A study of 57Co by the 56Fe(p, γ)57Co reaction

Nuclear Physics A153 (1970) 593-609; ( ~ North-Holland Publishin# Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permissionfrom the publisher I

1.E.1

A S T U D Y O F STCo BY T H E S6Fe(p, ?)STCo R E A C T I O N B. J. O'BRIEN and G. E. COOTE Institute of Nuclear Sciences, Lower Hutt, New Zealand Received 20 April 1970 Abstract: The yield curve for the SaFe(p, ~')57Co reaction was measured for proton energies from

1210 to 2575 keV. Gamma-ray spectra were measured with a Ge(Li) detector at 14 resonances and angular distribution measurements made at 5 resonances. A Q-value for this reaction of

6026.74-0.7 keV was obtained. The angular distributions were analysed to give the following J~r(keV) assignments of STCo bound states and resonance levels: J(1224) = ~, J~r(1757) = ~-, J~(1897) = ~-, J(1919) = ~, J(2132) = ~, J(3850) = ~, J(3989) = ~, J~(7252) = ~-, J~ (7266) = ½-, J(7523) = ~+, J"(7632) = ] - and J~(8192) : ~+. From spin assignments, the resonance E~ = 1262.1 keV was identified as the isobaric analog of the 57Fe ground state. A Coulomb displacement energy for ~7Co--57Fe of 8881.54-6.0 keV is deduced. The low-lying energy levels are examined with respect to the centre-of-gravity theorem. NUCLEAR REACTION 56Fe(p,),), E = 1.210--2.575 MeV; measured tr(E). 56Fe(p,7) E = 1.247--2.204; measured cr(E, Ey, 0), E7, Q. 57Co deduced levels, isobaric analog resonances, J, :~, t~. Enriched target.

I

[

I

1. I n t r o d u c t i o n

I n recent years several investigations o f the energy levels o f 57Co have been r e p o r t e d . T h e (3He, d), (t, ~), (~, p), (p, ~) a n d (p, 7) reactions have all been used to excite the 57Co nucleus 1-7). I n a d d i t i o n , a n u m b e r o f high resolution studies o f the fl+ decay o f SVNi have been m a d e 8-1o). H o w e v e r , uncertainties in the spin assignments o f several low-lying levels o f 57Co still exist. T h e level structure o f 57Co is o f some theoretical interest since the low-lying level structure is n o t in g o o d a g r e e m e n t with simple shell-model p r e d i c t i o n s 11,12). T h e use o f m o r e c o m p l i c a t e d m o d e l s including a greater a m o u n t o f configuration mixing o r the coupling o f core excitations with single-particle states has been necessary to p r o d u c e even an app r o x i m a t e similarity with the e x p e r i m e n t a l energy levels 13-15). I n the present w o r k the 56Fe(p, ~)57Co r e a c t i o n was used to determine the exc i t a t i o n energies a n d spins o f the low-lying levels o f STCo. A n excitation curve was o b t a i n e d for incident p r o t o n energies f r o m 1210 keV to 2575 keV. H i g h r e s o l u t i o n ~,-ray spectra have been m e a s u r e d at f o u r t e e n resonances using a G e ( L i ) detector. F r o m a n g u l a r d i s t r i b u t i o n m e a s u r e m e n t s m a d e at five resonances the spins o f these resonances a n d seven b o u n d states o f 57Co were deduced. 593

594

B.J.

O'BRIEN AND G. E. COOTE

2. Experimental procedure Protons, accelerated by the 3.0 MV Van de Graaff accelerator at the Institute of Nuclear Sciences, were passed through an analysing magnet which was controlled by a beam stabilising unit, capable of keeping the energy of the analysed protons ~6) constant to within ___0.20 keV. Targets were made from enriched 56Fe supplied by AERE, Harwell; its isotopic composition being 56Fe 99.95 ~ , S4Fe 0.04 ~ , 58Fe 0.01 ~ . These targets which were about 10 #g/cm 2 thick were prepared by evaporating the s 6Fe onto a 0.25 mm tantalum backing. The angular distribution measurements were made using proton currents of 20 to 40/~A and for these experiments the target was water cooled. A 12.5 x 15 cm NaI detector, placed at 90 ° to the proton beam and 18 cm away from the target, was used to monitor the reaction. Amplified pulses from the NaI detector were passed through a discriminator set at 3.7 MeV and then into a scaler and rate meter. A beam current integrator was used to measure the accumulated charge on the target. Gamma-ray spectra were recorded using a 30 cm 3 Ge(Li) detector, a Tennelec preamplifier, an Ortec 410 linear amplifier and a Kicksort 4096-channel analyser. An automatic gain stabiliser unit was used to control the gain and the zero of the detector-amplifier-analyser system. The stabiliser was locked on to the 511 keV annihilation peak at the lower end of the spectrum and to pulses from a precision pulser at the upper end of the spectrum. The Ge(Li) detector was mounted on a rotatable arm with the front of the detector at 3.5 cm from the centre of the target. The beam spot was centred on the target by using four micrometer adjusting probes for determining the beam position just in front of the target. In this way the beam spot on the target could be centred with respect to the y-ray table to about 0.1 cm. Final correction factors were determined using data from an isotropic angular distribution. For determining angular distributions, data were accumulated for a fixed count on the NaI monitor. Lead absorbers of 0.3 cm thickness were placed in front of both detectors in order to reduce the large low-energy count rate caused by bremsstrahlung and Coulomb excitation in the tantalum target backing. A standard N M R fluxmeter was used to calibrate the beam energies. By moving an aluminium target into the beam in front of the 56Fe target, resonances in the 27Al(p, 7)28Si reaction were used to precisely check the calibration of the analysing magnet during the experiments.

3. Analysis of data The spectra recorded on the multichannel analyser were analysed with the aid of a PDP-8 computer. The positions of peaks in the pulse-height spectrum were accurately determined by fitting a curve to each one. The number of counts in each peak was determined by subtracting a fitted linear or quadratic background.

561~e(p, ~')57CO REACTION

595

To determine the intensity of closely spaced doublets, two Gaussian curves were simultaneously fitted. Gamma-ray energies were determined from measurements made at 90 ° to the proton beam. The energy calibration was determined by using a least-squares polynomial fit program (similar to that described by Wolff et al. 17) for which the input data consists of energies from calibration sources, position of fullenergy, single and double escape peaks, and the requirement that the energies o f yrays emitted in cascade add up to the excitation energy of the resonance. For precise energy calibrations, 228Th, 6 ° C o and SSy sources were placed near the target while the 57C0 spectra were accumulated. The y-ray energies for these sources reported by Marion 18) were used in the calibration. At the higher proton energies the 6129.3 keV 7-ray from 160 was present, and was also used as a calibration point. All 7 rays excited at the Ep = 1262.1 keV resonance displayed the same angular distribution indicating that the true angular distribution was isotropic. Small variations in yield with angle found at this resonance (due to the target being off centre) were therefore used to correct all other data. The Ge(Li) detector used had a trapezoidal cross section. The analysis of angular distributions made with such a detector is a little more complicated than when a cylindrical detector is employed. As a detailed analysis will be published elsewhere 19), we shall here only outline the method. For a trapezoidal detector with a symmetry plane perpendicular to the reaction plane, the correlation function is given by;

W(O) = [l + ~A2 Q2z + ~-~a,2 A4 l + P2(cos O)[Q2A2-~Q22 A2 + ~Q42 A4] +P4(cos O)[Q4A4-½Q42A4] , where

Ak = Bk(Jt)Rk(J1J2) for no unobserved radiations and

Ak = Bk(J1)U~(J1 J2)Rk(J2 J3) for one unobserved radiation, with

Rk(J1 J2) = [Rk(F-,£J1J2) + 2tsRk(£LJ1J2) + t52Rk(LLJx J2)]/( 1 + t52), --_

where t5 and 3 are multipole mixing ratios. The notation used is that of Rose and Brink 20), where tables of the Uk and Rk coefficients can be found. The attenuation factors Qz, Q22, Q4 and Q4z [ref. 16)] were computed on a PDP-8 computer. A computer program was also used to calculate Qz, where Qz = ~ i Wi(N'~~p-N~h)z/ (n--2), N7 xp is the number of counts at angle 0i, N~h = CW(Oi), Wi is the inverse squared error of )Vie~p and n is the number of angles at which measurements were made. This method has been described in greater detail by Wolff et aL 21). The value of Qz was plotted against the multipole mixing ratio t5 for a number of possible spin assignments, for each transition studied. Values of Z 2 = Qmi~ 2 were determined, together with the values of the mixing ratio t5 and its error At5 at each minimum.

596

]}. ~'. O ' B R I E N

AND

G.

E.

COOTE

4. Results

4•1. EXCITATION CURVE The excitation curve obtained shown in fig. 1, extends from 1210 keV to 2575 keV in steps of about 1 keV. The part of this excitation curve between 1300 and 1800 keV has also been reported by August et aL 6). Over this region the results appear similar except for the broad resonance that we observed at 1370 keV and a strong narrow resonance at 1747 keV due to the presence of 13C. We extended the excitation curve 2

"~

r~eF'e(P' ¥) STC°

i/ii

;

..-, ...... j).:

...

....:-,,.

13

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,

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1.5

1.6

0 ~2

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1.6

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17

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~ ,,~ A i

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--

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'

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2'3

'

22

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1.9

210

2' 4

2

'~

h

PROTON ENERGY (MeV)

Fig. 1. Yield o f g a m m a rays o f energy greater t h a n 3.7 M e V plotted against energy• A n g u l a r distributions were m e a s u r e d at t h o s e r e s o n a n c e s m a r k e d with a n asterisk• T h e n a r r o w resonance at 1747 keV is f r o m 14N.

down to 1.21 MeV to include the isobaric analogue of the 57Fe ground state• Altogether, some 153 distinct resonances were observed. The energy of the resonance at about 1260 keV was accurately determined, by comparing the position of this resonance with that of the 1.262.2__ 0.3 keV resonance occurring in the Z7Al(p, 7)2ssi reaction 22). In this way the energy of the resonance was determined to be 1262.1 __+0.5 keV.

Srre(p, y)S?co REACTION

597

G a m m a - r a y spectra were recorded with the Ge(Li) detector at the following 14 proton resonances; 1247.9, 1262.1, 1267.6, 1523.4, 1620, 1634.5, 1648, 1786, 1930, 2064, 2204.2, 2270, 2311 and 2534 keV. In may cases the spectra obtained were very similar and of these only five resonances were chosen for angular distribution and branching ratio measurements. 4.2. DETERMINATION OF EXITATION ENERGIES G a m m a - r a y s of energy less than 2000 keV were recorded on art expanded scale, which enabled the doublet at 1900 keV to be completely resolved, and the energies

,'~. I

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I

l

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1

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l

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I

.

-.ll -

I

,

,

CHANNEL NUMBER

Fig. 2. Gamma-ray spectra obtained with a Ge(Li) detector at three resonances. Between peaks the points shown represent the average of 4 channels. Energies marked with 1 or 2 dashes refer to single escape and double escape peaks respectively. The peak at 439 keV is from 2aNa and that at 846.9 from ~rFe. determined to ___0.3 keV. For ?-rays of higher energy the accuracy was +__1.0 keV for the stronger transitions. Fig. 2 shows )'-ray spectra obtained at the 1262, 1634 and 2204 keV resonances. Using the measured ),-ray energies of direct ground state transitions and cascades to the ground state, together with the accurately determined proton energies, Qvalues were determined at five different resonances; the mean Q-value was 6026.7+0.7 keV. This is well within the error limits of the Q-value based upon the 1964 mass table 23) which is 6022.5-t-6.1 keV. In table 1 the energies deduced in this work are compared with the levels of s 7Co determined by other reactions.

598

B.J.

O'BRIEN AND G. E. COOTE

TABLE 1 Energy levels (in keV) of STCo from reaction data compared with those deduced in the present work 54Fe(~,p)

5aNi(t, ~)

0 1219 1374 1502 1679 1747 1896

0 1218 1369

2127 2305 2483 2511 2550 2606 2730 2794

2130 2303 2489

a)

2870 2980 3111 3165 3248 3343 3389 3436 3533 3613 3662 3696 3760 3834 3899 3973 4028 a) Ref. 2).

b)

1683 1747 1890

56Fe(aHe, d) o) 0 1379 1506 1763

2129 2309

2591 2721

2970

2880 2978

3171 3259 3354

3176 3259 3355

6°Ni(p, ~) ~) 0 1222 1375 1502 1687 1754 1894 1917 2127 2307 2481 2520 2559 2608 2727 2803 2880 2979 3111 3182 3271

Deduced from 57Ni(fl+ -~) o)

Deduced from present work

0 1223.5±0.4 1377.64-0.2 1504.74-0.3

0 1224.04-0.3 1378.1 4-0.3 1505.3 4-0.4

1757.64-0.2 1896.54-0.4 1919.54-0.2 2132.94-0.3

1757.54-0.3 1896.44-0.3 1919.54-0.3 2132.04-1 2479.0i 1 2514.04-1

2730.64-0.2 2803.94-0.2

3176.9±0.3 3269.8±2

3431.14-2 3536.04-2

3456 3539

3682

2614.54-1 2733.6i2

3651 3703 3850.7±2

3906 3989.0-4-1

4003 4038 b) Ref. s).

~) Ref. 1).

d) Ref. 4).

~) Ref. 9).

4.3. A N G U L A R DISTRIBUTIONS A n g u l a r d i s t r i b u t i o n m e a s u r e m e n t s w e r e m a d e at the Ep = 1248, 1262, 1523, 1634 a n d 2204 k e V r e s o n a n c e s u s i n g t h e G e ( L i ) d e t e c t o r . A t the 1523 k e V a n d 1634 k e V r e s o n a n c e m e a s u r e m e n t s w e r e m a d e at t h r e e angles a n d at five angles f o r t h e o t h e r r e s o n a n c e s . All y-rays e x h i b i t e d an i s o t r o p i c a n g u l a r d i s t r i b u t i o n at t h e 1262.1 k e V r e s o n a n c e . A c o m p a r i s o n , m a d e w i t h the N a I d e t e c t o r , o f t h e a n g u l a r d i s t r i b u tions o f y-rays f r o m the 1267.6 k e V r e s o n a n c e w i t h t h o s e f r o m the 1262.1 k e V r e s o n a n c e , s h o w e d t h a t the y-rays f r o m the 1267.6 k e V r e s o n a n c e d i d n o t h a v e a n isotropic distribution.

599

56Fe(p, }')57Co REACTION

The variation of Q2 with the multipole mixing ratios is displayed in figs. 3, 4 and 5 for transitions arising from the 2204, 1634 and 1523 keV resonances respectively. The results are summarized in tables 2 and 3 which shows the probabilities that Z2

5eFe (p,T)Src 0 Ep= 2204.2 keV I

....~.....~..:...::~..:<~ .........

10I

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k

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---:-~-

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;

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keY

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~

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........ ~.I/

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. -. .;.:. .". . ~. . .-. ... .........

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I -60

] -30

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I

[

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.

Io ~

' 1 8 9 6 . 4 . _ . 1224.0 keV ,,i i

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k.k-,"

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~922---'~1919.5 keV 5/2-----~J i

i 30

60

90

-90

-6O

.-

i

r

i

I

-3O

0

30

6O

90

tan"~ F i g . 3. A p l o t o f Q= a g a i n s t t h e m i x i n g r a t i o 6 f o r t r a n s i t i o n s e x c i t e d a t t h e Ep o n a n c e . F o r t r a n s i t i o n s w i t h 1J1 - - ] 2 1 > 1, 6 is a s s u m e d z e r o .

2204.2 keV res.

exceeds the measured values. These probabilities were determined from a table of the chi-squared distribution 23). In transitions where IJ 1 - J z [ > 1, zero multipole

600

B . J . O~BRIEN AND G. E. COOTE

mixing was assumed and t5 was taken as zero. The spin assignment for each resonance is based upon the angular distribution results of table 2, together with the measured branching ratios. For making these assignments, spins of ~}- and ½- are assumed for the 1378 keV and 1505 keV levels respectively, as measured by Konijn et al. 24) and other workers 6). These spin assignments are then used in analysing the angular distributions for transitions between the resonance and low-lying levels of 57Co. In analysing those cascades where the primary y-ray is unobserved, the mixing ratio used in computing U(J1J2) was that determined from the angular distribution of the primary transition. The mixing ratios and adopted spins are shown in table 4. 4.4. B R A N C H I N G

RATIOS

Branching ratios were determined for transitions from five resonances and from several low-lying levels. In order to nullify the effects of the P2(cos 0) and P4(cos 0) terms in the angular distribution, a normalized yield N was determined using the yields at three angles, 0 °, 45 ° and 90 ° to the beam axis. The normalized yield was given by N--- 0.067 N(0°)+0.533 N(45°)+0.4 N(90 °) where N(O) is the yield at angle 0. The branching ratios are shown in fig. 6. The relative accuracy is in the range 5 to 10 % except for very small values where the error is larger. The branching ratios given for transitions from the Ep = 1262.1 keV resonance can only be regarded as relative as there were several, small unidentified peaks around 4 MeV that were not included in the total transition strength. 4.5. S P I N S O F T H E R E S O N A N C E S

For the 8192.2 keV resonance, the angular distribution results in table 2 allow only the spin-~r assignment. The strong transition to the ~- ground state, together with the anisotropy of the angular distributions rule out a spin-½ assignment. The proton penetrability at 2200 keV on 56Fe is about 10 -4 for an lp = 3 resonance as against 10 - 3 for an Ip = 2 resonance. As this is a very strong resonance an assignment Ip = 2 seems more likely. Such an assignment is also supported by the small multipole mixing ratios measured for transitions from this resonance to the ground state and to the 1378 keV state of 0.004_ 0.008 and 0.01 +0.02 respectively. Using the Weisskopf estimates for single proton states one expects a mixing ratio of 0.005 for an E l / M 2 transition but 0.14 for an M1/E2 transition. With any E2 enhancement the latter value would be even larger and well outside the experimental limits. Assuming E l / M 2 transitions from the 8192 keV resonance determines the parity of this resonance as positive. The spin and parity of this resonance is therefore taken to be zs+ . It can be seen from table 2 that the angular distribution results allow only a spirt assignment of ~ or ~ for the resonance at 7632.5 keV. No transition to the ground state is observed but there is a strong transition of 13 % to the ½- level at 1505 keV, which strongly favours the ~t assignment. The magnitude of the multipole mixing ratios for transitions from this resonance also are consistent with M1/E2 transitions.

601

5 6 F e ( p , 'F)57Co REACTION

We therefore adopt an assignment o f ~ - for this resonance in contrast to the } ÷ assignment o f August et al. 6). ~eFe

(p .r)57C0 keY

Ep= 1634.5

o;,--:--~ ........./ I,

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I,,

0

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30

60

90

Fig. 4. A plot of Q2 against mixing ratio t~ for transitions excited at the Ep = 1634.5 keV resonance. For transitions with IJ'z--J21 > 1, ~ is assumed zero. For the 7523.4 keV resonance the angular distribution results o f table 2 are consistent with only a spin-} assignment. From proton penetrability arguments it would

602

B. J. O'BRIEN AND G. Eo COOTE

appear to be an lp = 2 transition indicating a positive parity resonance. This { + assignment differs from the 3 - of August et al. 6).

56Fe (p,y')5~o Ep = 1523.4 keV ,~,

................ -......::.~ . . . . . . . .

. .........

\? 7523.4 J -90

) 0 keV )7f2

I -60

I -30

~'1757..5 )J

10°-7523A 5/2 I 0

I 30

I 60

I

90 - 9 0

I

-60

-30

'J

k'evW I

I

0

30

i 60

90

t~n~S Fig. 5. A plot o f Q2 against mixing ratio 6 for transitions excited at the Ep = 1523.4 keV resonance. F o r transitions with Ida--J2[ > 1, 6 is a s s u m e d zero.

The resonance at 7266.7 keV produced isotropic ~-ray angular distributions as discussed above. This leads to an unambiguous spin assignment of ½. As discussed in subsect. 4.7 this resonance is probably the isobaric analogue of the 57Fe ground state, which has a spin of ½-. This resonance has therefore been given a spin and parity assignment of ½-. TABLE 2

A n g u l a r distribution results for u n b o u n d levels a n d probabilities that the value o f Z 2 exceeds those f o u n d experimentally a) Resonance

Transition (keV)

Probability for a s s u m e d spin of

Ep (keV)

Ex (keV)

~

2204.2

8192.2

8192 -+ 0 8192 --> 1378

<10 -4 0.88

0.46 0.88

`<10-* `
1634.5

7632.5

7632 -+ 1378

0.60

0.34

0.002

1523.4

7523.4

7523 -+ 0

1247.9

7252.7

7252 ~ 0 7252 -+ 1505

<10-* 0.57 0.51

~

0.2

<10 -4

<10 -4

-<10 - 4

a) Z z = Q2min. T h e probabilities listed here are for that m i n i m u m in Q2 with the smaller ]6[.

Assuming a spin of ½- for the 1505 keV level, the angular distribution results of table 2 are consistent only with a spin of ~ for the 7252.7 keV resonance. This assignment is consistent with the angular distribution results for the L = 2 transition

603

S6Fe(p, y)S7Co REACTION

to the ground state. The anisotropic angular distribution obtained, together with the 2 % branching to the 5- ground state rule out a spin-½ assignment. To account for the 2 % branching to the ground state, a relative hindrance to the E1 compared with M2 multipole of 104 would be needed. We therefore assume the transitions are M l/E2 and assign a negative parity to this resonance. 4.6. T H E S P I N A S S I G N M E N T S O F B O U N D L E V E L S

The spin and parity of the 1378 keV and the 1505 keV levels are well established as {- and ½- and will not be discussed here 6,24, 25). TABLE 3 A n g u l a r distribution results for b o u n d levels a n d probabilities t h a t the value o f Z 2 exceeds those f o u n d experimentally a) Level (keV)

Transition (keV)

1224.0

1897 --~ 1224

1757.5

8192 --~ 1757 7632 --~ 1757 7523 --~ 1757

1896.4

P r o b a b i l i t y for a s s u m e d spin o f

<10 -4

0.82

0.012

0.88

<:10-4 0.21 <10 -4

0.54 0.21 0.4

0.43 0.057 0.086

0.52 0.001 0.4

<10-*

8192 ~ 1896

<10-*

0.044

0.075

0.39

<10-*

1919.5

8192 ~ 1919 1919 ~ 0

<10 -4

0.31 0.77

0.20 0.77

0.28 0.38

0.28

2132.0

7632 --~ 2132 7252 ~ 2132

0.44 0.37

0.44 0.37

0.37 0.37

0.03 0.37

3850.7

7252 --~ 3850

0.014

0.014

0.0015

3989.0

7632 ~ 3989 3989 --* 0

0.066

0.066 10 - 4

0.066 0.29

<10 -a

<10-*

<10-* 0.29

~) Z 2 = Q2m~n. T h e probabilities listed here are for t h a t m i n i m u m in Q2 with the smaller [61.

The angular distribution results for the 1757.5 keV level are consistent with only a spin-{ assignment. This can be seen by multiplying the probabilities in table 3 for the same spin assignment together. For a spin of { the combined probability is 0.045 but less than 0.0022 for other spin assignments. The strong transition to this level from the ½- resonance at 7266 keV suggests a spin =< {. This spin assignment is in agreement with the reported lp = 1 transitions to this level in the (3He, d) and (t, ~) reactions 1,5) and also with the assignment of Gatrousis et al. 9), but does not agree with the ~:- assignments reported from the (p, 7?) measurements 6) and by Lingeman et al. 1o). The parity is taken as negative. A doublet at about 1900 keV appeared in the 54Fe(a, p) spectrum of Bouchard and Cujec z) and this doublet also appeared fairly well resolved in the 6°Ni(p, ~) spectra of Coop et aL 4). In the present work this doublet was strongly excited at

604

B.J.

O'BRIEN AND G. E. COOTE

the 8192 keV resonance. The 1919 keV level was observed in spectra taken at several spin-½ resonances but was not fed directly from any of these resonances. Neither of these levels is excited in the 56Fe(3He ' d)57Co reaction.

P

512 1/2-

3/2"-J

•,1

I 4

1(20)

145 [ 5 1(27)1 17 [ 29 I 13 I 8

512 3/2

I 56 I 9

I ~5

~

(~J>l

[ [

I [ [ I r I [ I [ I I [ I [ I

~uou.u 3850.0

I I I I 1(3)

512

912

O

712

o Fig. 6. Decay scheme of 57Co from the resonances excited at Ep = 1247.9, 1262.1, 1523.4, 1634.5 and 2204.2 keV determined in the present work. The energies at right are in keV. The branching ratios are shown in per cent, those in brackets are only approximate. Where no number is shown the branching is 100 %.

$6Fe(p, ~')STCo REACTION

605

The angular distribution to the 1896.4 keV level favours only a spin of *) or ~ with any significant probability. This level is deexcited almost solely by transitions to the 1224.0 keV state and to the ground state, there being no measurable branching to the *)- level at 1378.1 keV. The 1896.4 level is not excited by direct transitions from any of the spin 5 or *) resonances. A spin-*) would permit an allowed fl+ transition to this level from 5aNi, but no such direct fl+ transition has been observed 9). Blair and Armstrong assigned a ~- spin to the strong Ip = 3 level at 1890+ 15 keV excited by the 58Ni(t, ~)57Co reaction on the basis that the ground state of SaNi should contain much ~- proton strength but little }- proton strength 5). We therefore assign a spin of } - to this level. For the 1919.5 keV level, the angular distribution results both for the 8192 ~ 1919 keV and 1919 ~ 0 keV transitions are ambiguous, only the J = 5 spin being rejected. There is a small branch of about 2 ~ from the 1919 keV level to that at 1378 keV but most of the strength is in the ground state transition, however in no case is any branching to the } level at 1224 keV observed. The 1919 keV level is excited directly from a resonance at Ep = 1622 keV which also cascades strongly to the 5- spin level at 1505 keV; this would indicate a spin = ~. The above resonance was assigned a spin of*) by August et al. 6). This upper limit on the spin is also indicated by the logft values in the fl+ decay from 57Ni, which indicate an allowed decay 9). The following observations suggest that the 1919 keV level has spin greater than *): the small amount of branching to the J = *)- level at 1378 keV ( ~ 2 ~o), there is no observed transition to this level from the J = 5 resonance at 7266 keV. We therefore assign a spin to this 1919 keV state of ~, which is in agreement with that deduced from the (p, y~) work 6). The level at 1224.0 keV has been reported in the 5*Fe(~, p), 5SNi(t, , ) and 6°Ni(p, ~) reactions 2, 4, 5). In the present work this level was strongly excited at the 8192.2 keV and other resonances. It appeared to be almost solely fed by a 673.4 keV transition from the 1896.4 keV level. The angular distribution results for the 673.4 keV transition allow only a { or ~ spin assignment to the 1224 keV level, Since no direct transitions to this level from the 1378 and 1757 keV levels or from any of the 5, *) and ~r resonances is ever observed, the ~ spin assignment is chosen. This agrees with the assignments made by Dayras and Cujec based on the (,, p) reaction 3) and of Gatrousis et al. from the 5~Ni fl+ decay 9). A level near 2132 keV has been reported in the S6Fe(SHe, d), SaNi(t, ~) and the 60Ni(p ' a) reactions ~, 4, s). A y-ray of this energy was present at nearly all resonances studied. The angular distribution results limit the spin to 5, *) or {. The strength of the branching to the ground state (87 9/0) rules out the 5 spin assignment. A ½÷ spin would require an E1 transition to the 1378 keV level and an M2 to the ground state; this is unlikely to give the branching ratios observed. The observed branching ratio is compatible with a {- spin assignment or possibly a *)- spin if a relative E2 enhancement of 120 is assumed. The (SHe, d) reaction data shows a strong lp = 3 transition to a level ~) at 2129 keV. The transition from the 7632 keV resonance to

606

B.J.

O'BRIEN AND G. E. COOTE

this level was a doublet, the weaker component apparently feeding a level at 2160 keV. The S*Fe(~, p) results also indicated there may be doublet 2) at about 2140 keV. However the 2132.0 keV 7-ray energy measured in the present work seems close to the 2129_+20 keV level that was strongly excited in the 56Fe(3He, d) reaction 1). On the basis of these arguments we have assigned a spin of { - to this level. A transition to a level at 3850.7 keV was observed at the 7252, 7266.7 keV and other resonances. This level probably corresponds to the level at 3834 keV reported in the 5¢Fe(~, p) reaction 2). A level at about this energy was proposed by Persson and Arnell 7). There is a branch via a 2345 keV ~-ray to the 1505 keV level and via a 2472 keV 7-ray to the 1378 keV level, roughly about 48 ~ to each. It is difficult to estimate the branching ratios exactly as there is a level at 2479 keV corresponding to the levels 2483, 2489 and 2481 keV reported in the 5*Fe(a, p), 5SNi(t, ~) and 6°Ni(p, ~) reactions respectively 2, 5, 4), which was not very well resolved from the 2472 keY transition to the 1378 keV level. There is a small amount of branching from the 3850 keV level ( ~ 3 ~ ) to the ground state. The angular distribution results for the transition 7252 -~ 3850 keV show fairly poor statistics, but they do favour a spin of only ½ or {. The strong branching to the ½- level at 1505 keV supports this. Since a 3 ~ branch to the ground state would be unlikely for a ½ ~ { transition, the 3850.7 keV level was assigned a spin of ~:. At the 7632 keV resonance two cascade gamma rays at 3989 keV and 3642 keV were strongly excited. Since the latter showed a full Doppler shift in energy between 0 ° and 90 ° while the former showed none, the cascade corresponds to a level at 3989 keV. A gamma ray at this energy was also excited at the 7252 keV resonance. This probably corresponds to the levels found at 3973 keV in the 5*Fe(a, p) reaction 2) and at 4003 keV in the S6Fe(3He, d) work 1). The level decays almost solely to the ground state, which rules out a spin of ½. When one combines the probabilities from the angular distribution results for the 7632 ~ 3989 k e y transition with those for the 3989 ~ 0 keV transition, spins of { and -} are ruled out, resulting in a spin assignment for this level of {. There was a weak ;~-ray of 2092 keV present in these spectra indicating a very weak (m 1 ~ ) branching of the 3989 keV level to the :}level at 1896.4 keV. 4.7. MULTIPOLE MIXING RATIOS In table 4 the multipole mixing ratios measured for the various transitions analysed by means of angular distributions are shown, together with the adopted spin and parity assignments. The sign convention used is that of Rose and Brink 20). The error on the mixing ratio is the change needed in 6 to increase Q2 above its minimum value by a factor of 2.3 and 4.6 for three and one-degree(s) of freedom respectively. The only mixing ratio previously reperted was by August et al. 6) for the 1919 ~ 0 keV transition. The present result for this transition of 0.24+0.03 agrees with their value of 0.20-t-0.06.

607

s6Fe(p, y)S7Co REACTION TA~L~ 4 Multipole mixing ratios for transitions in STCo Ep (keV)

Transition (keV)

./1~r

J2 ~r

Mixing ratio

2204.2

8192 ~ 1919 8192 ~ 1896 8192 --->1757 8192 --->1378 8192 --> 0 1897 --~ 1224 1919 -~ 0

6+ 6+ 6+ ,~+ 6+ ½~

~ 56~~~ ~-

0.22i0.04 0.02~0.03 0.01 ~0.03 0.01 ±0.02 0.0044-0.008 --0.09 4-0.06 0.24 4-0.03

1634.5

7632 --> 3989 7632 --> 2132 7632 --~ 1757 7632 --~ 1505 7632 --~ 1378 3989 -+ 0

366~~~

~ ~ 6½~~-

--0.06 0.81 --0.06 --0.41 0.15 --0.06

1523.4

7523 ~ 1757 7523 --,'-0

6+ 3+

~-½-

--0.04 4-0.02 --0.13 4-0.08

1247.9

7252 --~ 3989 7252 ~ 3850 7252 --->2132 7252 -+ 1757 7252 --~ 1505

~~~~~-

~ ~ ,~ ~½-

--0.02 --0.20 0.44 0.07 --0.01

4-0.10 4-0.70 4-0.25 4-0.10 4-0.04 4-0.08

4-0.20 4-0.20 4-0.50 4-0.20 4-0.07

4.8. ISOBARIC ANALOGUE RESONANCE U s i n g the C o u l o m b d i s p l a c e m e n t energy AEc, for the isobaric a n a l o g u e p a i r 5 7 C 0 _ 57Fe given by Sherr 26) o f 8890"[-30 keV, t o g e t h e r with the Q-value for the s 6Fe(n ' ~)s 7Fe r e a c t i o n o f 7 6 4 1 . 5 _ 6 keV [ref. 27)], it can be seen t h a t the isobaric a n a l o g u e o f the 57Fe g r o u n d state s h o u l d occur at Ep = 1 2 7 0 _ 30 keV. O f resonances 2, 3 a n d 4 (fig. 1) o n l y r e s o n a n c e 3 has a spin assignment o f ½-, hence we assume t h a t this is the i s o b a r i c a n a l o g u e state o f the ½- g r o u n d state o f 57Fe" This r e s o n a n c e has an excitation energy o f 7 2 6 6 . 7 _ 1 keV c o m p a r e d with the value o f 7275 _+20 r e p o r t e d b y R o s n e r et al. 1) for the a n a l o g u e o f the s 7Fe g r o u n d state. H o w e v e r the s 6Fe(d ' p ) w o r k o f S p e r d u t o a n d Buechner 28) shows t h a t the t r a n s i t i o n to the 57Fe g r o u n d state is a b o u t 10 times w e a k e r t h a n t h a t to the level at 14 keV. It is p r o b a b l y this latter level t h a t was m e a s u r e d b y R o s n e r et al. 1). The spacing o f 14 keV between resonances 2 a n d 3 (fig. 1) h a s led some w o r k e r s to suggest that level 2 is the isobaric a n a l o g u e state o f the 57Fe g r o u n d state 29), A s s u m i n g the a n a l o g u e o f the 57Fe g r o u n d state is the r e s o n a n c e at 7266.7 keV, the C o u l o m b d i s p l a c e m e n t energy for the 5 7 C o - 57Fe p a i r is 8881.5_+6 keV.

5. Discussion In the simplest shell-model description o f the 57Co nucleus, in which the ( f ~ ) - i p r o t o n hole is c o u p l e d to the (P~)s=2 2 n e u t r o n configuration xl), o r in general to a

608

B. 1. O'BRIEN AND G. E. COOTE

J = 2 + core excitation2S), one expects a quintet of levels with spins from ½- to t ~ to occur in the 0--3 MeV energy range. In the present work no transition corresponding to a level of spin @ - was observed, but this is not unexpected since it is unlikely that a level with such a high spin would be excited by transitions from resonances with J < ~-. A level at about 1687 keV was excited in the 54Fe(e, p) reaction 2,3), the 5SNi(t, e) reaction s) and in the 6°Ni(p, e) reaction 4). Dayras and Cujec 3) have 11 determined its spin as-~-. The simple model proposed above does not predict energies that agree well with experiment 11), nor does it explain the appearance of a ½- state at such a low energy as 1503 keV. McGrory 12, 9) used a model in which the protons and neutrons outside an inert 4°Ca core were distributed among the f~, p~, f~ and p~ orbits. This gave a better account of the energies of the low-lying levels, but also predicted the presence of other levels with spins of ~, ½-~ and ~ that to the present time have not been observed. With the more complete spin assignments for the 57Co low-lying levels now available it is interesting to see how well the centre-of-gravity theorem 1 3 , 3 0 ) works in this case. It has been reported that this theorem works well in the case of 59Co ' although the spin assignments were not then k n o w n with much certainty ~3,25). For the case where the parent closed shell nucleus has a ground state spin of 0, this theorem can be written in the convenient form

(2j+ 1)AE= (24+ 1)-* Z (2Ji+ 1)w,Ei-Z (2Jk+ 1)WkEk. i

k

In the present case Jz --- 2 and j = ~}and Ji, Ei and wt refer to the spin, energy and weighting factor of the ith level of 57Co that is derived from the 2 + first excited state of 5SNi by the addition of a ~- proton hole, while Jk, Ek, Wk refer to levels in 57Co derived from the 0 ÷ ground state of 5SNi. For this calculation we assume all the ~ - strength is in the 1687 keV level. The 56Fe(aHe, d) results 1) indicate that the ~ strength involving core excitation, is probably split between the 1378 keV and 1757 keV levels, so using the (3He, d) spectroscopic factors as a guide, we partition 80 ~o of the {t strength to the 1757 keV level and 20 % to the 1378 keV level. All the ~ and ~- strength is assumed to be in the 1919 keV and 1224 keV levels respectively. Assuming all the -} strength is in the 1896 keV level, the centre of gravity lies at 1647 keV. This is somewhat higher than the 1452 keV 2 ÷ first excited state of 5SNi. In estimating the above result, it was assumed that a proton f~ hole couples to the ~SNi ground state configuration to form only the 57Co ground state, thus the last term on the right of the above equation contributes zero. But the 5SNi(t, cQ results 5) show an lp = 3 transition strength to a level at about 1890 keV that accounts for about 20 % of the f~ strength. This indicates that about 20 % of the 1896 keV level is derived from the 58Ni ground state configuration coupled to a f~ proton hole. Using this figure, the centre of gravity is at 1192 keV, ,xhich is somewhat too low. There are two possible causes for this low result; much

56Fe(p, ~:)57C0 REkCTION

609

of the 2 + strength of the 1452 keV level in saNi could be mixed into levels of 57Co above 1919 keV; the relative spectroscopic factor for the (t, ~) transition to the 1896 level of 57Co reported by Blair and Armstrong 5) may be a factor of two too large, such an over-estimation would occur if in reality the (t, co) transition populates both the 1896 keV and 1919 keV levels, which were not resolved in the above study. Considering these uncertainties, the results are reasonably compatible with the predictions of the c.m. theorem. The authors would like to thank R. J. Sparks for the efficiency calibration of the Ge(Li) detector and G. J. McCallum and G. Wallace for the use of computer programs used in the analysis. We also thank Miss Shirley Stuart and Mrs H. M. Henderson for assistance in preparing the manuscript. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30)

B. Rosner and C. H. Holbrow, Phys. Rev. 154 (1967) 1080 N. Bouchard and B. Cujec, Nucl. Phys. A108 (1968) 529 R. Dayras and B. Cujec, Nucl. Phys. A127 (1969) 545 K. L. Coop, I. G. Graham, J. M. Poate and E. W. Titterton, Nucl. Phys. A130 (1969) 223 A. G. Blair and D. D. Armstrong, Phys. Rev. 151 (1966) 930 L. S. August, C. R. Gossett and P. A. Treado, Phys. Rev. 142 (1969) 664 P. O. Persson and S. E. Arnell, Ark. Fys. 33 (1966) 371 C. J. Piluso, D. O. Wells and D. K. McDaniels, Nucl. Phys. 77 (1966) 193 C. Gatrousis, R. A. Meyer, L. G. M a n n and J. B. McGrory, Phys. Rev. 180 (1969) 1052 E. W. A. Lingeman, J. Konijn, F. Diederix and B. J. Meijer, Nucl. Phys. A100 (1967) 136 J. Vervier, Nucl. Phys. 78 (1966) 497 J. B. McGrory, Phys. Rev. 160 (1967) 915 D. R. Lawson and J. L. Uretsky, Phys. Rev. 108 (1957) 1300 R. Nordhagen, B. Elbek and B. Herskind, Nucl. Phys. A104 (1967) 353 L. Satpathy and S. C. Gujrathi, Nucl. Phys. Al10 (1968) 400 B. J. O'Brien, to be published A. C. Wolff, M. A. Meyer and P. M. Endt, Nucl. Phys. A107 (1968) 332 J. B. Marion, Nucl. Data 4A (1968) 301 B. J. O'Brien, to be published H. J. Rose and D. M. Brink, Rev. Mod. Phys. 39 (1967) 306 A. C. Wolff, W. C. R. Boelhouwer and P. M. Endt, Nucl. Phys. A124 (1969) 273 P. M. Endt and C. Van der Leun, Nucl. Phys. AI05 (1967) 140 E. L. Crow, F. W. Davis and M. W. Maxfield, Statistics manual (Dover, New York, 1960) p. 232 J. Konijn, H. L. Hagedoorn and B. Van Nooijen, Physica 24 (1958) 129 G. Chilosi, S. Monaro and R. A. Ricci, Nuovo Cim. 26 (1962) 440 R. Sherr, Phys. Lett. 24B (1967) 321 J. H. E. Mattauch, W. Thiele and A. H. Wapstra, Nucl. Phys. 67 (1965) 1 A. Sperduto and W. W. Buechner, Phys. Rev. 134 (1964) B142 D. R. Araham, L. D. Ellsworth, S. Hechtl, D. G. Megli and J. C. Legg, Bull. Am. Phys. Soc. 14 (1969) 1234 A. de Shalit and I. Talmi, Nuclear shell theory (Academic Press, New York, 1963) p. 472