The existence of three doublets in 56Fe

Volume 19, number 7

PHYSICS LETTERS

point charge and exp - g E (and the n e g l i g i b l e fact o r s involving the higher t e r m s in E) give the effect of finite n u c l e a r s i z e on the e n e r g y dependence "of the a b s o r p t i o n c r o s s section. With our r e s u l t we can now show how optical model a n a l y s i s at high e n e r g y can be u s e d to e x t r a p o l a t e to the v e r y low e n e r g i e s of i n t e r e s t in a s t r o p h y s i c s . F o r S we take the s i m p l e s q u a r e well r e s u l t (at the c o r r e c t s q u a r e - w e U r a d i u s , R 1 = Ro + AR) and m u l t i p l y it by the r e f i e c t i o n - f a c t o r . F o r g we s i m p l y take the black n u c l e u s s q u a r e - w e l l r e s u l t

g = 0.122 [~R

~,

(5)

where # i s the r e d u c e d m a s s in a . m . u . , Z 1 and Zt a r e charge n u m b e r s of i n c i d e n t and t a r g e t n u c l e i r e s p e c t i v e l y . The power of our method here is not, p r i m a r i l y , to f a c i l i t a t e the e x t r a polation to low e n e r g i e s , but to exhibit c l e a r l y the p r e c i s e dependence of the e x t r a p o l a t i o n on the v a r i o u s optical model p a r a m e t e r s d e t e r m i n e d at high e n e r g y . (3) The p r e s e n t t r e a t m e n t of the diffuse n u c l e a r edge can be u s e d to accomodate the idea of this edge in the c o n v e n t i o n a l R - m a t r i x t h e o r i e s which a r e tied to a fixed choice of the n u c l e a r r a d i u s , as d i s c u s s e d in ref. 3 for s - w a v e n e u t r o n s . {4) The m o s t e x t r e m e case of b a r r i e r p e n e t r a t i o n with which we were able to t e s t the above idea on the Chalk R i v e r G-20 c o m p u t e r was that of 12C + 160 r e a c t i o n s (with Vo = -50 MeV, R o = 6 . 0 1 1 5 f m , Wo = - 1 0 MeV, a = 0 . 5 f m ) . We find f r o m fig. 1 that f = 6.4 and AR = 0.86 fm. At 6.6 MeV we find that the l = 0 t r a n s m i s s i o n func-

THE

EXISTENCE

OF

15 December 1965

t.ion of the diffuse-edge potential is 6.6 t i m e s that of the e q u i v a l e n t s q u a r e - w e l l , in e x c e l l e n t a g r e e m e n t with the r e f l e c t i o n factor. With AR = 0 the r a t i o of t r a n s m i s s i o n function is l a r g e r than 100 at low e n e r g i e s . (5) In an e x t e n s i o n of the work r e p o r t e d h e r e Scherk and Vogt [8] have shown that in the alpha decay of heavy n u c l e i the u s u a l W. K. B. t r e a t m e n t of d i f f u s e - e d g e s i s in e r r o r by an o r d e r of m a g n i tude or m o r e . The diffuse-edge t r a n s m i t s alphap a r t i c l e s m u c h m o r e r e a d i l y than the W. If. B. app r o x i m a t i o n s u g g e s t s . This c o r r e c t i o n s u b s t a n t i a l l y r e d u c e s the d i s p a r i t y between o b s e r v e d and c a l c u l a t e d r e d u c e d widths for alpha p a r t i c l e e m i s sion. Many p a r t s of this work have benefitted f r o m d i s c u s s i o n s with D, M c P h e r s o n and f r o m the u s e of c o m p u t e r p r o g r a m s p r e p a r e d by him and Miss Joanne Drake.

~ e f e'Fe#lces 1. H. Feshbach, C. E. Porter and V. F. Weisskopf, Phys. Rev.96 (1954) 448. 2. D.C.Peaslee, Nuclear Phys.3 (1957) 255. 3. E.Vogt, Rev.Mod.Phys.34 (1962) 723. 4. E.H. Auerbach and C. E. Porter, Nuclear Phys. 57 (1964) 603. 5. J.P.Schiffer, Nuclear Phys.46 (1963) 246. 6. R.D.Woods and D.S.Saxon, Phys.Rev.95 (1954) 577. 7. H.Reeves, G.Michaud and E.W.Vogt, to be published. 8. L.Scherk and E.W.Vogt, to be published.

THREE

DOUBLETS

IN 56Fe

*

M. H. SHAPIRO **, P. F. HINRICHSEN and R. MIDDLETON University of Pennsylvania and R. K. MOHINDRA *** Bartol Research Foundation

Received 19 November 1965 P r e v i o u s d e t e r m i n a t i o n s of the e n e r g y l e v e l s of 56Fe have been made by s t u d i e s of the r a d i o * Work supported by the National Science Foundation. ** National Science Foundation Co-operative Fellow. *** Present address: Physics Dept., Brown University, Providence, R.I.

active decay [1, 2] of 56Mn and 56Co, and by m a g n e t i c s p e c t r o g r a p h m e a s u r e m e n t s on the 56Fe(p, p ' ) b 6 F e , 59Co(p, ct)56Fe and 54Fe(t, p) 56Fe r e a c t i o n s [3-8]. S e v e r a l spin and p a r i t y a s s i g n m e n t s have been made on the b a s i s of studies of the ~ decay [1] of 56Mn and 56Co, the 54Fe(t, p) 573

Volume

19, number 7

PHYSICS LETTERS

56Fe r e a c t i o n [8] and by v - r a y a n g u l a r d i s t r i b u tion m e a s u r e m e n t s f r o m the (n, n'v) r e a c t i o n [9] and (p, p'y) r e a c t i o n [10]. P a r t i c l e v - r a y c o i n c i d e n c e s [11] f r o m 56Fe(p, p ' v ) 5 6 F e have e s t a b l i s h e d the m a j o r d e c a y m o d e s of l e v e l s below 4.0 MeV. M a r k e d d i f f e r e n c e s in the o b s e r v e d b r a n c h i n g r a t i o s , and s p i n a s s i g n m e n t s for the 3.12, 3.44 and 3.60 MeV l e v e l s s u g g e s t that t h e s e l e v e l s a r e doublets. The ~ decay of 56Co p o p u l a t e s a l e v e l at 3.12 MeV which d e c a y s p r e d o m i n a n t l y to the 2.083 MeV 4 + s t a t e , with l e s s than 1% b r a n c h e s to the g r o u n d s t a t e and 0.844 MeV 2+ s t a t e [1]. G a m m a r a y s of 2.27 and 3.12 MeV have been o b s e r v e d f r o m the 56Fe(n, n ' v ) 5 6 F e r e a c t i o n [9,121, and c o i n c i d e n c e s t u d i e s [11] of 56Fe(p, p ' v ) 5 6 F e e s t a b l i s h that the 2.27 MeV T - r a y o r i g i n a t e s f r o m a l e v e l at 3.12 MeV. F u r t h e r m o r e , the b r a n c h i n g of the 3.12 MeV l e v e l w a s o b s e r v e d to change with i n c i d e n t p r o t o n e n e r g y . T h e s e r e s u l t s a r e c o n s i s t e n t with the p o s t u l a t e of two l e v e l s at 3.12 MeV, one of which d e c a y s 100% to the 2.083 MeV 4 + s t a t e while the o t h e r g i v e s r i s e to the 2.27 and 3.12 MeV t r a n s i t i o n s .

15 December 1965

The 3.44 MeV l e v e l i s a l s o p o p u l a t e d in the E - d e c a y of 56Co and i s o b s e r v e d to d e c a y 25% through the 2.083 MeV 4 + s t a t e and 75% through the 0.844 MeV 2 + s t a t e . T h e s e r e s u l t s s u g g e s t a s p i n of 3 + [13]. In the ( n , n ' y ) and ( p , p ' y ) s t u d i e s a ground state v-ray is observed arising from a s t a t e at about 3.44 MeV and the a n g u l a r d i s t r i b u tion m e a s u r e m e n t s e s t a b l i s h the s p i n to be 1. Thus it s e e m s l i k e l y that the 3.44 MeV l e v e l i s a doublet having a 3 + m e m b e r and a m e m b e r of spin I. A s t r o n g 3.60 MCV v - r a y h a s b e e n o b s e r v e d [9, 10] in 56Fe(n, n ' y ) 5 6 F e and 56Fe(p, p ' y ) 5 6 F e s t u d i e s , and c o i n c i d e n c e m e a s u r e m e n t s e s t a b l i s h it a s a g r o u n d s t a t e t r a n s i t i o n [11], while the ang u l a r d i s t r i b u t i o n s s u g g e s t s p i n 2 f o r this level. However, r e c e n t m e a s u r e m e n t s [8] of the p r o t o n a n g u l a r d i s t r i b u t i o n s f r o m 54Fe(t, p)56Fe show good L = 0 double s t r i p p i n g p a t t e r n s for both the 0 + g r o u n d s t a t e g r o u p and a l e v e l at 3.60 MeV. A 0 + s p i n a s s i g n m e n t was a l s o s u g g e s t e d by ine l a s t i c p r o t o n s c a t t e r i n g m e a s u r e m e n t s [6], so that t h e r e was evidence f o r a s s u m i n g that t h i s l e v e l w a s a l s o double.

PROTON ENERGY (MeV) 6.0 I

45C

6.5

ZO

,~

7.5 I

T

40(:

8.0

~

%

35C 30C 25C 20C

E

I(/)

15C

E E

I OC

--I~ t,,,. I.Ll a.

i!

1

1

50

C"

60

65

70

75

80

U') l-Z 0 tJ

oo~

i

0L

5

_

~t" I0

i 15

,4

,3 "

__1' 20

"" ~':~

25

i

::

} ~

[ ;" ~ " ~ 30

-'t~_i:~ 35

~I II

i :~-..''.:. 40

I 45

~ ' F

..... 50

~'_~.~ bb

DISTANCE ALONG PLATE IN cm

Fig. 1. Spectrum of protons scattered from 56Fe at 90°. Incident proton energy 8.0 MeV. 574

i

Volume 19, number 7

PHYSICS LETTERS

In o r d e r to o b s e r v e the doublets d i r e c t l y we have r e p e a t e d the 56Fe(p, p ' ) 5 6 F e m e a s u r e m e n t s u s i n g a 65 c m b r o a d - r a n g e m a g n e t i c s p e c t r o g r a p h u n d e r conditions of o p t i m u m e n e r g y r e s o lution. E x p o s u r e s w e r e made with a 99.7 p e r c e n t e n r i c h e d 56Fe t a r g e t at an i n c i d e n t e n e r g y of 8.0 MeV and angles of 90 ° and 50 °. The e l a s t i c and f i r s t two excited s t a t e groups w e r e not r e c o r d e d on these e x p o s u r e s , a s the s p e c t r o g r a p h field was s e t so that the doublets were in the r e gion of the focal p l a n e for which the a b e r r a t i o n s a r e a m i n i m u m . A t h i r d exposure r e c o r d i n g the e l a s t i c g r o u p s for i m p u r i t y identificaUon was made at 90 ° and this s p e c t r u m i s shown in fig. 1. The chief i m p u r i t i e s o b s e r v e d w e r e 12C, 160, 14N, 32S and 138Ba, none of which would give r i s e to g r o u p s i n the r e g i o n of i n t e r e s t . Despite the r e l a t i v e l y high background, due to s l i t s c a t t e r i n g , a l l l e v e l s below 4 MeV in 56Fe, except those at 3.386 MeV and 3.747 MeV w e r e o b s e r v e d . The e n e r g y v a l u e s d e r i v e d f r o m the t h r e e m e a s u r e m e n t s axe l i s t e d in table 1. F o r the two exp o s u r e s in which the e l a s t i c group was not r e corded, the i n c i d e n t e n e r g y was f i r s t c a l c u l a t e d a s s u m i n g a value of 2.657 MeV for the e n e r g y of l e v e l 3, and was i n e x c e l l e n t a g r e e m e n t with that obtained f r o m the e l a s t i c group in the t h i r d exposure.

the high e n e r g y edge of the 3.60 MeV group as shown i n fig. 2. The r e s i d u a l peak was found to be b r o a d c o m p a r e d to that for a single level, i n d i cating that this m a y p o s s i b l y be a t r i p l e group. A s i m i l a r p r o c e d u r e , when applied to the 3.12 and 3.44 MeV groups, leads to a n e s t i m a t e of a p p r o x i m a t e l y 3 keV for the doublet s p a c i n g in both c a s e s . Since the c o m p l e t i o n of this work it was l e a r n e d that the e x i s t e n c e of the 3.12 and 3.44 MeV doublets has b e e n independently c o n f i r m e d by MacDonald and Grace [14], who u s e d a l i t h i u m d r i f t e d g e r m a n i u m c o u n t e r to o b s e r v e the 7 r a y s f r o m the decay of 56Co and 56Mn, and f r o m the 56Fe(p, p'7)56Fe r e a c t i o n .

i

1 2 3 4 5 6a,b 7 9a, b 10a 10b 12 13 mean

90°

50°

(849) (z085) 2657 2940 2958 3118 3366 3442 3599 3605 3831 3856 ,5

5.7 5.3 5.0 5.3 6.8 5.7 6.8 13.3

4.7 4.5 4.3 4.8 6.4 4.7 6.9 11.7

5.2 6.4 5.6 6.7 7.2 6.2 8.6 12.3

5.6 6.5 5.5 * 0.4

4.7 4.7 4.6 ± 0.2

7.4 7.7 6.5 -~ 0.9

The 3.12, 3.44 and 3.60 MeV groups a r e shown in fig. 2 together with the s i n g l e 3.368 MeV group for c o m p a r i s o n . The doublet a r e not r e s o l v e d except in the c a s e of the 3.60 MeV group, but the 3.12 MeV and 3.44 MeV groups axe definitely b r o a d e r than those f r o m a d j a c e n t single l e v e l s . This behaviour was o b s e r v e d in a l l t h r e e expos u r e s , a s shown i n t a b l e 1. A s t a n d a r d line shape was d e r i v e d f r o m the single groups and fitted to

I

/,,

I

I

,~

/

IO( 50

._/

I

1

I

3.601 MeV Group %

\

\\

i// ...,,,

\ \

. ....

•

20

E E -I,,:r 90°

I

/

/

I00

Full width (keV) E(keV)

I

'-"'~x,~//j:._.~,,

Table 1 Widths of observed proton groups. Level number

15 December 1965

r,,.* uJ 0. u') I..-. Z 0rj,

%

5C

3.443 MeV Group

/*"-,

2O

/

...

~ .

,

3.118 MeVGroup

,

\ 5O

-

S - •

/

~

.oy 20I 2

/

I I

o

I I

I 2

3.368 MeV Group

elee~ee

••eeeee

I 3

I 5

I 4

I 6

e

I 7

DISTANCE ALONG PLATE (ram) Fig. 2. Line shapes of the 3.60, 3.44 and 3.12 MeV doublets at 50° , for an incident proton energy of 8.0 MeV. The line shape of the group from the 3.37 MeV level is shown for comparison.

575

Volume 19, number 7

PHYSICS LETTERS

We would like to thank Dr. D. M. Van P a t t e r and Dr . R. W. B e n j a m i n f o r helpful d i s c u s s i o n s during the c o u r s e of this work and f o r m a k i n g t h e i r r e s u l t s a v a i l a b l e p r i o r to publication. We would also like to thank Dr. J. R. MacDonald f o r c o m m u n i c a t ing his r e s u l t s p r i o r to publication.

References 1. P.Kienle and R.E.Segel, Phys.Rev. 114 (1959) 1554. 2. J.H.Hamilton, L.M.Langer and D.R.Smith, Phys. Rev.123 (1961) 189. 3. A. Sperduto and W. W. Buechner, Phys. Rev. 134 (1964) B142. 4. A. Aspinall, G, Brown and S. E. Warren, Nuclear Phys.46 (1963) 33.

15 December 1965

5. G. Brown, S.E. Warren and R. Middleton, to be published. 6. K.Matauda, Nuclear Phys.33 (1962) 536. 7. M.Mazari, A.Sperduto and W.W. Buechner, Phys. Rev.107 (1957) 365. 8. R. Middleton and B. L. Cohen, private communication. 9. R.W. Benjamin, PhD. thesis, University of Texas, June 1965. 10. D.M.Van Patter and P.N.Trehan, private communication. 11. P.F.Hinrichsen, M.H.Shapiro and D.M.Van Patter, Bull. Am. Phys. Soc. 10 (1965) 427. 12. D.M.Van Patter and R.W.Jackiw, Proc. Int. Conf. Nuclear Structure, Kingston (University of Toronto Press, Toronto, 1960) p.224. 13. K.Way et al., Nucl.Data Sheets. 14. J.R.MacDonald and M.Grace, private communication.

* * * * *

NEGATIVE

P A R I T Y AND ISOBARIC ANALOGUE STATES IN 3 1 p W. G. DAVIES, W. K. DAWSON and G. C. NEIL~ON *

Nuclear Research Centre, Physics Department University of Alberta, Edmonton, Alberta, Canada Received 19 November 1965

The a n g u l a r d i s t r i b u t i o n s of the n e u t r o n g r o u p s f r o m the r e a c t i o n 30Si(d, n)31p have b e e n s t u d i ed u s i n g a high r e s o l u t i o n n e u t r o n t i m e - o f flight s p e c t r o m e t e r [1, 2]. Spins and p a r i t i e s have b e e n a s s i g n e d to the five l e v e l s of 31p shown in table 1. S p e c t r a w e r e obtained by b o m b a r d i n g an enr i c h e d 30Si t a r g e t ** with d e u t e r o n s of 4 and 5 MeV. The angular d i s t r i b u t i o n s of the n e u t r o n s leading to the 5.012, 6.46 and 6.61 MeV s t a t e s of 3 1 p and the a s s o c i a t e d DWBA fits a r e shown in fig. 1 for a d e u t e r o n b o m b a r d i n g e n e r g y of 5 MeV. Since the r e s u l t s obtained at E d = 4 MeV a r e cons i s t e n t with those obtained at E d = 5 MeV only the 5.0 MeV data will be p r e s e n t e d h e r e . In a ll c a s e s it is s e e n (fig. 1) that the lp = 1 fit i s f a v o u r e d o v e r lp = 2 e s t a b l i s h i n g o d d p a r i t y f o r t h e s e s t a t e s . The olSticai m o d e l p a r a m e t e r s u s e d to fit the ang u l a r d i s t r i b u t i o n s a r e shown in the i n s e r t of fig. 1. The spin dependent s t r u c t u r e found by S c h i l l e r * Work supported in part by the Atomic Energy Control Board of Canada. ** The 210 g / c m 2 thick target, enriched to approximately 90% 30Si was supplied by A. E. R.E., Harwell, U.K., in the form of SiO2 deposited on gold. 576

Table 1 Negative parity and isobaric analogue states in 31p Previous work

Ex (a) (MeV) 5 .Ol

j~"

'[i-[- ,~3 + )

[6]

Present work lp

J~

T

1

3-~ 3+ z

3 ~-

1

6.38

2

6.46

i

½-

½

6.61

1 o

i - - 3-(4 ,~) i+ ~

1

7.15

½

(a) Ref. 4 except where indicated otherwise (see refs. 4-8 for further information on the levels of 31p). and Lee [3] f o r / n = 1 t r a n s i t i o n s in (d, p) r e a c tions can be s u m m a r i z e d as follows. The J = ½ s t a t e s show a s h a r p m i n i m u m in the r e g i o n b etween 0 = 90 ° and 0 = 145 ° but the J = ~ s t a t e s do not show this m i n i m u m . Inspection of the angular d i s t r i b u t i o n s g i v e n in fig. 1 c l e a r l y shows the m i n i m u m m e n t i o n e d above in the an g u l ar d i s t r i bution of the n e u t r o n s leading to the 6.46 MeV st at e of 31p, while the an g u l ar d i s t r i b u t i o n of the n e u t r o n s leading to the 5.012 MeV state does