in-beam γ-ray spectroscopy of 56co

N U C L E A R PHYSICS A

ELSEVIER Nuclear Physics A 627 (1997) 162-174

In-beam y-ray spectroscopy of 5 6 C o

M. Palacz a,b, D. Seweryniak c,d, A. Ataq f, J. Blomqvist b, B. Cederwall b, C. Fahlander c, A. Johnson b, A. Kerek b, J. Kownacki e, L.-O. Norlin b,

J. Nyberg c, R. Wyss b, E. Ideguchi g, R. Julin h, S. Juutinen h, S. Mitarai g, M. Piiparinen h, G. Sletten i, S. T6rm~inen h, A. Virtanen h

a Sottan Institute for Nuclear Studies, ,~wierk, Poland b Physics Department Frescati, Royal Institute of Technology, Stockholm, Sweden

c The Svedberg Laboratory, Uppsala University, Uppsala, Sweden d Institute of Experimental Physics, University of Warsaw, Warsaw, Poland

e Heavy Ion Laboratory, University of Warsaw, Warsaw, Poland f Department for Radiation Science, Uppsala University, Uppsala, Sweden

g Department of Physics, Faculty of Science, Kyushu University, Fukuoka, Japan h Department of Physics, University of Jyviiskylii, Jyvi~skylii, Finland

i The Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

Received 28 February 1997; revised 29 August 1997; accepted 9 September 1997

Abstract

Excited states of 56Co were studied in the reaction 27 A1(32 S,2p 1 n)56Co. The NORDBALL array with a Neutron Wall and a Silicon Ball was employed. The excited states were interpreted in terms of particle-hole excitations with respect to the doubly magic N = Z = 28 core. © 1997 Elsevier Science B.V.

Keywords: NUCLEAR REACTIONS 32S(27Al,n2p), E = 95 MeV; measured yy coin, yy(0). 56Co deduced high-spin levels, J, ~r, configurations, particle-hole excitations. Shell model calculations.

1. Introduct ion

Nuclei close to doubly magic shell closures are a subject of extensive experimental

and theoretical investigations. The heaviest doubly magic nucleus with an equal number

of protons and neutrons and with excited states experimentally accessible today is 56Ni.

The shell gap at N = Z = 28 is due to the spin-orbi t lowering of the high-j , f7/2 orbital

from the next major shell. As such, it resembles very much the shell closure in the

region of ~°°Sn. The gap is relatively small, so that the par t ic le-hole excitations across

the gap have relatively low energies and are easier to study than in the case of heavier

0375-9474/97/$17.00 (~) 1997 Elsevier Science B.V. All rights reserved. PH S0375-9474(97)00507-1

M. Palacz et al./Nuclear Physics A 627 (1997) 162-174 163

doubly magic nuclei. Many aspects of the nuclear shell model, applicable also to heavier nuclei, can be tested in the region of 56Ni.

In this paper we present new results on excited states of 56Co. This nucleus, with only one particle and one hole outside the doubly magic core, has a relatively simple shell model structure. The most recent results on 56Co were published in Refs. [ 1,2]. The highest known ,evel had an excitation energy of 5274.6 keV and a spin assignment of 10 +. The available experimental information on 56Co is reviewed in Ref. [3] and additional data on low spin states come from a recent (d, ce) experiment [4]. In the present study, the level scheme of 56Co has been extended up to an excitation energy of 14 MeV and a spin of about 14h. An attempt to interpret some of the observed levels in terms of particle-hole configurations is presented.

2. Experiment

When using heavy-ion induced fusion reactions to reach neutron deficient nuclei far from the line of r-stability around A = 60 many reaction channels are open. With the moderate energy above the Coulomb barrier the relative cross section is largest for nuclei produced with the emission of a few protons. Channels with small proton multiplicity, o:-particle emission and, most important of all, neutron emission, have very small relative cross sections but lead to the most interesting, neutron deficient nuclei around 56Ni. This sets special requirements on the detector system. It should provide means to detect and identify charged particles and neutrons in addition to the usual requirement of having a large yg'-coincidence efficiency.

An experiment with the aim to populate and observe excited states of nuclei in the vicinity of the doubly magic nucleus 56Ni was performed at the Tandem Accelerator Laboratory of the Niels Bohr Institute, Riso, Denmark. The reaction 32S + ZTA1 was used at a beam energy of 95 MeV, leading to the compound nucleus 59Cu. The target consisted of a stack of three thin self-supporting 27A1 foils ordered in decreasing thickness relative to the beam (700, 420 and 320/zg/cm2). The NORDBALL multidetector array [5,6] was equipped with 15 Ge Compton suppressed spectrometers, a Neutron Wall consisting of 11 liquid scintillator neutron detectors [7], a Silicon Ball consisting of 21 silicon AE detectors for the identification of charged particles [8] and 30 BaF2 scintillators for "y-ray multiplicity and sum energy filtering. The BaF2 detectors also provided the time reference for all other signals. The experimental setup is described in more detail in Ref. [9].

The discrimination between protons and ce particles in the Silicon Ball was achieved by means of a hardware threshold on the energy deposited in the A E silicon detectors. The average efficiency for detection of protons was about 60% whereas te particles were detected with an efficiency of about 40%.

The discrimination between 9'-rays and neutrons detected in the neutron detectors was done combining two techniques, namely the pulse shape discrimination based on the zero-cross-over principle and the time-of-flight method. The zero-cross-over time and

164 M. Palacz et al./Nuclear Physics A 627 (1997) 162-174

the time-of-flight signals were stored on tapes and a two-dimensional gate was set on these signals in the off-line analysis (see also Ref. [ 10] ). In this way the discrimination between v-rays and neutrons is improved by an order of magnitude in comparison to a discrimination using one-dimensional gates only. The probability that a ~/-ray was interpreted as a neutron was about 0.5%, whereas the total efficiency to detect a neutron was about 23%.

Totally about 100 million Compton suppressed TT-coincidence events were collected. The trigger condition required two 3,-rays to be detected in the Ge detectors and two ~,-rays in the BaF2 ball. Fifteen different residual nuclei have been identified with a relative population ranging from about 20% to less than 0.3%. The two strongest reaction channels led to 56Co and 56Fe with approximately the same relative population (20% each).

3. Data evaluation

Gamma-rays originating from evaporation residues in a thin target experiment are emitted in-flight and exhibit Doppler shifts, which must be corrected for. In the experiment described here, the compound nucleus is relatively light and the velocity of the evaporation residues is very much dependent on the type, number, direction and energy of the emitted particles. This influences the energy of the observed ~,-rays. Due to the

non-isotropic efficiency for detection of particles, the measured ~,-ray energy also de- pends on the number and kind of particles detected in the Silicon Ball and the Neutron Wall detectors. All this results in a large Doppler broadening of the ~,-ray peaks.

The average velocity of the evaporation residues used for the Doppler correction was determined separately for each evaporation channel, using the uncorrected T-ray peak positions in spectra collected at specific angles. The differences in the average

velocity of the residues for different reaction channels are large, up to 10%. In addition, the method of Doppler correction described in Ref. [9] was used in an attempt to minimize the Doppler broadening of the peaks arising from particle evaporation and to improve the accuracy of the T-ray energy determination. The method includes an event-by-event procedure of Doppler correction using the information from the Neutron Wall and the Silicon Ball on the direction of the emitted particles. For the particular reaction channel leading to 56Co the improvement in peak widths resulting from the event-by-event correction is small, about 5%. Note that more significant improvements were obtained for reaction channels involving a-particle emission [9]. The full width at half maximum of the peaks belonging to 56Co are 8.0 keV at 1094 keV and 20.3 keV

at 2707 keV after corrections. A prompt 3~,-coincidence matrix has been produced with the requirement that one

neutron and one or two protons were detected. This condition was found to be the most favourable for enhancing the 56Co channel. A ~/-ray spectrum gated with one or two protons and one neutron is presented in Fig. 1. Due to the limited efficiency of the particle detectors, the spectra gated with one or two protons contain strong


C t - O t -

O

C~.

¢-

0 o

110

90

70

50

30

10

a )

(D I,

~" Reoction: 32S.(95 MeV) + 27AI LO I Gore: In ond (lp or 2p)

Q)

(1) I-i-

Pc) h ( D

;to o - - Lo ~ - ~ • - - ~ '3 0 0 - - O 0

• , Z - r i D , ~ - -

1 ~-~ 220

× ~ 18o

t -

o"

~ 10o O_

-~ 6 0 C

0 ~ 20

r,-. o

,~i-I'--

t~ r¢ ~ r,-,

r--0o _ t¢31 ¢ )

2000 2400 2 ~ ~200 36oo E, (keV)

Fig. 1. Projection of the yy-coincidence matrix gated with one or two protons and one neutron.

lines from nuclei produced via the emission of three or more protons and also nuclei produced via a-particle emission. On the other hand, the requirement of detecting one

neutron efficiently suppresses reaction channels without neutrons emitted. An example

of a coincidence spectrum is shown in Fig. 2. Gamma-ray spectra and yy-coincidence matrices were analyzed with the aid of the RadWare software package [ 11 ].

The multipolarity of the transitions could, in principle, be determined by analyzing an-

gular correlations and/or angular distributions of y-rays. The angular correlation method

applied to the NORDBALL geometry [ 12] requires that a separate yy-coincidence matrix is analyzed for each of the eight possible geometrically non-equivalent pairs of detectors. Due to the limited statistics of data, such an analysis was not feasible. On the other hand, single y-rays which are necessary for the analysis of angular distributions

were not collected during the experiment. Instead the following method was used. Two yy matrices with one y-ray detected in any detector and the second y-ray detected at

a specific angle with respect to the beam axis (0) were created. There are two non- equivalent 0 angles in the NORDBALL geometry: 79 ° (equivalent to 101 °) and 143 °. Spectra of y-rays observed at the angle 0, gated with the coincident y-ray detected at

any direction, were analyzed. Ratios Rang = 1143/179,101 were then calculated, where 1143

is the intensity of a y-ray line at 0 = 143 ° and 179,101 is the intensity at 0 = 101 ° and 0 = 79 °. Spectra used to determine 1143 and I79,101 are gated by an identical condition for a coincident y-ray transition observed at any angle.

Theoretical angular distributions in such gated spectra have been calculated using

166

35 g-. o

-~ 25! e- c- o t -

o ~. 15

oO O~ tN

M. Palacz et al./Nuclear Physics A 627 (1997) 162-174

Reaction: 32S (95MeV) + 27AI Gate: In and (lp or 2p), 577 keY

p~

00

oJl#~ O0

-t

200 ¢..

(9

r~ 120

(--

o o

4O

I'-.

tDcq e q

CO O~ t"q t r ) tad tO

r-- t o r - - t D - -

rr3

2000 2400 2800 3200 3600

E~, (keY) Fig. 2. Spectrum gated with one or two protons and one neutron and the 577 keV transition.

the geometrical relations of Ref. [ 12] and a program [ 13] based on the formalism of Refs. [ 14-16]. A typical dependence of Rang on the multipolarity of a gating transition is presented in Fig. 3. The dependence is weak, the variations of Rang being smaller than the typical uncertainty in the determination of Rang. Thus, the dependence of Rang on a gating transition can be neglected and each T-ray transition can be characterized by one value of Rang, determined using gates in which the transition in question is clean and relatively strong.

The Rang value is about 1.5 for a stretched quadrupole transition and for about 0.8 for a stretched dipole. Calculated values of Rang for the 11 --~ 10 and 10 --, 10 transitions as a function of the mixing ratios of these transitions are presented in Fig. 4. The gating transition was assumed to be a stretched 10 ~ 8 transition. The values presented in Fig. 4 are typical values expected for transitions analyzed in the present work, assuming a complete spin alignment of the initial state. The measured values of Rang may be distributed between the calculated values and the unity due to an attenuation of the alignment.

The method described above makes it possible to analyze angular distributions using gated spectra and requires much less statistics than a full angular correlation analysis. Together with the fact that a state, in many cases, decays with several branches, it gives the most probable spin assignments. However, the method still suffers from the fact that the Ge detectors in NORDBALL are situated at only two non-equivalent angles with respect to the beam axis, so a determination of the A2 and A4 angular distribution


1.6

o Or ~

1.5

o) i l l l h l l l l l l t l l , l ~ l l l l l l l l j J I I J i l l * l J l l l l l L

- 1 - O 5 0 O5 1 • (~gote "

gate 1 0 - - ) ' 8

E2

0.8

0.7

b) I L l ~ l l l l l l l l l , , , i , J , l l l l l l l l l l l I J l l l l , l l l l

-1 -O .5 0 0.5 1 (~gote

gate 1 0 - - - > 8

E2

Fig. 3. The Rang value of (a) a stretched quadrupole ( 12 ~ 10) transition and (b) a pure stretched dipole transition ( 11 ~ 10), as a function of the mixing ratio of the gating transition, t~gate. The gating transition is a mixed 10 ~ 9 dipole/quadrupole (the left-hand part of the plots) or a stretched quadrupole 10 --~ 8 (the right-hand part of the plots).

coefficients is not possible. Only for the special case of Rang < 1.0 the firm conclusion can be drawn that a spin difference of 2 between the states is excluded. Thus, the results of the method are ambiguous, and all new spin assignments presented in this work are

tentative.

4. Results

The level scheme of 56Co constructed in this study is presented in Fig. 5. The information about the observed T-ray transitions is summarized in Table 1. The placement of most of the transitions in the level scheme is firmly established by coincidence relation- ships. The few transitions which have less certain placement are marked with dashed lines. The width of the arrows is proportional to the intensities of transitions as seen in the reaction studied here. Wherever possible, the intensities have been determined from the projected spectrum. This, however, was only possible in the case of the strongest lines. The relative intensities of weaker transitions, with respect to the strong ones, have been deduced from coincidence spectra. The proposed spin assignments are discussed below. Only magnetic dipole and electric dipole and quadrupole transitions are consid- ered. Note that the Shell Model does not predict negative parity states in 56Co within the excitation energy and spin limits of this work (see the discussion section below).

168 M. Palacz et al. /Nuclear Physics A 627 (1997) 162-174

r Y

1.5

1

0.5

1.5

o

6 6

0--> loj/ b)

o5. ' 4 - -'J 6 2 6

Fig. 4. The Rang value as a function of the mixing ratio of (a) an 11 --, 10 and (b) a 10 --~ 10 transition. The gate is set on a stretched ( 10 --~ 8) quadrupole transition.

The two previously published studies of 56Co gave contradicting spin assignments for

the 4179 keV level, namely 8 + [ 1] and 9 + [2] . The results of the present work with

respect to this spin assignment are not conclusive, either. The Rang value for the 1897 keV

transition is equal to 1.33 5:0.09. This allows either a stretched E2 transition or a M1/E2

mixture. However, the angular distributions of the 542 keV and 1355 keV transitions

measured in Ref. [2] , suggest that the correct spin assignment for the 4179 keV level

is 9 + and this value is adopted in Ref. [3]. The 542 and 1355 keV transitions, were

not observed in Ref. [ 1 ]. In the work of Ref. [2] it was reported that the shape of the 1355 keV Doppler

broadened peak was changed, as the beam energy was increased. This was interpreted as an indication of a direct population of the 3637 keV level by particle emission.

These shape changes could have a simpler reason, namely the growing intensity of the

previously unknown 1352 keV transition as the beam energy was increased.

Continuing above the 10 + state at 5273 keV, the Rang values obtained for the 2707

and 656 keV transitions are significantly below 1.0 and thus exclude the possibility that d l is equal to 2. The Rang value obtained for the 1156 keV transition is less conclusive,

being slightly different in different gates. In Table 1 the value obtained in the cleanest, 2707 keV, gate is given. We expect that a stretched E2 transition positioned relatively

M. Palacz et aLINuclear Physics A 627 (1997) 162-174 169

14046

1389 126571

11799 11934 11767 I --~1190 T 11273 V I --1--- [ ~11467--~L--~-

1 18!6 10216 3! j1~ 7 1 9 ! 8 2 7 1 ~ ; 9 J 8 ~ 5 5 3 3 :73 , l , 9z8 _I_ 3) 11 12434

( 13 ) 1 9378 --^~ ,,~o I / . . . . . . . . . . . . 1920 I • ~)~¢~-~ L:~" 1156 I I 1#52 2886 (11~T Sa~.3 1 (':~ . . . . . J J ! 02 +) ! 8026 8525~ I 7977656 01)

I 1,2 +" I 7330] I I 650 I ~ I ~37634 1172 ( ) I ~ 956 (11 + ' I 6854 I I q38163'. _7 1734-4- 14o2 X 70231 I 63,07005

, • I 3253 I 7 / o04 6. 1620227 2 20128 I I 5739 (9 +) | 14.~4~t ~ I I 3113 / 19.91 / 2015 f

2~oa23 °t~ ......... l l~ t ! 52731 1 I / 1¢1o+ ) 15174 [49912918 4470 211oll I + I 154 . . . . 1 2 9 7 4 - - ~ 3 2 89--~-Q | I

I I 9 1635 41/~ 88 904 T34861 ' I [ 1394 l ~ l - ~ 0 8 7 1

21818 ] ' 9 ~ ~ , , 0106t1/17~791 i

I ~ q 1274 1794 1361 [ ! l . - . 5+1 1009 19702 +

8+ I 577 432 ...... I . . . . . . . . . . . oz , , .=~= 4~ T ' 1009 ~,.-'~ 671 . + 812

5% Fig. 5. Level scheme of 56Co.

high in the level scheme and thus exhibiting large spin alignment should have a Rang

value larger than 1.2. This is not the case for any of the values obtained for the 1156 keV

transition. The spin values of 11, 12 and 13 are, thus, tentatively assigned to the states at 7977, 8633 and 9789 keV, respectively.

A d l = 2 value for the 2023 keV transition feeding the 9 + level at 4179 keV is excluded. On the other hand, the 2674 keV transition feeding the same level has an Rang value in good agreement with a stretched E2 transition. The value obtained for the

651 keV line is not conclusive, but it is rather too low for a stretched E2 transition. The 464 keV transition is not a stretched quadrupole, whereas the Rang value for the

3455 keV transition suggests a stretched E2 character of this transition. Thus, we assign spin and parity of 9 +, l0 + and 11 + to the 5739, 6203 and 6854 keV levels, respectively. The 1172 and 1352 keV lines have values of Rang similar to the value obtained for the

651 keV. Again, we expect larger Rang values for high-spin E2 transitions. The 2752 keV transition is likely a stretched quadrupole. We therefore assign spins 12, 13 and positive parity to the 8026 and 9378 keV levels, respectively.

We assign AI = 2 to the 2058 and 1394 keV transitions giving spins and parities 12 + and l0 + for the 7330 and 5032 keV levels, but the possibility that these transitions have


Table 1 Gamma-ray transitions assigned to 56Co. The transition energy (E~,), the excitation energy of the initial level (Ei), the initial (Ji) and the final spin ( J f ) , the intensity of the transition ( I t ) and the Ran~ values are presented. The uncertainty of E;, ranges from about 0.03% for the strongest transitions to about 0.15% for the weak ones

E- r Ei Ji ~ J f 1~, Rang

158.0 179.2 297.6 343.0 432.5 463.6 541.6 576.5 630 630 651.4 656.5 671 745.0 812 890 903.8 914 928 956

1009 1094.1 1155.7 1172.0 1190 1273.6 1352 1354.8 1360.7 1389 1394.2 1405 1419 1635 1678 1706.0 1717 1793.7 1896 1896.7 1920 1978 1991

158 3 + ~ 4 + 4.3 i 0.5 1009 5 + ~ 4 + 0.5 -t- 0.2 4087 0.6 -]- 0.1 0.79 -4- 0.14 7977 ( 11 ) ~ 2.3 4- 0.3 1009 5 + ----+ 5 + 0.8 4- 0.3 1.33 4- 0.47 6202 (10 +) ~ (9 + ) 2.54-0.3 0.594-0.07 4179 9 + ~ 8 + 28 4- 3 0.91 4- 0.02

576.5 5 + ----+ 4 + 100 -k- 10 0.84 4- 0.01 7977 ( 11 ) ----+ 1.3 4- 0.5 7634 1 4- 1 6854 (11 +) ~ (10 +) 124-2 1.084-0.04 8633 (12) ~ (11) 154-2 0.904-0.03

829 4 + ----* 3 + 1.6 4- 0.5 4288 4.3 4- 0.6

970 2 + ~ 3 + 0.7 4- 0.2 5179 4.0 4- 0.4 4991 6.54-0.7 0.764-0.11

11467 0.84-0.1 6202 ( 10 +) ~ 10 + 1.9 4- 0.2 7977 ( 11 ) ~ 0.5 4- 0.2 1009 5 + -----*4 + 1.1 4-0.2 0.724-0.08 5273 10 + ---* 9 + 41 4- 4 0.94 q- 0.02 9789 (13) -----* (12) 7.94-0.8 0.834-0.11 8026 (12 +) ~ (11 +) 194-2 1.204-0.04

12 657 2.0 4- 0.3 2283 7 + - - ~ 5 + 3.9 4- 0.4 1.29 4- 0.17 9378 (13 + ) ~ (12 + ) 84-5 1.134-0.12 3637 8 + ~ 7 + 47 4- 6 1.32 4- 0.02 2370 4.6 4- 0.5

14046 <0.5 5032 (10 + ) -----~ 8 + 7.34-0.8 1.47 4- 0.21 7977 (11) ~ 1 4- 0.5 3791 2.4 4- 0.3 5273 10 + ~ 8 + 3.1 4-0.8 1.364-0.20

11467 -----* (13) <0.5 2283 7 + ----~ 5 + 1074- 10 1.17-t-0.04 4087 5 + 2 2370 ----~ 5 + 94- 1 1.044-0.15

11273 ~ (13 + ) 24- 1 4179 9 + ----*7 + 554-6 1.334-0.03

10553 ---* (12) 1.3 4- 0.2 11767 -----*(13) 1.14-0.2

7023 ---* ( 10 +) 1.5 4- 0.2


Table 1 - - continued

Er ei Ji ~ & I r 8a.g

2006 4288 ---* 7 + 4 + 1 2015 7005 0.8 4- 0.2 2023.3 6202 ( 10 +) ~ 9 + 13 4- 2 0.84 4- 0.05 2058 7330 (12 + ) ~ 1 0 + 5.94-0.6 1.284-0.10 2101 5739 (9 +) -----, 8 + 2.04-0.2 2147 11936 ~ (13) 0.9-4-0.1 2188 4470 ----~ 7 + 1.94-0.3 2643 7634 1.6 4- 0.2 2674 6854 (11 +) ----*9 + 144-2 1.274-0.07 2707 7977 (11) ~ 10 + 134-2 0.704-0.03 2752 8026 (12 +) ~ 10 + 2.24-0.3 1.23-I-0.15 2782 3791 ~ 5 + 1.1 4- 0.2 2798 7977 (11) ~ 0.54-0.1 2834 11467 ~ (12) 1.74-0.3 2868 12657 ~ (13) <0.5 2886 10216 ~ (12 + ) 1.3 4- 0.4 2918 7005 <0.5 2934 6572 ------, 8 + 1.8 4- 0.2 2967 3543 ---* 5 + 6.4 4- 0.7 3173 7349 ~ 9 + 2.7 4- 0.3 3253 8525 (11) ----* 10 + 1.64-0.3 0.734-0.16 3303 11936 ---* (12) <0.5 3455 5739 (9 + ) ----+7 + 2.24-0.3 1.304-0.47 3773 11 799 2.0 4- 0.2 3816 9088 ---* 10 + 2.2 4- 0.3 3927 9199 ~ 10 + 1.4 4- 0.5

171

a m i x e d E 2 / M 1 cha rac t e r and AI = 1 c a n n o t be exc luded. The 3253 keV t r ans i t ion

c a n n o t be a s t r e t ched E2, so the spin va lue o f 11 is p roposed for the 8525 k e V level.

N o t e tha t s o m e o f the obse rved t r ans i t ions have an energy o f a lmos t 4 MeV, w h i c h

is the m a x i m u m o b s e r v a b l e ene rgy in the e x p e r i m e n t desc r ibed here. I f t r ans i t ions o f a

yet h i g h e r ene rgy pa r t i c ipa te in the deexc i t a t ion p rocess o f the d i sc re te levels o f 56Co,

they have r e m a i n e d u n o b s e r v e d in ou r exper imen t .

5. D i s c u s s i o n

A full shel l m o d e l ca lcu la t ion for 56C0, i nc lud ing the f7/2, f5/2, P3/2 and Pl/2 shel ls

for p r o t o n s and n e u t r o n s is ou t o f ques t ion due to the large s ize o f the numer i ca l

p r o b l e m . Ins tead , o n e m a y l imi t the ca lcu la t ion by exp lo i t i ng the par t ia l shel l c losu re at

n u c l e o n n u m b e r 28, af ter the f7/2 shel l has been filled. In such a ca lcu la t ion , 56Ni is

c o n s i d e r e d as a d o u b l e - m a g i c core, and the lowes t levels in 56C0 wou ld be cha rac te r i zed

as o n e - p a r t i c l e - o n e - h o l e ( l p l h ) states, w i th one neu t ron par t ic le in one o f the f5/2, P3/2, Pl/2 she l l s and o n e p r o t o n ho l e in the f7/2 shell . H i g h e r s tates w o u l d be f o r m e d by

exc i t ing a s e c o n d f7/2 nuc l eon up in to the f sn , P3/2, PU2 she l l s to give a two-par t i c l e -

t w o - h o l e ( 2 p 2 h ) state, and sti l l h i g h e r s ta tes by add i t iona l exc i t a t ions across the shel l

172

2357

0 + 1 +


247~P ,/2 :f }/2 2290.-" 2370 Vf s/2~f 7 ~

",,2060, i - - , t t

, i I

i I

',1115 1009, 970, "", 829.."

", 577 vP3/27cf71 ", 158. 0 '"'

2 + 3 + 4 + 5+ 6+

Fig. 6. lplh excited states in 56Co.

gaps. Such a classification scheme may form a convenient basis for a limited shell model

calculation, by providing a natural truncation scheme in terms of the maximum number

of nucleons allowed to be excited from the f7/2 shells. A crucial question concerns

the magnitude of configuration mixing between basis states with different numbers of particles and holes. We believe that such mixing is not so large as to invalidate the classification scheme. However, the mixing with certain excitations of the 56Ni core,

such as the lowest 2 + state, would probably have large influence on the calculated energies. Therefore, we have refrained from making a large shell model calculation, and

instead try to interpret some of the lower yrast levels of 56Ni, using general arguments

and comparisons with known levels in neighbouring nuclei.

5.1. l p l h states

The level schemes of 57Ni and 55Co show that the low-lying single particle levels

uP3/2, vfs /2 , vpt/2 and 7 r f ~ are well separated in energy from the next higher levels of mainly 2plh and lp2h nature. This makes it reasonable to try to interpret the levels in 56Co below about 3 MeV, as lp lh states belonging to the three multiplets vP3/2~fT-/12 ,

ufs/zTrfT-/~ and upl/21rf~12 . An attempt of this kind is shown in Fig. 6. Levels both observed in the present work and unobserved here but known from other studies [ 3 ] are included. The assignments for the lowest seven levels are relatively clear, but we do not claim that configuration mixing between the three multiplets is necessarily small. The assignments for the five levels above 2 MeV is more questionable. Note that it was not possible to assign a definite spin value to the level at 2370 keV in our experiment. In fact, these l p lh states occur at similar energies as states of the 2p2h nature, starting with a 0 + level at 1451 keV. Such 2p2h states can be brought down in energy by strongly attractive interactions in the two-particle and two-hole channels.

M. Palacz et aL/Nuclear Physics A 627 (1997) 162-174 173

5.2. 2p2h states

Energetically favourable 2p2h yrast configurations are obtained by lifting a neutron from the f7/2 shell. Such an excitation allows for the coupling of the neutron and proton holes to the maximum spin of 7 + . This maximum-spin, two-hole configuration corresponds to the low-lying I 'r = 7 +, T = 0 state in 54Co at 199 keV. This state, when combined with the two-neutron-particle configuration of the I ~ = 0 +, T = 1 ground state of 58Ni, must correspond to the 7 + state of 56Co at 2283 keV. Similarly, the 8+(3637)

and 9+(4179) states are most naturally described as the 7 + two-hole configuration coupled to the pr = 2 +, T = 1 first-excited state of 58Ni at 1454 keV. The larger

spacing 9 + to 7 + in 56Co, compared to the 2 + to 0 + spacing in 58Ni, can be ascribed

to the larger P3/2 particle-fT/2 hole repulsion for maximum alignment of the angular momentum vectors. Continuing upwards to higher energies and spins, the assignments soon become ambiguous. The 10 + (5273) state probably corresponds to the coupling of the 7 + two-hole configuration to the I ~ = 4 +, T = 1 state of 58Ni at 2459 keV. The 11 +

maximum-spin state of the same type has no obvious experimental counterpart.

5.3. 3p3h states

In the same energy region above 5 MeV, where the 2p2h high-spin states become

scarce, one expects to find yrast 3p3h states, in particular those built on the three-hole state with the 1'~ =T19 - , T = 3,1 which occurs as an yrast trap in 53Fe at 3041 keV. When

combined with yrast three-particle states in 59Cu, which are formed by putting the parti-

cles in the P3/2 and f5/2 shells, e.g. the 3 - ground state and the 7 - (1399) , ~ - ( 2 1 8 7 )

and the ~ - ( 3 4 4 8 ) states, this gives rise to a multitude of high-spin, positive-parity states in 56Co. It is tempting to associate the experimental 9+(5739), 10+(6202) and 11+(6854) levels in 56Co with those states arising from the 3 - particle configuration, and possibly the 12+(8026) and 13+(9378) levels in 56Co with those arising from the

higher particle configurations. In view of the complexities of the states and the large

number of two-body interactions in a 3p3h configuration, in order to make a meaningful

calculation it would be necessary to fit some of the crucial interaction matrix elements to a larger body of experimental energies, including levels in neighbouring nuclei with the same active shells.

6. Conclusion

The level scheme of 56Co has been considerably extended. Some of the low-lying levels have been classified in terms of one-particle-one-hole and two-particle-two-hole configurations in respect to the doubly magic 56Ni. The classification was done on the basis of a qualitative reasoning and a comparison to neighbouring nuclei. Better experimental information on nuclei in the region of 56Ni, and more precise experimental spin assignments in 56C0, as well as the determination of two-body interaction matrix elements are needed in order to identify and assign higher-order excitations.


Acknowledgements

This work was part ial ly supported by the Swedish Natural Sc ience Research Counci l ,

the Pol i sh Scient i f ic Research Commi t t ee , the Academy of Fin land and the Danish

Natural Sc ience Research Counci l . The excel lent cooperat ion o f the staff o f the Tandem

Acce le ra tor Labora tory o f the Nie ls Bohr Inst i tute and the assistance o f the group f rom

Cha lmers Univers i ty o f Technology with the preparat ion o f the neutron detectors is

appreciated.

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in-beam γ-ray spectroscopy of 56co

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