Gamma rays produced in the 56Fe(n, n′γ)56Fe reaction

Nuclear Physics 79 (1966) 241--256; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

G A M M A RAYS P R O D U C E D I N T H E S6Fe(n, n'7)S6Fe R E A C T I O N R. W. BENJAMIN, P. S. BUCHANAN and I. L. MORGAN Texas Nuclear Corporation, Austin, Texas t

Received 21 October 1965 Abstract: Cross sections for the production of gamma rays by inelastic neutron scattering from iron

have been measured for incident neutron energies from 0.95 MeV to 4.0 MeV. Angular distributions for nine gamma rays produced by the (n, n'y) reaction in ~eFe were measured over the same energy range and compared with the theoretical predictions of the Satchler formalism using three different sets of neutron penetrabilities. On the basis of these comparisons, a doublet at 3.45 MeV is proposed and the following spin and parity assignments made to levels in the SSFe nucleus: 3.45 MeV (1+ : 3+) and 3.60 MeV (2+). The possibility of a doublet at 3.12 MeV has also been investigated. Branching ratios for the gamma rays originating at these levels have been determined experimentally. El

NUCLEAR REACTIONS 8SFe(n'n'Y)' En = 0"95--4"0 MeV; measured y-spectra, or(E; E~,, 0), deduced J, ~. Natural target.

I

1. Introduction

The analysis of angular distributions and cross sections of g a m m a rays produced by inelasticaUy scattered fast neutrons and comparison with the theoretical predictions of the Satchler formalism 1) provides yet another method for the study of spins and parities of excited nuclear levels. The shapes and anisotropies of gamma-ray angular distributions derived from Satchler's work are dependent upon the spin, parity and branching ratios chosen for the nuclear levels involved; and comparison of theory and experiment m a y give unambiguous spin assignments for excited nuclear levels. Although m a n y authors have studied inelastic nucleon scattering in iron, only a few have measured gamma-ray angular distributions and none have reported angular distributions for g a m m a rays originating above the second excited level in 56Fe at 2.085 MeV. The recent S6Fe(n, n')56Fe experiments of Hopkins and Silbert 2) and Gilboy and Towle 3) have helped to establish the differential and total (n, n') cross sections at several energies and to indicate some of the spin possibilities. Hosoe and Suzuki 4), Day and Walt 5) and Boring and McEllistrem 6) have measured angular distributions for the 0.845 MeV transition f r o m the first excited state in S6Fe at incident neutron energies of 2.95 MeV, 2.56 MeV, and 2.87 MeV, respectively. Using reactor neutrons with a very wide energy spread, Donahue and Roberts 7) measured angular distributions of the 0.845 MeV g a m m a ray and the 1.24 MeV g a m m a ray, t Work supported in part by the U.S. Atomic Energy Commission. 241 April 1966

242

S.W. BENJAMINet aL

which cascades from the second excited level at 2.085 MeV. The results of each of these experiments were compared with the Satchler formalism using several different sets of neutron penetrabilities with a fair degree of success. The aim of the present work was to provide substantial gamma-ray angular distribution and cross-section data for natural iron over a wide range of energies and, where possible, to establish spin and parity assignments for those levels in S6Fe whose spin and parity were unknown or uncertain.

2. Experimental Method The experimental equipment used in these measurements consisted of a pulsed beam time-of-flight spectrometer similar to that at Los Alamos s) used in conjunction with a total absorption gamma-ray spectrometer of the type developed by Trail and Raboy 9). The operation of this system is described in detail in a Texas Nuclear Corporation report lo) and elsewhere by Ashe et al. 11). Three reactions were used to provide neutrons of the desired energies with the Texas Nuclear Corporation 2.0 MeV Van de Graaff acceleratort; i.e., the data around 1 MeV were taken with a solid tritium (tritium absorbed in titanium) target using the T(p, n)3He reaction; 1.5 MeV neutrons were obtained with the 12C(d, n)13N reaction with a thin carbon target; and a 1 cm long 2 atm gaseous deuterium target was used for the data at and above 2.5 MeV with the D(d, n)3He reaction. These targets gave neutron energy spreads of -t-35 keV, -t-50 keV and from _ 120 keV to __.200 keV (dependent upon the incident deuteron energy), respectively. All of the data below 2.5 MeV were taken without using the time-of-flight system in order to decrease substantially the data accumulation time. It should also be pointed out that at the lower neutron energies the background problems are less severe. The scattering sample was a solid cylinder of better than 99 ~o pure natural iron 2.54 cm in diam. and 5.08 cm long. The isotopic composition of natural iron is 56Fe-91.66 ~o, 54Fe-5.82 ~/o, 57Fe-2.19 ~o and SaFe-0.33 ~o. For all measurements, except the 2.5 MeV cross-section measurement, the scatterer was placed at 0 ° with respect to the incident charged particle beam and at distances of from 2 to 6 cm from the face of the target to the surface of the scatterer. For the 2.5 MeV measurement the scatterer was placed at 70 ° to the incident deuteron beam and at a distance of 5 cm from the centre of the target to the surface of the scatterer. "Scatterer-in" and "scatterer-out" runs were made at each angle for a predetermined charge collected at the target. Neutron flux was continuously monitored with a calibrated long counter placed at 90 ° to the charged particle beam incident on the target. A typical gamma-ray spectrum for iron at an incident neutron energy of 4.0 MeV is shown in fig. 1. Gamma-ray peaks at 0.845, 1.03, 1.24, 1.40, 1.81, 2.12,2.30,2.60, ? This acceleratorhas sincebeen modifiedto reach 3.2 MeV.

5eFe(n, n'y)SeFe REACTION

243

2.76, 3.45 and 3.60 MeV are clearly resolved with small peaks at about 2.99 and 3.12 MeV which are poorly defined. Gamma rays have been stripped from the overall spectrum using experimentally determined line shapes. Original data points are outlined in heavy lines while the stripped peaks, along with their associated Compton distributions and one-escape peaks, are outlined in finer lines. Experimental errors are in two separate categories. Relative errors for the angular distributions represent only the relative errors of each data point in the distributions which evolve from: statistical deviations of the scatterer-in and scatterer-out runs; the subtraction of the Compton distribution from the photopeaks in the spectra; and the statistical deviation in the long counter counts used for the normalization of the data runs. Errors for the differential cross-section values include as well errors in determination of the long counter efficiency and neutron flux in the scatterer;

¢',-X I0 40K

Fe(n,n'),,)Fe En = 4.0-J:.12 MeV

J

Otob =3o*

~

z~30K i 50X~

(/3 i-

g2oK

I

o

IO~

.~

/ 0 ~

1.0

1.5

2.0

E--

2.5

3.0

3.5

E), (MeV)

Fig. 1. Gamma-raypulse-height spectrum for the "Fe(n, n'7)56Fe reaction at En = 4.0 MeV. The "scatterer out" background has been subtracted. errors in the determination of the gamma-ray spectrometer efficiency and selfabsorption of gamma rays in the scatterer; and errors due to line shape changes in the Compton distribution from gamma scattering in the sample. Relative errors in these measurements range from about 2 % to 10 % while errors in the differential cross sections range generally from 17 % to 20 %. 3. Results and Discussion

Differential (n, n'y) cross sections at 0 = 90° have been determined for natural iron from E, = 0.95 MeV to 4.0 MeV, and for the 0.845 MeV gamma ray to E. = 4.750 MeV. These cross sections are tabulated in table 1. With the exception of the 1.41

244

R. W. BENJAMIN et aL

TABt~ 1 Experimental (n, n'7) cross sections for natural iron at 90 ° (mb/sr/-#20 %) E~(MeV) 0.845

0.95

1.00

1.05

11.8

19.4

25.5

En(MeV) 1.5 2.5 32.6

76.1

3.1

3.5

4.0

78.8

81.7 2.0 9.5

98.9

1.03

1.24

4.71

1.40

1.81 2.12 2.30 2.60 2.76

8.9 2.9 11.3 7.3

3.1

10.4 7.7 4.4 3.3

3.00

3.12 3.45 3.60

3.9

15.8 4.0 13.7 11.1 6.2 8.4 2.9 < 2 ~) < 1 a) 3.9 2.6

Cross sections for 0.845 MeV g a m m a ray only 3.75 4.20 4.43 4.70 90.9

85.2

86.7

89.7

a) These peaks were too small for accurate cross-section evaluations. The values given are estimates. 5.856

.60 (2")

:3.369

3.45 3.388

(r3(5-).

2÷

"b~"

• -

"

T1

,, 2.956,

3.12

•

•

2 ,0

'"Y/ 2.660

4"

j

0.845

o o*

0 56Fe

Fig. 2. Energy level and decay scheme for " F e . G a m m a rays with listed energies were observed and identified in this experiment. Angular distributions have been measured for the g a m m a rays whose energies are underlined.

SSFe(n, n'F)SSFe REACTION

245

150C

EF=0.845 MeV

100(1

5~

0 -~¢ 20C ..5 b IOC c 20G

E~, = 1.24

MeV

v ET, = 1.81

MeV

lOG C 20O

Er= 2.12 MeV

IOC

%

'''

;''

':;

i''

l,,,,, 3

4

En(MeV) Fig. 3. Excitation curves for four gamma rays from 68Fe. The dashed portion of the 0.845 MeV gamma-

ray curve indicates the cross section for direct excitation of the 0.845 MeV level. Error bars represent statistical deviations only. See text for discussion of errors. TABLE 2 Experimental (n, n'F) cross sections for natural iron (mbq-20 ~ ) Er(MeV)

0.845 1.03 1.24 1.40 1.81 2.12 2.30 2.60 2.76 3.00 3.12 3.45 3.60

En(MeV) 0.95

1.05

1.5

261

400

557

3.1 1198 159 36 a) 170 92

3.5 1141 25 a) 154 39 4) 163 113 55 41

4.0 1399 49 a) 240 50 4) 180 172 78 106 36 < 25 4, b) < 12 4, b) 49 36

.) Reliable angular distributions could not be obtained for these gamma rays, but they appeared to be isotropic and were assumed to be so for the purpose of determining total cross-section values. b) These peaks were too small for accurate cross-section evaluations. The values given are estimates.

246

R.W.

BENJAMIN e t al.

MeV gamma ray from the first excited state in 54Fe, all of the observed gamma rays are attributed to S6Fe. The gamma rays and spectra can be explained with reference to the level diagram and decay scheme of 56Fe shown in fig. 2. The levels, spins, parities and transitions are a composite of information from the Nuclear Data Sheets 12), more recent experiments which will be discussed below and the results of this experiment. Excitation curves for the predominant transitions from the first four excited levels of 56Fe are shown in fig. 3. The error bars indicate statistical errors TABLE 3 Comparison of gamma-ray and inelastic-neutron cross sections En (MeV) 2.5

Eleve I (MeV) 0.845 1.24 2.085 total at 2.5

tr'n (rob) ~)

ay(direct ext. only) (mb)

9604-80

10394-226 894-18

(704-35) b) 1030-4-90 960 4- 80 e) 161 4-13 e) (90 4- 45) e)

11204-227

3.1

O.845 2.085 2.660 2.956 total at 3.1

12104-90

777 4- 245 1594-32 170 4- 34 924-18 12004-250

3.5

0.845 2.085 2.660 2.956 3.119 3.45 total at 3.5

5404-80 1904-13 2254-10 2054- 8 (804-40) (30 4-15) 12704-90

6144-234 1244-31 1634-33 1134-23 964-13 66 4-10 11804-240

4.0

0.845 2.085 2.660 2.956 3.119 3.45 3.600 total at 4.0

4704-80 1504-13 1674-10 1734- 8 1974-10 2474-12 (684-35) 15004-90

5604-283 1754-49 180-4-36 1674-33 1504-19 1684-23 724-14 14704-293

s) Hopkins and Silbert 6). b) The cross sections in parentheses were not measured but were estimated. e) The neutron data were taken at En = 3.0 MeV.

only. Absolute cross-section errors are about 20 %. These cross sections have been determined by integration of least-squares Legendre polynomial fits to the experimental data points. The (n, n'y) cross sections for natural iron listed in table 2 were determined in the same manner. Hopkins and Silbert 2) and Gilboy and Towle 3) have recently measured (n, n') cross sections for excitation of the levels in S6Fe. Gilboy and Towle measured angular distributions of the elastically and inelastically scattered neutrons at 0.98, 2.01, 3.01

247

uFe(n, n'y)S6Fe REACTION

and 3.99 MeV. Hopkins and Silbert measured the inelastically scattered neutrons at 0 = 50 ° for several incident neutron energies in order to determine the (n, n') cross sections for the various excited levels. An angle of 50 ° was chosen because the P2 term of a Legendre distribution is very nearly zero at 50 ° and the P4 and higher terms are generally quite small. The differential cross section at 50 ° may then be multiplied by 4:~ to obtain the total cross section for excitation of a given level. The gamma-ray and neutron data may be compared by summing the cross sections for ,

a

~

=

En= 4.0 MeV

•

*

En=3.1MeV 1.0 En=l.50 MeV

En=l.05 MeV

2.(; En=0.95 MeV

1.0

05

o COS 8

- 05

- I.O

Fig. 4. Relative angular distributions for the 0.845 MeV gamma ray at several incident neutron energies. Curves are Satchler fits with the penetrabilities of Beyster et al. 14). Error bars represent relative errors.

all gamma rays originating at a given level and subtracting from this value the cross sections for all cascades to the given level. A comparison of these results is shown in table 3. Comparisons of some experimental and theoretical gamma ray angular distributions are displayed in figs. 4-7 on both relative and differential cross-section scales. The relative errors are described by the solid portion of the error bars. Errors in the differential cross-section values have been denoted by the dashed error bars. Theo-

248

R.W. nENHAMIN et al.

retical distributions have been derived according to the Satchler formalism t, 13) using the neutron penetrabilities of Beyster et aL 14) and of Auerbach and Percy 15), who calculated penetrabilities using the potentials of Bjorklund and Fernbach 16) and of Perey and Buck 17). These penetrabilities are denoted on the curves as B (Beyster et aL), B and F (Bjorklund and Fernbach) and P and B (Perey and Buck). Theoretical differential cross sections are of the form

£2

da(O) =

d,O

E),E2) = 1.24 MeV

1.6

Ev = 2.60 MeV

1.4 ~

,.o~

1.2

0.8

1.4.

(1)

12

ID

t ~ ~

1.21 ~

ET(MI~ E2) = 1'81MeV

/

.

E7 (MI) = 3.45 MeV

LOI , 0.8

'

~" 1.0 0 1.6

1.2"•

~" 1.4 ~

~A,P,(cos 0),

4(23"0 + 1) (2si + 1) "7

E;¢ = 2.76 MeV

1.0

1.2

..... I - - - t . . . . . . . . . . . . . . .

20 1.81

l-4r ,.21M.,

/

Er= 2.30 MeV t./t

~

ET(E2} = 3.60MeV

t61 1.41 121

1.0

0.5

0 COS 8

-0.5

- 1.0

1.0t 1.0

0.5

0 COS 8

-Q5

-I.0

Fig. 5. Relative angular distributions for gamma rays originating above the 0.845 MeV level at an incident neutron energy of 4.0 MeV. Solid curves are Satchler fits with Beyster et aL a,) penetrabilities. Dashed curves are least-squares fits to the experimental points. Error bars represent relative errors.

where ~t is the reduced wavelength of the incident particle in the centre-of-mass system, Jo the ground state spin of the initial nucleus, st the spin of the incident particle, the A, constants involving the Clebsch-Gordan and Racah coefficients and the/),(cos 0) are Legendre polynomials. The spins and parities which were assumed for each level in the final theoretical calculations are as indicated in fig. 2. These values were selected on the basis of several trials, the results of which are discussed below. For gamma rays which were calculated as other than pure transitions the

6eFe(n, n'7)SSFe REACTION

249

multipole mixing ratio is expressed as the multipole mixing coefficient 6, defined by 62

_

I,+1 ,

(2)

h where It. is the intensity of the lowest order multipole transition possible and IL+ 1 the intensity of the lowest order multipole plus one. The theoretical distributions whibh are shown include calculations for all observed cascade contributions from higher levels. Angular distributions for gamma rays originating from levels above the first four excited levels, whose spins and parities

1401

En = 0 95 MeV B&F

80 "

En: 3IMeV

60 40 20

:!

:,

B

0

IOOr

B~F

60l140~-T T

En= 105 MeV

En=5.5 MeV

i i

T

120 L ' ~~ P&B

4or--

-

"

0

/ /

~

" 1601-[ T

En:l.5MeV

"l

En=4.0MeV

i

T

40~-, ,

i

'

,

'

~'

~

40

1,0

0

T

~

~ B "

60 "

20

I

,.

20 i00 ~

i

~

~

[,

8

0.5

0 COS

-0.5

-I.0

60

O

1.0

Y.

05

, ......

0 COS 8

-0.5

, , ,

-I0

Fig. 6. Experimental and. theoretical differential cross sections for the 0.845 MeV gamma ray. B, B and F and P and. B refer to distributions calculated using the penetrabilities of Beyster e t al., Bjorklund and Fernbach and Percy and Buck, respectively. The solid error bars represent relative errors and the dotted bars the absolute errors.

are well known, were calculated with a number of the more likely spin and parity possibilities. A summary of previous spin and parity assignments for 56Fe appears in table 4. A discussion of the results obtained for each level is given below with the gamma rays which were observed listed by their respective level of origin. 3.1. T H E 0.845 MeV L E V E L (2+), E:, = 0.845 M e V

The spin and parity of this level have been well established I The decay of the 0.845 M e V level to the ground state (0 +) can go only by a pure E2 transition. The t See ref. 12) and earlier papers cited here.

250

R . W . BEN$AMIN e t al.

angular distributions and cross sections predicted for this gamma ray agree quite well with the experimental results, except in the region of threshold where the theoretical cross sections were appreciably high. E~ = 1.24 MeV

E r = 1.81MeV

-'

E n =3.1MeV

_

[ , ,

E n = 3.1 MeV

2O I0

,c~a__!~________

5 E~= 3.5 MeV

/

~2o

asL

E.=35o M~V

2C -

T :

~

~. i l\l

2o

E~=4.o~v

'

T

['

i

,

T,

~

,

T

Pe~B

.~

,o

~! /

'

-~o'

~

f

T

T ;

,.

,

: ,

F

i

~

' ,'

~

,

~

15

T

~

T

~

T :

', :

~Jf~:

,

i

I

I

I

I

~

J

'

1.0

0.5

ri 20~-~

Ey =2.12MeV

[

'f~!

' T I I 151~:~I'~"~

,o . . . .

i

I

,

,

,

0

,

I

i

,

i

- 0.5

I

]

~= T '

J

- 1.0

En = 4 . 0 M e V

PaB, T /T I I ' '

o

T

I

'

'

'o' cos 8

I

,

I

I

I

E~

I 0

- 0.5

E n :3.5MeV

\

'i

'

-,.o

- IO

:2.12MeV

/

15 , ,

I

' ' '-o.~ . . . .

,

0.5

P&B

~i

J.o

'

•

"

I

ols"

,

20

/

!/'~

,

I0

I

,

I

I

o.5

,

,

i

i

I

i

o cos 8

I

i

i

[

-os.

i

i

i

i

-,.o

Fig. 7. Experimental and theoretical differential cross sections for the 1.24, 1.81 a n d 2.12 MeV g a m m a rays. Theoretical curves for the 1.81 and 2.12 MeV g a m m a rays are calculated for a pure M I transition. The solid error bars represent relative errors a n d the dotted bars the absolute errors.

S(IFe(n, rt'T,)SeFe REACTION

251

3.2. THE 2.085 MeV LEVEL (4+), E~ = 1.24 MeV T h e s p i n a n d p a r i t y o f this l e v e l h a v e a l s o b e e n w e l l e s t a b l i s h e d t. T h e 2.085 M e V l e v e l d e c a y s w h o l l y t o t h e 0.845 M e V l e v e l b y a n E 2 t r a n s i t i o n . A g a i n , t h e t h e o r e t i c a l p r e d i c t i o n s a n d t h e e x p e r i m e n t a l v a l u e s a g r e e q u i t e well. 3,3. THE 2.660 MeV LEVEL (2+), E~ = 1.81 MeV T h e b r a n c h i n g r a t i o s s h o w n in fig. 2 are f r o m ref. 12). O n l y t h e 1.81 M e V t r a n s i t i o n was o b s e r v e d . T h e s p i n a n d p a r i t y o f t h e level h a v e b e e n w e l l e s t a b l i s h e d t. TABLE 4 Spin and parity assignments for the energy levels in 8*Fe below 4 MeV Energy level (MeV) a) 0 0.845 2.085 2.685 2.940 2.958 3.119 3.369 3.388 3.45

0+ 2+ 4+ 2+ 2+ (5 +)

b)

c)

d)

e)

0+ 2+ 4+ 2+

0+

0+ 2+ 4+ 2+ 2+

0+ 2+

3+

3-

2+ 3+ (4+, 3-)

2+ 3-

2+ 3+

(3 +, 3-)

2+

f) 0+ 2+ 4+ 2+ (6 +) 2+ (2-1-, 3-)-) (3 +) (5 +) (2-)-, 3-4-)

3.60

3.84 s) b) c) a) e) ~) g) h)

(4+)

(3 +)

5a(3 ~)

g) 0+ 2+ 4+ 2+ 0+ 2+ (3- : 1+) doublet

h) 0+ 2+ 4+ 2+ 2+ (3- : 1 or2) doublet

2+ (1 + : 3+) doublet 0+(2) poss. doublet

(1 + : 3+) doublet 2+

(5 +)

Kienle and Segel is), ssCo and 6SMn beta decay. Poppema et al. 111)) S$Co beta decay. Bellieard and Barreau 20), 150 MeV electron scattering. Matsuda zx), 14.65 MeV proton scattering. Jacmart et aL n), 155 MeV electron scattering. Gilboy and Towle s), inelastic neutron scattering. Hinrichsen et aLla), (p, p,7) coincidence measurements. This experiment.

T h e 1.81 M e V t r a n s i t i o n t o t h e 0.845 M e V l e v e l (2 +) a p p e a r e d t o b e a l m o s t e n t i r e l y M 1 . A c o m p a r i s o n o f M 1 , E 2 a n d m i x e d m u l t i p o l e t h e o r e t i c a l c u r v e s w i t h t h e 3.5 M e V e x p e r i m e n t a l d a t a is s h o w n in fig. 8. A s i m i l a r c o m p a r i s o n f o r t h e 4.0 M e V d a t a is i n c l u d e d in fig. 5. T h e m i x i n g c o e f f i c i e n t ~ f r o m r a d i o a c t i v i t y m e a s u r e m e n t s v a r i e s f r o m 0.15 t o 0.20 12). t See ref. 1~), and earlier papers cited there.

252

R.w. BENJAMINet aL

3.4. THE 2.956 MeV LEVEL (2+), Er = 2.12 MeV As in the case of the preceding level the branching ratios shown in fig. 2 are f r o m ref. 12). Apparently only the 2.12 MeV transition to the 0.845 MeV level (2 +) was observed, although the ground state transition could be a part of the 2.99 MeV peak which appeared at En = 4.0 MeV. The spin and parity of this level have been well established t. The 2.12 MeV transition appears to be mostly M1 as in the case of the 1.81 MeV transition. A comparison of M1, E2 and mixed curves for the 2.12 MeV transition yields the results shown in fig. 8 and in fig. 5. The value of 6 from radioactivity measurements 12) is 0.28. 2.0

I

• E n = 3.5 MeV E), = 1.81 MeV

O

i

=

i

i

i

'1

I

~2.C

1.0

i

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

En= 3.5 MeV

~

(

= I

1.0

E

2

1

i

i

=

0.5

i

=

=

i

I

0

I

I

I

-0.5

-I.0

COS 8

Fig. 8. A comparison of the experimental angular distribution with theoretical distributions calculated with different mixing ratios for the 1.81 and 2.12 MeV gamma rays at an incident neutron energy of 3.5 MeV. Error bars are relative errors. 3.5. THE 3.119 MeV LEVEL(S) (3- : 1 or 2), E r = 1.03, 2.30, 3.12 MeV The branching ratios shown in fig. 2 for these transitions were determined through graphical integration of the 2.30 MeV gamma-ray angular distribution and the assumption of isotropy for the 3.12 and 1.03 MeV transitions. The spin and parity of this level, or pair of levels, have not been established. The high-energy electron scattering measurements of Bellicard and Barreaux 20) and the high-energy proton scattering studies of Jacmart et aL 22) indicate the presence of a 3 - level at this energy. The (p, P'7) coincidence studies of Hinrichsen et al. za) indicate, because o f

6eFe(n, n'~,)56Fe REACTION

253

the marked difference in the y-spectrum with a change of proton energy, that this level is an unresolved doublet. The gamma decays are as follows: the 3.12 MeV transition is to the ground state (0 +) and is quite small ( ~ 9 ~ ) ; the 2.30 MeV gamma ray goes to the 0.845 MeV level (2 ÷) and is the only gamma ray from this level for which a reliable angular distribution could be obtained; and the 1.03 MeV transition goes to the 2.085 MeV level (4+). The existence of a ground state transition in this case suggests that, if there is indeed a 3- state (which seems likely), then there is in all probability an additional level of spin 1 or 2. Theoretical fits to these data were quite ambiguous; a single 3-, a 3 and a 1~-, or a 3- and a 2 ÷ all fit the data fairly well although the singlet 3- state was slightly favoured. The gamma-ray yield was not sufficient to determine reliably the shape of the 3.12 MeV gamma-ray angular distribution, thus the spin of the level from which it came could not be determined unambiguously. 3.6. THE 3.45 MeV LEVEL (1+ : 3+), Er = 1.36, 2.60, 3.45 MeV Either a single level or, more likely, a doublet at 3.45 MeV was the source of three transitions. Measured angular distributions for the 3.45 and 2.60 MeV gamma rays were almost isotropic (see fig. 5). The 1.36 MeV gamma ray was not resolved from the 1.41 MeV gamma ray coming from the first excited state in 54Fe. An approximate value of 1.1 mb/sr for the (n, n'y) cross section at 90 ° was determined for the 1.36 MeV transition, however, by assuming that the (n, n'y) cross section for the 1.41 MeV gamma ray remained essentially constant between 3.1 and 4.0 MeV. The calculated branching ratios for gamma rays from the 3.45 MeV level are shown in fig. 2. Two of these transitions, which have been observed in the beta decay of 56Co, are shown in the Nuclear Data Sheets 12) with branching ratios of 25 ~ for the 1.36 MeV transition and 75 ~ for the 2.60 MeV transition. These ratios were in poor agreement with those shown in fig. 2 and, in addition, the ground state transition from the 3.45 MeV level was not observed in the work on 56Co. The spin and parity assignment given this level by most investigators is 3 +. A theoretical relative angular distribution for the 2.60 MeV gamma ray, based upon this assignment (a 3 ÷ to 2 + transition), fits the experimental points with suitable manipulation of the multipole mixing ratio, but the theoretical cross section obtained is half the experimental value. The experimental relative angular distribution for the 3.45 MeV ground state transition, however, will only match the theoretical distribution calculated for a spin assignment to the 3.45 MeV level of 1 as shown in fig. 5. This assignment also gives a fit for the shape of the 2.60 MeV gamma ray (a 1 + to 2 ÷ transition in this case) for a pure M1 transition. The cross sections obtained with a single 1 ÷ assumption are still only half the experimental cross sections. Furthermore, a spin assignment of 1 to this level is in direct contradiction to the results of beta decay experiments 18, 19) with 56Co. The ground state of 56Co has been established as 4 ÷ and it is unlikely, on the basis of the logft measurements of Kienle and Segel 18), that the spin of the 3.45 MeV level observed in their experiments is other than 3,

254

g.w.

BENJAMIN e t al.

4 or 5. In addition, no ground state transition from the 3.45 MeV level has been observed in any of the beta decay experiments. In order to correlate these results, a doublet at 3.45 MeV has been assumed. The existence of this doublet has recently been confirmed by the (p, p'~) work of Hinrichsen et al. z3). Assignments of 1 + and 3 + were made to the levels of this doublet where the 1 + level decays to the ground state (0 +) and to the 0.845 MeV level (2+), while the 3 + level decays to the 0.845 MeV level and also to the 2.085 MeV level (4 +). The appearance of a 1 + level in beta decay from either s 6Mn (ground state 3 +)

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or 56Co would be unlikely because of the beta-decay selection rules. Theoretical calculations based upon the doublet assumption have been carried out and are shown in fig. 9 along with the experimental points. Theoretical curves based upon a single level with spin 1 + are also shown. The results, though not entirely conclusive, indicate a good possibility for a 1 + : 3 + doublet at 3.45 MeV. 3.7. T H E 3.60 M e V L E V E L (2+), E~ = 2.76, 3.60 M e V

Two observed gamma rays originated from the 3.60 MeV level, the 2.76 MeV cascade to the 0.845 MeV level and the 3.60 MeV ground state transition. Angular

5°Fe(n,n'y)6~FeREACTION

255

distributions were measured for both gamma rays (fig. 5) and were integrated graphically. Branching ratios are shown in fig. 2. The spin and parity of this level have not been established. Gilboy and Towle a) have given a possible assignment of 4 + to this level on the basis of a small inelastic cross section. This assignment appears highly unlikely due to the relatively large (n, n'~) cross section for the 3.60 MeV ground state transition. The shape of the 3.60 MeV gamma ray angular distribution was consistent with 2 + (E2)0 ÷ shapes calculated for other levels. Theoretical angular distributions which assume 2 + and 4 + assignments to the 3.60 MeV level are shown in fig. 10 along with the experimental points.

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The 2 + assignment gives the best fit. As further corroboration, the theoretical curves calculated for the 2.76 MeV transition with a 2 + assignment and either an E2 or M1 transition give a reasonable fit to the data. This comparison is shown in fig. 10. The 2.76 MeV transition is most likely a mixture of dipole and quadrupole radiation. 3.8. O T H E R L E V E L S B E L O W 4.0 M e V

Of the remaining levels which have been reported below 4.0 MeV (see fig. 2 and table 4) only the 3.83-3.85 MeV doublet was observed. The 2.99 MeV transition from this doublet to the 0.845 MeV level is clear, though somewhat broader than expected. The only indication of the 1.76 MeV transition to the 2.085 MeV level is a slight broadening at the low-energy side of the 1.81 MeV peak in some of the spectra.

256

R.w. BENJAMINet aL

G a m m a rays f r o m the level at 3.369 M e V were either n o t p r e s e n t o r t o o small to be resolvable f r o m g a m m a rays o f nearly the same energy a n d m u c h larger p r o d u c t i o n cross sections. This level has been o b s e r v e d in b o t h r a d i o a c t i v e decay i s ) f r o m S6Mn a n d in p, p ' m e a s u r e m e n t s 12, z3) a n d has been assigned spin a n d p a r i t y values o f 2 +. T h e 2.52 M e V p e a k , if present, was substantially smaller t h a n the Satchler f o r m a l i s m p r e d i c t i o n (i.e., a b o u t 7 m b / s r at 90 ° a n d E n = 4.0 M e V with Beyster penetrabilities) a n d was b u r i e d in the tail o f the 2.60 M e V g a m m a rays f r o m the 3.45 M e V d o u b l e t . T h e 3.37 M e V g r o u n d state t r a n s i t i o n was n o t observed. T h e 2.940 a n d 3.388 M e V levels were n o t o b s e r v e d in this e x p e r i m e n t a n d it is p r o b a b l e t h a t their spins are >= 5. T h e results o f the m e a s u r e m e n t s a n d calculations w h i c h have been described indicate the a p p l i c a b i l i t y o f the Satchler f o r m a l i s m to the s t u d y o f g a m m a - r a y a n g u l a r distributions f r o m inelastic n e u t r o n scattering. T h e utility o f the t h e o r y in the d e t e r m i n a t i o n or c o r r o b o r a t i o n o f the spin o f a given excited level is quite m a r k e d , p a r t i c u l a r l y w h e n a g a m m a r a y originating at the excited level is o f a single m u l t i p o l a r i t y (e.g., a t r a n s i t i o n to a level o f spin 0). T h e a u t h o r s w o u l d like to express their a p p r e c i a t i o n to the staff o f Texas N u c l e a r C o r p o r a t i o n for m u c h advice a n d assistance with p a r t i c u l a r t h a n k s to Dr. S. M a t h u r for the use o f his F O R T R A N code T R A N S E C , a n d to Dr. D. M . V a n P a t t e r a n d Dr. P. F. Hinrichsen for suggestions a n d c o r r e s p o n d e n c e related to their (p, P'7) w o r k on the S6Fe nucleus.

References I) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23)

G. R. Satchler, Phys. Rev. 94 (1954) 1304, 104 (1956) 1198, 111 (1958) 1747 J. J. Hopkins and M. G. Silbert, Nucl. Sci. Eng. 19 (1964) 431 W. B. Gilboy and J. H. Towle, Nuclear Physics 64 (1965) 130 M. Hosoe and S. Suzuki, J. Phys. Soc. Japan 14 (1959) 699 R. B. Day and M. Walt, Phys. Rev. 117 (1960) 1330 J. W. Boring and M. T. McEllistrem, Phys. Rev. 124 (1961) 1531 D. J. Donahue and R. D. Roberts, Nuclear Physics 50 (1964) 641 L. Cranberg and J. S. Levin, Phys. Rev. 103 (1956) 343 C. C. Trail and Sol Raboy, Rev. Sci. Instr. 30 (1959) 425 Texas Nuclear Corporation Annual Progress Report, Contract AT-(40-1)-2791 (15 August, 1964) unpublished J. B. Ashe, I. L. Morgan and J. D. Hall, to be published K. Way et aL, Nuclear Data Sheets (NAS-NRC) Washington, D. C., (1959) p. NRC 59-4-51 D. M. Van Patter, unpublished (1964) J. R. Beyster, R. G. Schrandt, M. Walt and E. W. Salmi, Los Alamos Scientific Laboratory Report No. 2099, unpublished E. H. Auerbach and F. G. J. Percy, Brookhaven National Laboratory Report No. 765, unpublished F. Bjorklund and S. Fernbach, Phys. Rev. 109 (1958) 1295 F. Percy and B. Buck, Nuclear Physics 32 (1962) 353 P. Kienle and R. E. Segel, Phys. Rev. 114 (1959) 1554 O. J. Poppema, J. G. Siekman, R. Van Wageningen and H. A. Tolhoek, Physica 21 (1955) 223 J. BeUicard and P. Barreau, Nuclear Physics 36 (1962) 476 K. Matsuda, Nuclear Physics 33 (1962) 536 J. C. Jacmart etaL, Phys. Lett. 8 (1964) 273 P. F. Hinrichsen, M. H. Shapiro and D. M. Van Patter, Bull. Am. Phys. Soc. 10 (1965) 427; P. F. Hinrichsen, private communication