Beta decay of 58Cu

Nuclear Physics A162 (1971) 35-41; Not to be reproduced by photoprint

@ North-Holland Publishing Co., Amsterdam

or microfilm without written permission from the publisher

BETA DECAY OF 58Cu L. E. CARLSON t, D. A. HUTCHEON, A. G. ROBERTSON, E. K. WARBURTON tt and J. J. WEAVER Nuclear Physics Laboratory,

D. F. H. START,

Oxford, England

Received 24 September

1970

Abstract: The /?’ decay of the 1+ ground state of ssCu to excited states of 58Ni has been investigated by a study of the subsequent de-excitation y-rays using a Ge(Li) detector. Branching ratios for positon transitions to the following 5sNi states were obtained: 1.454 MeV (2+), 2.Okl.l %; 2.775 MeV (2+), < 0.22 %; 2.902 MeV (l+), 3.Ok1.2 %; 2.943 MeV (O+), 9.911.6 %; 3.038 MeV (2+), 0.29kO.09 %; 3.263 MeV (2+), 1.0610.14 %; 3.531 MeV (O+), < 0.14 %; 3.593 MeV (I+), 0.67&0.10 %; and 3.898 MeV (2+), <0.18 %. Positive parity is assigned to the 2.902,2.943, 3.263 and 3.593 MeV levels of 58Ni and the log ft values deduced from the above branching ratios are compared to shell-model predictions. E

RADIOACTIVITY 5sCu[from ssNi(p, n)]; measured Er, Z,,; Deduced ssNi levels deduced 7~. Enriched target, Ge(Li) detector.

log ft.

1. Introduction

The positon decay of 58Cu to ‘sNi was first observed by Martin and Breckon ‘) in 1952. In 1960 Miller “) investigated the positon spectrum and found it to be complex with an end-point energy for the highest energy group of 7443 + 25 keV. The half-life was measured with good precision by Sutton “) in 1961 to be z+ = 3.21 kO.02 sec. A more recent value is 3.204+0.007 set [ref. “)I. Sutton observed y-rays following the 58Cu decay, and by /?y and yy coincidences established that positon decay occurs to several excited states of 58Ni near 2.9 MeV excitation as well as to the 58Ni ground state and possibly to the first excited state at 1.45 MeV. For these three branches Sutton obtained branching fractions of 0.15+ 0.06, 0.83 f0.07 and 0.02+ 0.02, respectively. The positon decay scheme was complicated by the fact that the 58Ni 2.9 MeV level involved decays by y-ray emission to the 1.45 MeV first excited state and this transition is practically degenerate in energy with the subsequent decay of the first excited state. The decay modes found by Sutton were consistent with the positon spectrum measured by Miller ‘). In particular, Sutton examined Miller’s spectrum and found it to yield branching fractions of 0.82 and 0.18 approximately, for positon end-point energies of 7.44 and 4.54 MeV. t Present address: Queens University, Kingston, Ontario. tt National Science Foundation senior post-doctoral fellow, 1968-1969. Permanent address: Brookhaven National Laboratory, Upton, New York. Work partially performed under the auspices of the US Atomic Energy Commission. 35

36

L. E. CARLSON

et al.

Sutton’s reported log ft value for the decay of ‘*Cu to the J” = O+ ground state of 58Ni was 4.83kO.05. This is clearly not a superallowed O+ to O+ transition but is in the allowed class; so the decay takes place from a level with J” = l+. For some time it was thought

possible

that the observed

positon

decay was from an isomeric

Ea+ (Mev)

“I.

3.954 4.016

0.67,OJO < 0.14

4.264 4.509 4.605 4.646

1.06tO.14 0.29tao9 9.921.6 3.OZ1.2

4.772

<0.22

6.093

2.OW

7.547

03:7

1.454 2’

V

, ”

Fig. 1. The proposed

state

0

o*J

decay scheme of 3.2 set 58Cu in which the properties of the 58Ni levels have been taken from ref. lo).

and that the 5sCu ground state was O+ and decayed by a much more favoured (log to the 5*Ni ground state. Searches 3, “) for such an activity were not successful. Subsequently the 58Ni(p, n)58Cu [refs. “,“)] and58Ni(3He, t) 58Cu [refs. ‘,“)I reactions have been used to locate the J” = O+, T = 1 58Cuanalogue of the 5*Ni ground state at 202f2 keV above the J” = l+, T = 0 58Cuground state. The 58Ni(p, n)58Cu reaction also provides an accurate value for the 58Cu(/?+)58Ni

ft = 3.49) transition

=Cu BETA DECAY

37

end-point energy. From the threshold energy for this reaction, 9515252.9 keV [ref. “)I, we find an end-point energy of 7547.3 f 2.9 keV. Thus, at the time this work was undertaken it was known that the 58Cu ground state has J” = 1 + 9 T = 0 and decays to 58Ni with an accurately known half-life and an accurately known energy release. However there was only rudimentary knowledge of the decay modes to excited states of 58Ni. The present search for such decay modes was motivated by an interest in the structure of mass-58 nuclei and, in particular, by the fact that nuclear /I’ decay matrix elements provide useful nuclear structure information. The experiments consisted of measuring the relative intensities of y-rays following the p’ decay and the positon branching ratios obtained are summarized by the decay scheme shown in fig. 1. The spins, parities and branching ratios of the 58Ni levels have been taken from a recent summary by Start et al. lo). 2. Experimental

procedure and results

A 3 mg/cm2, self-supporting foil of 98 % enriched 58Ni was bombarded by a 0.03 PA beam of 11 MeV protons to form 58Cu by the (p, n) reaction. A mechanical shutter arrangement permitted a 3.5 set irradiation to be followed by a beam interrupted period of 14 set throughout which y-rays from the activated target were observed using a 50 cm3 Ge(Li) detector with 5.5 keV resolution for 1.33 MeV y-rays. The data was stored in a PDP-7 on-line computer and the accumulation was advanced to a new subgroup every 3.5 sec. With this procedure we were able to record four spectra from which y-rays associated with the /I’ decay of 58Cu could be identified by both their energy and decay rate. The activation of the target and the data collection were cycled automatically and the spectrum obtained in the first subgroup after 27 h is shown in fig. 2. Most of the y-rays can be attributed to the decay of 58Cu but there are a number from longer-lived activities created by the 58Ni(p, E)~~CO, 60Ni(p, n)60Cu, 27Al(n, y)28A1 and “‘In(n, y) ‘161n reactions, the last of which occurred in the indium electrical contacts of the germanium counter. Several lines could not be identified but in each case the decay rate was significantly different from that of 58Cu. The efficiency of the Ge(Li) detector was measured between 0.83 and 4.80 MeV using a (j6Ga source situated at the target position and the intensities of the 58Ni y-rays combined with the known decay modes of the 58Ni levels (fig. l), yielded the positon branching ratios given in table 1. Only the known 58Ni J” = O+, If and 2+ levels below an excitation energy of 4 MeV are listed and there was no evidence for decay to any states other than these. The analysis was facilitated by a second experiment in which a 15 cm3 Ge(Li) counter with 2.5 keV resolution was used to measure accurately the intensity ratio of the 1.448 and 1.454 MeV y-rays. Our results are in good agreement with the preliminary results of Raman l’) except that this author did not observe the branch to the 3.593 (1’) MeV level.

38

L. E. CARLSON

0

,450

,350

1850

,750

,650

1550

Chanral

et al.

Number

Fig. 2. Singles spectrum ofy-rays following the /?* decay of 58Cu to excited states of 58Ni. The peaks are labelled by their energies in MeV and those arising from other radioactivity are labelled by their parent nuclei where these could be identified.

TABLE 1 Branching

ratios

and logf,t

values

for the B+ decay

(J”, n) “1

WeV)

Branching ‘) ratio (%)

(Of, 0)

0 1.454 2.115 2.902 2.943 3.038 3.263 3.531 3.593 3.898

83 f7 2.0 kl.1 <0.22 3.0 11.2 9.9 11.6 0.2910.09 1.0610.14 <0.14 0.671tO.10 <0.18

5*Ni level

e+,0)

c2+, 1) cl+, 0)

co+,1) a+, 2) (2+, (0’9 (l+, (2+,

3) 2) 1) 4)

of 58Cu to states

fat

of 58Ni

loizfot

(set) (7.010.6) (1.110.6) >3.1 x (2.0+0.8)x (5.9&1.0)X (1.8hO.6) (4.010.5) > 2.2 x (4.3hO.7) > 1.1 x

x lo4 x lo6 106 lo5 104 x lo6 x 105 106 x 105 106

“) The value of n orders the states in excitation energy. b, The ground state branching ratio is taken from ref. 3, and the excited are assumed to sum to 17 0/Owith no uncertainty.

4.85kO.04 6.0 f0.3 > 6.5 5.30&0.22 4.77f0.08 6.3 f0.2 5.60&0.06 >6.3 5.63 ho.09 > 6.0

state

branching

ratios

=Cu BETA DECAY

39

The relative intensities of table 1 were corrected to partial half-lives assuming Sutton’s value “) of 17 % for the branching ratio to excited states, a “Cu half-life of 3.204+0.007 set [ref. *)I and a /3’ end-point energy for the ground state transition of 7547.3 +2.9 keV [ref. ‘)I. The Fermi function, fO, for allowed transitions was calculated using the computer programme of Warburton et aI. 12) which includes Coulomb and finite-size corrections. Screening and radiative corrections are negligible. The 58Ni states listed in table 1 are those to which allowed transitions are possible. Beta decay systematics indicate that transitions with log fat 5 6 are most likely allowed and there are no known exceptions to the rule that “beta transitions with logf,t < 5.8 from nuclei with 2 < 80 are allowed” 13). Thus, the even parity assignment for the 2.943 MeV level of 58Ni is actually based on the present determination of the beta branch to this level and its assignment as allowed. In addition the allowed transitions to the 2.902, 3.263 and 3.593 MeV states confirm previous positive parity assignments based on (aa’) cross-section measurements 14) and y-ray transition probability arguments ’ “). 3. Shell-model predictions The Gamow-Teller

matrix elements connecting the 58Cu (J”, T) = (l’, 0) ground assuming a 56Ni core (doubly closed f%shell) and two nucleons in the 2p,, If+ and 2p+ oscillator shells. The effective single-particle energies were taken from the experimental spectrum of “Ni:

state to Of, 1+ and 2+ states of 58Ni were calculated

E(P*) = 0, E(f+) = 0.78 MeV, E(p+)

=

1.08 MeV.

Wave fnn~tions and energy spectra were obtained from these single-particle energies and Kuo-Brown ’ “) two-body matrix elements. These latter were appropriate to a 56Ni core and include renormalisation corrections. They were provided by Kuo ’ “) ‘. The resulting 58Ni and %u energy spectra appear to match experiment just about as well as previous calculations of a similar type 18-2o). These spectra are discussed elsewhere ’ 0Z21).Th e wave functions of the “8Ni and 58Cu ground states are: IO’, 1) = 0.754~pf)+0.589[f~)+0.290~p~), Il+, O> = 0.3491p;) +0.6931p,f,> -0.5841p,p,) +0.172(f~)+O.l69~p~). The p-decay matrix elements and logf,t values calculated from the wave functions are listed in table 2. The relation between the Gamow-Teller matrix element and the fat value was taken to be fat = (4.04If:O.O7) x 103/2.

+ Dr. I. S. Towner kindly diagonaiized the interaction matrices for us.

40

L. E. CARLSON ei al. TABLE 2

Shell-model predictions -Ni

Excitation energy

level (Jr, n) “)

for the Gamow-Teller


/?+ decay of 58Cu to 5sNi Jog&

=

experiment

theory

-experiment b,

0 2.94 3.53 2.90 3.59 1.45 2.78 3.04 3.26 3.90

0.4045 0.2764 0.1253 0.0026 0.0057 0.2249 0.2905 0.0155 0.0040 0.0978

0.058 *to.005 0.069 I-to.012
theory b,

experiment

_-. (o+,o) to+, 1) (O’, 2) (lf,O) fl’, 1) 0+, 0) (2+, 1) (2+, 2) (2+, 3) (2+, 4)

0 2.56 4.18 2.85 2.98 1.34 2.21 2.86 3.24 3.84

4.000 4.165 4.508 6.190 5.851 4.254 4.143 5.416 6.004 4.616

4.85AO.04 4.77AO.08 >6.3 5.30f0.22 5.63 f0.09 6.0 +0.3 >6.5 6.3 kO.2 X60+0.06 > 6.0

“) The value of n orders the states in excitation energy. “) We have used for = (4.04 x 103)/2.

It is seen from table 2 that these shell-model calculations give a very poor description of the 58Cu p’ decay t. What can we learn from this? The question we ask is whether it is the Kuo-Brown matrix elements that are at fault or some more fundmantal deficiency in the calculation, To answer this question we consider also the electromagnetic transitions in 58Ni. We consider spe cifically the B’ decay to, and the ydecay of the two 1 + states of 58Ni generated by the assumed shell-model space. These states have wave functions of the form Ilf, 1) = alP+P+)+BIP*f& The /” matrix element, (G,)’ is proportional to ~1~(the p+f* term does not contribute); so if we associate the 2.902 and 3.593 MeV states of 58Ni with these shellmodel states we have from table 2, 01~(3.593)/~~~(2.902)= 0.47hO.20 (from fi* decay).

(1)

The Ml ground state rates of these 1’ states are also proportional to c? [also no contribution from the p+f+ term) and the known partial lifetimes yield ‘“)I ~2(3.593)~(2.902) = 12.9k4.1 (from Ml decay).

(2)

Since eqs. (1) and (2) are incompatible we have definite proof that the shell-model space is too small. This is in agreement with the suggestion 17,21) that the 56Ni ground state is not very well described as the doubly closed f%shell. * The wave functions given by Phillips and Jackson 20) yield (G0)2 = 0.8972 for the 8’ decay t0 the 58Ni ground state, in even worse agreement with experiment.

58Cu BETA DECAY

We wish to thank Professor matrix elements and Dr. I. S. us (D.F.H.S., A.G.R. and J. for financial support and two fellowships from the National

41

T. T. S. Kuo for providing us with the two-body Towner for assistance with the calculations. Three of J. W.) wish to thank the Science Research Council of us (L.E.C. and D.A.H.) acknowledge receipt of Research Council of Canada.

References 1) W. M. Martin and S. W. Breckon, Can. J. Phys. 30 (1952) 643 2) J. H. Miller, III, Thesis, Princeton University (1960) 3) D. C. Sutton, Thesis, Princeton University (1961) 4) J. M. Freeman, J. H. Montague, G. Murray, R. E. White and W. E. Burcham, Nucl. Phys. 69 (1965) 433; 65 (1965) 113 5) M. Harchol, A. A. Jaffe, Ch. Drory and J. Zioni, Phys. Lett. 20 (1966) 303 6) J. A. Cookson, Phys. Lett. 24B (1967) 570 7) R. Sherr, A. G. Blair and D. D. Armstrong, Phys. Lett. 20 (1966) 392 8) N. Williams, J. A. Nolen, Jr., J. P. Schiffer and G. C. Morrison, Bull. Am. Phys. Sot. 13 (1968) 105 9) J. B. Marion, Rev. Mod. Phys. 38 (1966) 660 10) D. F. H. Start, L. E. Carlson, A. G. Robertson, R. Anderson and M. A. Grace, to be published 11) S. Raman, private communication 12) E. K. Warburton, G. T. Garvey and I. S. Towner, Ann. of Phys. 57 (1970) 174 13) N. B. Gove in Nuclear spin-parity assignments, eds. N. B. Gove and R. L. Robinson (Academic Press, New York, 1966) pp. 83-103 14) 0. N. Jarvis, B. G. Harvey, D. L. Hendrie and J. Mahoney, Nucl. Phys. A102 (1967) 625 15) T. T. S. Kuo and G. E. Brown, Nucl. Phys. All4 (1968) 241 16) T. T. S. Kuo, private communication 17) P. Goode and L. Zamick, Phys. Rev. Lett. 22 (1969) 958 18) N. Auerbach, Phys. Rev. 163 (1967) 1230 19) S. Cohen, R. D. Lawson, M. H. MacFarlane, S. P. Pandya and M. Soga, Phys. Rev. 160 (1967) 903 20) E. A. Phillips and A. D. Jackson, Phys. Rev. 169 (1968) 917 21) S. S. M. Wong and W. G. Davise, Phys. Lett. 28B (1968) 77