ni deducedy-multipolarities and branching ratios. Ge(Li)-NaI&) detector. Enriched targets.

1. Introduction Over the period of the past several years there have been many theoretical attempts to explain the structure of the nickel isotopes within the framework of the shell model using either (a) exact configuration mixing lw8) * or (b) approximate quasiparticle calculations ‘-13). Generally, the neutrons outside the 56Ni core are allowed to occupy only the 2p+ If+ and 2p+ shells. Roy et al. “) extended their quasiparticle calculations to include the lg, shell, but found little improvement for the energy spectra or transition rates. A thorough summary of these theoretical studies has been given by Jongsma 14). While the energy spectra for the lowest few states of the doubly even nickel isotopes have been fairly well described by these various approaches 14*I’), there are major differences in the predicted transition rates 14), as well as some outstanding discrepancies with experimental rates ‘, 14-2o). Several of these shell-model calculations have yielded predictions for the E2 rates from the 2: and 2: states of 5886‘, 62Ni, and for the ratio of reduced E2 transition t Present address: Odenwaldstr. 9, D6908 Wiesloch, West Germany. Agia Paraskevi, tt Present address: Nuclear Research Centre “Democritos”, Greece. ++t Work supported by the National Science Foundation. : Transition rates for 58Ni [ref. *)I have been corrected in ref. 6). 355

Attikis,

Athens,

356

D. M. VAN PATTER et al.

probabilities, B(E2: 2: + 2l)/B(E2: 2: -+ 0:). From available nuclear spectroscopic data including recent lifetime measurements 7,18), this ratio is now well known for ‘*Ni and 60Ni, and the absolute transition rates well established for ‘*Ni. At the present time, there is only a limit of > 2 ps given for the lifetime of the 2: state of 60Ni [ref. ‘*)I. In the case of 62Ni alifetime of l.lOTg$$ ps has been reported for the 2: level is). Unfortunately there is an ambiguity for the E2/Ml mixing, with the possible values of 6 = -(1.7Zi:z) or -0.07+0.18, which would correspond to E2 rates of either 7.7 f2.7 or 2 0.3 W.U. [ref. l*)]. While it is true that studies 21) of the systematics of S-values and B(E2) ratios for 2, + 2r transitions would indicate a preference for the larger E2 rate, there is a considerable d-variation in this mass region. For example, the 22 -+ 2, transition in 46Ti has 6 = - 1.29kO.26 +, while the corresponding value reported “) in the cross-conjugate nucleus “Cr is - 0.03: 0”:;:. Therefore, an improved measurement of this b-value for 62Ni would be worthwhile, especially one which would remove this ambiguity. One reaction-independent method ‘“) of measuring such a b-value involves ratios of the coefficients of the same order of Legendre polynomial from correlation data for transitions a + b and a + c: A&

--, b)/A,(a + c) = F,(a, b)lF&,

c).

(1)

Since this method is independent of cascade transitions from higher levels, it can be applied to either angular correlation or y-ray distribution measurements. Examples of measurements involving direct (singles) y-ray spectra have been presented 27), including some analyses of (p, p’y) spectra to evaluate &values for 2: -+ 2: transitions. It is well known 28*29) that it is quite difficult to distinguish between the two &solutions usually obtained from such a (p, p’y) analysis, since the A4 values for such solutions generally differ by 5 0.05. However, with sufficiently precise angular distribution data (x 1 % errors), it is possible to obtain a unique a-determination, such as has been described 27) in the case of the 2: level of 42Ca. It was decided to attempt such an analysis for the 2: level of 62Ni, and to try to obtain an unambiguous b-value for the 2; + 2: transition in 60Ni using this method. 2. Experimental procedure Angular distribution data (0” to 90”) were obtained for 60Ni at E, = 6.72 and 6.92 MeV using a 3.9 mg/cm2 (99.0 % enriched) target mounted at 45” and bombarded by a proton beam from the University of Pennsylvania tandem accelerator. Gammaray spectra were obtained using a Ge(Li)-NaI(T1) spectrometer, which consisted of a 20cm3 Ge(Li) detector located at 30 cm from the target, and at the center of a 30.5 cm x 20.4 cm o.d. NaI(T1) annulus. In this investigation, the central Ge(Li)detector was operated in the anticoincidence mode, which suppresses Compton scattering events by a factor of about four in this geometry. Spectra were recorded in a 4096+ Average value from refs. Z2.Z3). Error estimate revised by ref. f4).

E2-M1 MIXING

RATIO

357

channel TMC analyser. A more complete description of this system including the procedure used to calibrate the efficiency of the 20 cm3 detector has been presented previously 19*30). The present measurements which concern the 2158.9 keV 2: state of 60Ni were obtained during a more extensive investigation 31) of the y-ray decay properties and spin values of the 60Ni states below w 4.1 MeV excitation. Three sets of angular distribution data (0” to 90’) were taken for 62Ni under varying experimental conditions, all for an incident energy of 4.8 MeV, just below the 62Ni(p, n) threshold, and with the 2.5 mg/cm’ target (98.7 y0 enriched) placed at a large angle (50”-70”) from the perpendicular position in order to increase the effective target thickness. For the first run, spectra were obtained with a 55 cm3 Ge(Li) detector placed at 38 cm from the target, and shielded with 1 cm Pb to reduce the relative intensity of low-energy y-rays. For the second run, singles spectra were recorded using a 33 cm3 coaxial detector placed at about 15 cm from the target. In the third run, the 33 cm3 coaxial detector was placed in the NaI(T1) annulus to provide Compton suppression. The relative efficiency of the 33 cm3 detector was determined utilizing the accurately known intensities of the prominent y-transitions from 56Co [ref. “‘)I and 207Bi, 20L(Tl[ref. ““)I. The efficiency versus y-ray energy curve was fitted to a straight line on a log-log plot by a weighted least-squares procedure in the region Ey = 0.8 to 3.5 MeV. This full-energy efficiency calibration was good to f 1.3 % with oJ@in = 0.8. In order to achieve an accuracy of s 1 *Afor angular distribution data, it is best to provide a normali~tion of each spectrum. Fortunately, both 60Ni and 62Ni (p, p’y) spectra contain a prominent peak arising from the 0: + 2: transition, which provides an automatic normalization because of its isotropy. This procedure eliminated any uncertainties associated with dead-time in the analyser, charge collection, and target thickness at the beam spot.

3. Results 3.1. THE NUCLEUS

60Ni

The angular dis~ibutions of the 826.4 (2, -+ 2,) and 2158.9 (Z2 -+ 0,) keV 60Ni (p, p’y) radiations were measured at E, = 6.72 and 6.92 MeV, using the 952.3 keV O2 + 2, transition for normalization. At these bombarding energies there is considerable cascade feeding of the 2: level 29), and as indicated in table 1 the A4 coefficients for both distribution measurements become very small ’ “). The results were then used to obtain two values of the ratio A;/A2 = A,(2: + 2:)/A2(2: -+ 0:) with an average value of 1.378f0.075. From the error limits on this ratio, a S-value of -0.68+0.22 is obtained, using the ellipse shown in fig. 1. This A’,/A, ratio has been previously measured I”) as 1.37+0.10 (with 6 = 0.7 20.3) using a low-resolution NaI(T1) detector at B, = 4.90 MeV. When combined with the present result, average values of AL/A, = 1.375 _tO.O60and 6 = -0.67 kO.21

D. M. VAN PATTER et al.

358

TABLE

Angular distribution

1

results for the 826.4 keV 22+ + 2,+ and 2158.9 keV 22+ + 01+ transitions in 60Ni

22+ +2,+

6.72

0.86

6.92

0.70

0.264 7 0.258 12

22 + *or+

0.015 8 0.000 I5

0.87

0.75

0.74

1.70

0.185 16 0.191 10

0.019 20 -0.020 12

1.65

1.33

1.18

0.48

1.43 13 1.35 9

“) Average normalization error from O2+ + 21 + y-ray yield. “) Average error (including normalization) for angular data.

ApA t

A;/A,=(0.700-2.049%0.214

621/(1+62)

A;/A,=0.28662/(I+62) 2’ 2 n

T”.J

Fig. 1. Reaction-independent ellipse in A4 versus A2 space for the ratios of Legendre polynomial coefficients from angular correlations involving the 2’ + 2 and 2’ -+ 0 y-transitions and as a function of the mixing parameter 6. The hatched box represents the error limits of the present measurements (run 3) for the 2301.6 keV state of 62Ni.

are obtained. It should be noted that taking a weighted average of these two &determinations would have yielded too low an estimated error. Previous results from y-y angular correlation measurements using NaI(T1) detectors are 6 = -0.72 [ref. ““)I and 6 = - 1.1 f0.2 ‘. If we assume that each of these measurements should have the same weight as our combined value of -0.67kO.21, then we calculate an average value of 6 = -0.83 +O. 13, corresponding to (40.8 + 7.5) per cent E2 radiation. t The 22+ +21 + d-value reported in ref. 35) has been slightly modified by S. Raman, Data Sheets B2-5-41 (1968).

Nucl.

E2-Ml

MIXING

359

RATIO

In order to evaluate the y-branching of the 2: level, the statistical errors for the peak area determinations were negligible compared with the + 5 % error attached to the efficiency calibration ’ 9S30) for the 20 cm3 detector. A value of R = crossovers/ cascades = 0.161+0.008 was obtained. This result was combined with earlier values of 0.162f0.028 [ref. 36)], 0.201 f0.036 [ref. 30)]t, 0.154f0.008 [ref. ““)I and 0.139f 0.032 [ref. “‘)I, to yield a weighted average ” R = 0.158 +0.007, corresponding to a ground state branch of (13.6f0.5) %. Taking the energy values listed by Rauch et al. 30) together with the above weighted averages, a ratio of B(E2: 2: -+ 2:)/ B(E2: 2: --P0:) = 315k60 is obtained for 60Ni. 3.2. THE NUCLEUS

62Ni

The angular distributions of the 1128.8(2: -+ 2:) and 2301.6(2: -+ 0:) keV transitions in 62Ni were measured at E, = 4.8 MeV, using the yield of 875.6 keV 0, + 2, radiation for normalization. The first set of spectra were recorded at six angles; however the 0, = 70” data has associated errors about twice those of the other spectra. Computer analysis of these spectra combined with least-squares fits to Legendre polynomials yielded the angular distribution coefficients listed in table 2. The calculated AilA, ratio was insufficiently precise to distinguish between the two possible 6solutions of -3.2+0.2(x2 = 1.7) and 0.14f0.02(x2 = 1.3). A careful hand analysis of the spectra yielded the same result. For the second run, an attempt was made to improve the statistical accuracy for each observation angle. Due to time limitation, spectra at only four observation angles were recorded. A substantial improvement in the statistical errors for each y-ray peak area was achieved, as well as in the derived angular distribution coefficients. A careful hand analysis of each peak revealed some small systematic errors (averaging 1.6 %)

Angular distribution

TABLE2 results for the 1128.8 keV 22+-+21+ and 2301.6 keV 22+-+01+ transitions in e2 Ni at Ep = 4.8 MeV

22+ -+2,+ Run no.

UN”) (%)

AZ

1

1.52

2

0.92

3

0.49

0.179 20 0.194 13 0.188 8

A4

-0.018 29 -0.029 14 -0.053 9

22+ + or+ o “) (%)

a*, 0,

2.20

1.19

1.39

0.82

0.95

0.76

‘42

0.431 21 0.401 20 0.413 7

A4

-0.212 31 -0.172 24 -0.207 8

o “) (%)

ocr a,

-A’2 A2

2

1.91

1.46

1.26

1.75

0.90

0.76

0.415 53 0.483 39 0.453 21

0.082 136 0.166 87 0.258 44

“) Average normalization error from 02+ --f 2r+ y-ray yield, excluding t$, = 70” in run 1. b, Average error (including normalization) for angular data, excluding f&, = 70” in run 1. t The results of Fass et al. are quoted in ref. 30). tt We note that both Bartol values are subject to the same &5 % uncertainty

in detector efficiency.

360

D. M. VAN PATTER et al.

in an initial computer analysis, caused by incorrect choices of channels for background evaluation. At the level of an error of M 1 % in relative peak area determination, it is extremely important to make a consistent analysis for all angles. If there is some broadening of the peak profile due to counting rate at one particular angle, then essentially this means that one must include the extreme tails of each peak in the area analysis. Two S-solutions of -3.010.2(x2 = 0.8) and O.lOf0.02(~’ = 1.7) were determined from this run. While the probability of the first value was larger by more than a factor of three, the second value could not be ruled out. In an effort to reduce the statistical errors for the 875.6 and 1128.8 keV peaks, a third run was taken using the Ge(Li)-NaI(T1) spectrometer in the Compton suppression mode. An improvement of almost a factor of two was achieved for the normalization error at seven observation angles, and also for the errors associated with the ratios A;/A, and AL/A,. As indicated in fig. 1, the results represent an unambiguous determination of 6 = - 3.19 fO.11, where the associated errors correspond to the overlap of the experimental value of AL/AZ = 0.413 kO.007 with the theoretical ellipse in A, versus A, space. Another method of analysing these angular distribution data is to apply eq. (1) by generating the angular distribution for the 2: -+ 2: transition (as a function of 6) from the AZ and A, coefficients of the least-squares fit for the 2z(E2)0: transition, i.e.,

4422 + 21) =

M22 + 21) A,(22+ 01). fit22 -+ 01)

(2)

The experimental angular distribution data for the 2: + 2: transition can then be compared with this generated curve. On the left side of fig. 2 is shown the solid curve for6 = -3.19 generated from the least-squares fit for the 2,(Q)O, 2302 keV transition (solid curve on right). Also the 2,(D, Q)2, curve generated for 6 = 0.11 is indicated. For this third run, the data clearly do not fit the second S-solution permitted by the first two runs. It is also possible to calculate a normalized x2 representing the fit between the 22 + 2, angular data and curves generated for each value of the mixing ratio. In fig. 3, we note two x2 minima at 6 = -3.19 and 0.12; however the latter value has an exceedingly poor fit (x2 = 7.6) with a probability much less than 0.1 %. Using our usual procedure “) in estimating the uncertainty at a position of one-half that of the maximum probability value, we obtain a value of - 3.19 + 0.17. This error included a negligible contribution from the uncertainties associated with the A, and A, coefficients of the 2:(E2)0: transition. Taking an overall average for the three runs, A; = A, = 0.455 50.018 and Ak/A, = 0.227 kO.038, which, when applied to the ellipse of fig. 1 yields S = - 3.18 kO.09. Since this is nearly identical to the results of the third run which gave an unambiguous S-choice, we prefer to take the value 6 = - 3.19 fO.11. The intersection of the experimental error bars with the A, versus A4 ellipse appears in this case to be a realistic representation of the uncertainty associated with this S-determination. We note that

Fig. 2. The curve on the right shows a least-squares fit to the angular distribution data at Ep = 4.8 MeV for the 2r+(E2)01 + transition. From this fit are generated the two curves on the left for &values of&l 1 and -3.‘ti), whkh are compared to the experimenta data (run 3) for the 22* (@2,* transition.

a=-3.1930.17 0

I -45

I 0 ARG

I +45

t II t i 70" 72" 74 I i-90

TGS

Fig. 3. The xs VWsus arctg 6 plot represents the St of the =Nifpl p=y] angukr &stribution data for the 2rf(ir)z,c transition to curves generated from the least-squares fit to the 22+(B2(E2)oS4 angdar data (see fig. 2). The inset at right shows an enlargement of the x2 minimum.

362

D. M. VAN PATTER et al.

it is substantially different than the previously reported value I*) of b = - (1.7+::9,). The A0 coefficients for the 1129 and 2302 keV transitions had statistical errors of 0.35 % for the third run. .4fter including the uncertainty for relative detector efficiency, the y-ray branching ratio of the 2; level of 62Ni was measured as R = 1.242+0.017. The more accurate values previously reported for this branching ratio are (a) from 62Cu spectra, 1.36kO.16 [ref. ““)] and 1.27+0.09 [ref. r4)]; (b) from 1.4 min 62Co, 1.40 kO.08 [ref. ““)I and 1.21 i 0.11 [ref. 14)J- When combined with the present value, the weighted average is R = I .250&0.017, with a ground state branch of (55.5 f 0.3) %. Our determination of 6 corresponds to a 22 -P 2, transition with (91.0f0.6) % E2 radiation. Weighted averages of available data r4*’ ‘* 38-39) yield transition energies of 2301.6fO.l and 1128.8&0.1 keV. Combining these results, we obtain B(E2: 2: + 2:)/ B(E2: 2: -+ 0:) = 25.7+0.4 for 62Ni. On the basis of the experimental lifetime Is) of l.lO?~:$~ ps, absolute transition rates of 6.4& 1.9 and 164+49 e2 * fm4 are calculated for the 2; -+ 0: and 2: --r 2: transitions respectively. The 2: -+ 2: Ml rate is found to be 1.4hO.4 pi, which is considerably smaller (factor of 2.5) than previously reported l’), due to our revised &value for this transition. 3.3. THE NUCLEUS

5aNi

For purposes of completeness, we have surveyed available information concerning the y-decay properties of the 2775.2 2: state of 58Ni. Three recent 58Ni(p, p’y)studies have reported &values of 1.14?~::~ [ref. I”)], l.lL-0.2 [ref. ‘)I and 1.28+::; [ref. ““)I, yielding a weighted average of 6 = 1.14~~:~~. These have included two values ‘*lg) for the y-ray branching of (3.5kO.5) %, and (4.3f0.3) % which are in reasonable agreement, yielding an average branching ratio of R = 0.042640.0038. In this recent study of the 58Cu decay scheme, Jongsma 14) lists y-ray intensities corresponding to R = 0.071+0.015. Since these y-rays are only weak components of the 58Cu spectrum, we have not included his result in our average value. Taking the transition energies previously listed “), we obtain B(E2: 2: + 2:)/ B(E2: 2; -+ 0:) = 542F65 for “Ni. Jongsma 14) lists a value of 301 i 76 for this B(E2) ratio. Evidently this result is based on his branching value, and does not include the more accurate branching values from the “Ni(p, p’y) studies 7*’ “). 4. Conclusions The reaction-independent method used in this present experiment has given an unambiguous and precise determination of S = - 3.19 + 0.11 for the 2: (E2, M 1)2: transition in 62Ni. From weighted averages of available nuclear spectroscopic information, the values of the ratio B(E2: 2: -+ 2:)/B(E2: 2: -+ 0:) are found to decrease from 58Ni to 62Ni (table 3). This trend is in the opposite direction to that predicted by the shelf-model calculations of Cohen et al. ‘). Auerbach “) and Hsu I’) using exact configuration mixing. Hsu has also calcuIated the electromagnetic tran-

E2-Ml

Electromagnetic Nucl.

58Ni 60Ni 62Ni

Experimental

Branching

2715.2 2 2158.9 2 2301.6

0.0426 36 0.158 7 1.250 17

1

RATIO

363

TABLE3 y-decay properties of the 22+ level of the nickel isotopes

average

E(22+) (keV)

R “)

MIXING

B(E2: 22+ + 21 +)/B(E2: 2a+ -+ or +) 6

22 +&

1.14 II -0.83 13 -3.19 II

Exp. average 542 65 315 60 25.7 4

ref. ‘) 0.03

Exact shell ref. 2, ref. 12) 0.034

20

45

33

1308

0.058

Quasiparticle SeniorTD2 PTD4 ity V2 0.75

10.5

2.9

4x103

1.22

0.71 95 230

0.058 350 12.4

Theoretical values for quasiparticle and seniority calculations are those of Hsu I*). “) R is defined as the ratio $(2, + -+ O,+)/f,(2,+ + 2r+) = crossovers/cascades.

sition rates using various approximation methods including seniority and quasiparticle calculations. None of these theoretical results show even qualitative agreement with the trend of the observed values from 58Ni to 62Ni. As has been pointed out 6 ‘*18), one major source of such disagreement is the improper treatment of core excited states, which should be more important in 5*Ni than in 6o*62Ni. Nevertheless, most of the various theoretical calculations generally do not reproduce the absolute E2 transition rates in 62Ni to better than about an order of magnitude ’ *), and usually fail to predict the decrease (factor of 12 rt 2) in the B(E2) ratio between 60Ni and 62Ni, although we note that the seniority calculation (V2) of Hsu I’) succeeds quite well in both instances. We wish to acknowledge the participation of Dr. Cyrus Moazed in the initial phase of this work, and the assistance provided by Mr. Shing-kwan Alan Woo and Miss Evelyn Monsay, National Science Foundation undergraduate research participants. References 1) S. Cohen, R. D. Lawson, M. H. Macfarlane, S. P. Pandya and M. Soga, Phys. Rev. 160 (1967) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11)

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D. M. VAN PATTER et al.

364

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