- Email: [email protected]
An experimental test for the nature of fluctuations in the reaction cross sections
Volume 1O, number 1
PHYSICS LETTERS
15 May 1964 Nb de particules
Nb de ~rticul~
i 1
t- 1
2
E o
2
4
6
4
6
F MeV
Fig. 3
MeV
Fig. 2 Note that the f i r s t t e r m of eq. (7) i s j u s t the cont r i b u t i o n given by the m o d e l of Watson (see eq. (3)). We have c a l c u l a t e d the cz p a r t i c l e e n e r g y s p e c t r u m u s i n g the a m p l i t u d e A given by eq. (2) (Wats o n ' s model) and eq. (4) ( B o n n e v a y ' s model). Act u a l l y , the r a t i o between the 3rd t e r m and the 2nd t e r m in eq. (7) has been evaluated and found to be of the o r d e r of ~ , t h e r e f o r e the c o n t r i b u t i o n due to the ~2 s i n g u l a r i t y has been neglected in our r e sults. T h e s e a r e shown in fig. 2 and 3; the dotted l i n e s r e p r e s e n t the e x p e r i m e n t a l r e s u l t s 3) of the C 12 p h o t o d i s i n t e g r a t i o n by 17.6 MeV y - r a y s . F r o m these f i g u r e s one can e a s i l y r e a l i z e that
the additional effects due to the l o g a r i t h m i c s i n g u l a r i t i e s a r e i m p o r t a n t enough to give a r a t h e r good a g r e e m e n t with e x p e r i m e n t a l r e s u l t s . I am v e r y g r a t e f u l l y indebted to the late P r o f e s s o r G. Bonnevay for having suggested to m e the subject of this study and for his constant help and e n c o u r a g e m e n t .
References
1) M.Watson, Phys. Rev. 88 (1952) 1163. 2) G. Bonnev~y, Nuovo Cimento 20 (1963) 1325. 3) R.Chastel, Thesis, Universit6 de Paris (1952), unpublished; V. L. Telegdi, Phys. Rev. 84 (1952) 60O; M. Garnier, H. Gauvin and W. Sebaoun, J. phys. r a dium 21 (1960) 893.
AN EXPERIMENTAL TEST FOR THE NATURE OF FLUCTUATIONS IN T H E R E A C T I O N CROSS SECTIONS
P. STROHAL, P. KULI~I~, Z. KOLAR and N. CINDRO Institute 't Ruder Bo~kovi6 u, Zagreb , Yugoslavia
Received 22 April 1964
S t a t i s t i c a l f l u c t u a t i o n s in the c r o s s s e c t i o n s as a function of e n e r g y , r e c e n t l y pointed out by E r i c son 1,2), have been o b s e r v e d in m a n y n u c l e a r r e actions in the r e g i o n of low and m e d i u m energy. Most of these e x p e r i m e n t s have been p e r f o r m e d by m e a s u r i n g p r o c e s s e s leading to s e p a r a t e single f i n a l s t a t e s , for the obvious r e a s o n that m a n y f i n a l s t a t e s d e c r e a s e the amplitude of fluctuations. In a few a r t i c l e s 3-5) h o w e v e r , the e x i s t e n c e of 104
s t a t i s t i c a l fluctuations in the total r e a c t i o n c r o s s s e c t i o n s for (n,p) and ( n , a ) r e a c t i o n s has been reported. We have t r i e d to find m o r e evidence for the existence of f l u c t u a t i o n s in the total c r o s s sections of n e u t r o n induced r e a c t i o n s and to e s t a b l i s h the A - d e p e n d e n c e of the p e r i o d of fluctuations and t h e i r amplitude dependence on the n u m b e r of f i n a l states. In the p r e s e n t work fine r e s o l u t i o n m e a s u r e -
Volume 10, number 1
PHYSICS LETTERS
m e n t s of the total r e a c t i o n c r o s s s e c t i o n s for the r e a c t i o n s F19(n,2n)F18~ Mg24(n,p)Na 24 and Fe56(n,p)Mn56 a r e r e p o r t e d for n e u t r o n e n e r g i e s around 14 MeV. F o r these e x p e r i m e n t s p l a t e s of m a g n e s i u m and i r o n 3 x 10 x 10 m m each were used and teflone p l a t e s 1 m m thick and 28 m m in d i a m e t e r were mounted r a d i a l l y around the n e u t r o n s o u r c e on a r i n ~ - s h a p e d h o l d e r , as des c r i b e d p r e v i o u s l y 3). N e u t r o n s of e n e r g y f r o m 14.13 to 14.78 MeV in the case of m a g n e s i u m and i r o n and f r o m 13.94 to 14.82 MeV in the case of teflone t a r g e t s were obtained by the a n g u l a r v a r i a t i o n of the d i r e c t i o n of the beam. The e n e r g y s p r e a d due to the finite g e o m e t r y of the e x p e r i ment was of the o r d e r of a few keV while the total
o.,, o
tttitt!tttt!tttt t tt tt
-
;
o,.o.
t
-; -1o
15 May 1964
e n e r g y s p r e a d was about 50 keY 6). The r e l a t i v e m e a s u r e m e n t s of the c r o s s sections were p e r f o r m e d by the activation method u s i n g a 3" × 3" NaI(T1) s c i n t i l l a t i o n c r y s t a l . The e x p e r i m e n t a l r e s u l t s a r e shown in fig. 1. The e x p e r i m e n t a l data were i n t e r p r e t e d in t e r m s of the E r i c s o n t h e o r y of s t a t i s t i c a l f l u c tuations. The a n a l y s i s of the r e s u l t s shows that f l u c t u a t i o n s of the total r e a c t i o n c r o s s sections a r e v i s i b l e in the e n e r g y r a n g e studied for all r e actions except for the Fe56(n,p)Mn56. The width and the amplitude of the fluctuations for a p a r t i c u l a r r e a c t i o n do not change a p p r e c i a b l y in the m e a s u r e d i n t e r v a l . Qualitatively the e x p e r i m e n t al r e s u l t s c o m p a r e well to the t h e o r y of s t a t i s t i c a l fluctuations as p r e s e n t e d by E r i c s o n 1,2). The p e r i o d of fluctuations i . e . the width of the c o h e r e n c e i n t e r v a l F d e c r e a s e s with i n c r e a s i n g atomic n u m b e r and r a n g e s from about 200 keV for f l u o r i n e to about 120 keV for both the r e a c t i o n s Mg24(n,p)Na24 and A127(n,~)Na 24. In the case of the r e a c t i o n Fe56(n,p)Mn56 f l u c t u a t i o n s , if existent, were e x p e r i m e n t a l l y undetectable in our case (period l e s s than 80 keV). A f u r t h e r inf e r e n c e f r o m fig. 1 c o n c e r n s the a m p l i t u d e s of the f l u c t u a t i o n s , which as i s well known, a r e r e duced by the n u m b e r of open outgoing channels. This is p a r t i c u l a r l y d i s c e r n i b l e f r o m the comp a r i s o n of the fluctuations in the r e a c t i o n A127(n, ~)Na 24 and Mg24(n,p)Na 24. The extent of the quantitative a g r e e m e n t b e tween theory and e x p e r i m e n t is shown in t a b l e s 1 and 2. The t h e o r e t i c a l v a l u e s of the c o h e r e n c e e n e r g y ~i m a x
=~-', giMi j" r=V'~ri
•
11)/
"
""
' 14'0
I
I 14"2
1
I 14"4
Fig. I
I
I !4'6
I 1"1'8
o
-~ ~2~2
2 ~u~-E/)
(~ici e (u
_.l ,_%2
dEi
Pc(U )
have been obtained by using the t h e o r e t i c a l p e n e t r a b i l i t i e s of Mani, Melkanoff and I o r i for n e u t r o n s 7) and p r o t o n s 8) and those of Huizenga and Igo for alphas 9), while the level d e n s i t y p a r a m e t e r s used have been listed in table 1. As seen f r o m table 1 t h e r e e x i s t s a f a i r a g r e e m e n t between the e x p e r i m e n t a l and the t h e o r e t i c a l v a l u e s of the coherence e n e r g y F. Another t e s t for the m e a n i n g f u l n e s s of these r e s u l t s i s p r e s e n t e d in table 2. In the p r e s e n t worl~ we have d e l i b e r a t e l y t r i e d to adjust the s t a t i s t i c a l model p a r a m e t e r s so as to obtain a g r e e m e n t with the e x p e r i m e n t a l values of the c o h e r e n c e e n e r g y F and then to use these p a r a m e t e r s to calculate some c r o s s sections for n e u t r o n induced r e a c t i o n s for these nuclei. We 105
Volume 10, number 1
PHYSICS LETTERS
15 May 1964
Table 1 Reaction
a (MeV-1)
Fn,
F19(n, 2n)F18
20.54-21.42
3.5
120
Mg24{n,p)Na 24
22.00- 22.65
3.5
A127(n, c0Na24
21.34 -21.99
Fe56(n, p)Mn56
21.99 -22.64
Fp
Fa
Ftheor_E Fi
Fexp.
Theor.
Exp:
11
152
283
220
2.1
3.1
74
33
36
143
160
5.7
5.1
4
82
15
28
125
130
6.3
5.8
8
6.3
-
96.1
0.3
Table 2
Reaction
F19(n,p)O 19 F19(n, ~.)N16
Theoretical Average values calRatio of experi- culated with v(n,p)/v(n,a) mental parameters cross sec- of table 1 tions (rob) (rob) Exp. Theor. 15 57
45 635
Mg24(n, p)Na24
200
213
A127(n,p)Mg27 A127(n, ~)Na24
73 115
116 218
Fe56(n, p)Mn56
116
65
0.263 0.071 -
-
0.635 0.532 -
-
have chosen this d i r e c t i o n r a t h e r than the opposite for the following r e a s o n s : (i) the c a l c u l a t i o n of F viz. T c o m p r i s e s the u s e of l e s s p a r a m e t e r s than the c a l c u l a t i o n of the total c r o s s s e c t i o n s ; (ii) a d j u s t i n g the s t a t i s t i c a l model p a r a m e t e r s to fit the c o h e r e n c e p e r i o d r a t h e r than the c r o s s s e c t i o n s we have avoided the c o m p a r i s o n of the s t a t i s t i c a l t h e o r y with q u a n t i t i e s which m a y include d i r e c t effects. It is obvious f r o m table 2 that the s t a t i s t i c a l t h e o r y in its s i m p l e f o r m i s not adequate to exp l a i n proton or alpha e m i s s i o n f r o m f l u o r i n e . It is a l m o s t c e r t a i n that c l u s t e r effects in the s t r u c t u r e of f l u o r i n e i n v a l i d a t e the s u p p o s i t i o n s of the s t a t i s t i c a l theory. The a g r e e m e n t between theor e t i c a l e s t i m a t e s and e x p e r i m e n t a l r e s u l t s for the other r e a c t i o n s listed in table 2 i s a c c e p t a b l e , e s p e c i a l l y if the r a t i o s of (n,p) vs. {n,~ ) e m i s s i o n p r o b a b i l i t i e s a r e compared. T h i s c o m p a r i s o n has to be r e g a r d e d in view of the fact that it would be u n r e a s o n a b l e to expect a b e t t e r a g r e e m e n t u s i n g a set of p a r a m e t e r s p r e v i o u s l y adjusted to fit a
106
Half-life of the compound..... nucleus (in 10.20 sec)
F (keV)
Excitation energy (MeV)
-
7
different set of data. It i s however i m p o r t a n t to note that the s a m e c o n s i s t e n t set of p a r a m e t e r s (with a ~-A) which s a t i s f i e s the e x p e r i m e n t a l values of the coherence e n e r g i e s gives an a c ceptable fit to the e x p e r i m e n t a l c r o s s sections, T h e r e i s little doubt that a m o r e c a r e f u l choice of p a r a m e t e r s would p e r m i t an even b e t t e r a g r e e m~nt, but would not change the e s s e n t i a l f e a t u r e s of t a b l e s 1 and 2. Recently Agodi and P a p p a l o r d o 1 0 ) h a v e i n t e r p r e t e d fluctuations in n e u t r o n induced r e a c t i o n s at low e n e r g y 4 , 5 , 1 0 ) by a s s u m i n g ' s t a t i s t i c a l fluctuations in the level d e n s i t i e s in the r e g i o n of n o n - o v e r l a p p i n g states of the compound nucleus. In our case the excitation of the compound n u c l e u s was c o n s i d e r a b l y higher and well inside the continuum r e g i o n (F >D) except p e r h a p s in the c a s s of F 20, and this kind of r e a s o n i n g could not be applied. The a u t h o r s a r e indebted to Mr. I. B a s a r and Mr. K. Kova~evi~ for c a r r y i n g out p a r t of the n u m e r i c a l work. 1) T.Ericson, Adv. Phys. 9 (1960) 425. 2) T.Ericson, Phys. Rev. Letters 5 (1960) 430. 3) N.Cindro, P.Kuli~i6 and P.Strohal, Physics Letters 6 (1963) 205. 4) G. Calvi, R. Potenza, R. Ricamo and D. Vinciguerra, Nuclear Phys. 39 (1962) 621. 5) J. Konijn and A. Lauber, Nuclear Phys. 48 (1963) 191. 6) B.Antolkovi6, M.Pai6, K. Prelec and P.Toma~, Glasnik m a t . - f i z . i astron. 15 (1960) 61; B. Antolkovi6, Thesis, University of Zagreb. 7) G.S. Mani, M.A. Melkanoff and I. Iori, Rep. CEA No. 2380. 8) G.S.Mani, M.A.Melkanoff and I. Icri, Rep. CEA No. 2379. 9) J.R.Huizengaand G.Igo, Nuclear Phys. 29 {1963) 462. 10) A.Agodi and G.Pappalardo, Nuclear Phys. 47 (1963} 129.
PHYSICS LETTERS
15 May 1964 Nb de particules
Nb de ~rticul~
i 1
t- 1
2
E o
2
4
6
4
6
F MeV
Fig. 3
MeV
Fig. 2 Note that the f i r s t t e r m of eq. (7) i s j u s t the cont r i b u t i o n given by the m o d e l of Watson (see eq. (3)). We have c a l c u l a t e d the cz p a r t i c l e e n e r g y s p e c t r u m u s i n g the a m p l i t u d e A given by eq. (2) (Wats o n ' s model) and eq. (4) ( B o n n e v a y ' s model). Act u a l l y , the r a t i o between the 3rd t e r m and the 2nd t e r m in eq. (7) has been evaluated and found to be of the o r d e r of ~ , t h e r e f o r e the c o n t r i b u t i o n due to the ~2 s i n g u l a r i t y has been neglected in our r e sults. T h e s e a r e shown in fig. 2 and 3; the dotted l i n e s r e p r e s e n t the e x p e r i m e n t a l r e s u l t s 3) of the C 12 p h o t o d i s i n t e g r a t i o n by 17.6 MeV y - r a y s . F r o m these f i g u r e s one can e a s i l y r e a l i z e that
the additional effects due to the l o g a r i t h m i c s i n g u l a r i t i e s a r e i m p o r t a n t enough to give a r a t h e r good a g r e e m e n t with e x p e r i m e n t a l r e s u l t s . I am v e r y g r a t e f u l l y indebted to the late P r o f e s s o r G. Bonnevay for having suggested to m e the subject of this study and for his constant help and e n c o u r a g e m e n t .
References
1) M.Watson, Phys. Rev. 88 (1952) 1163. 2) G. Bonnev~y, Nuovo Cimento 20 (1963) 1325. 3) R.Chastel, Thesis, Universit6 de Paris (1952), unpublished; V. L. Telegdi, Phys. Rev. 84 (1952) 60O; M. Garnier, H. Gauvin and W. Sebaoun, J. phys. r a dium 21 (1960) 893.
AN EXPERIMENTAL TEST FOR THE NATURE OF FLUCTUATIONS IN T H E R E A C T I O N CROSS SECTIONS
P. STROHAL, P. KULI~I~, Z. KOLAR and N. CINDRO Institute 't Ruder Bo~kovi6 u, Zagreb , Yugoslavia
Received 22 April 1964
S t a t i s t i c a l f l u c t u a t i o n s in the c r o s s s e c t i o n s as a function of e n e r g y , r e c e n t l y pointed out by E r i c son 1,2), have been o b s e r v e d in m a n y n u c l e a r r e actions in the r e g i o n of low and m e d i u m energy. Most of these e x p e r i m e n t s have been p e r f o r m e d by m e a s u r i n g p r o c e s s e s leading to s e p a r a t e single f i n a l s t a t e s , for the obvious r e a s o n that m a n y f i n a l s t a t e s d e c r e a s e the amplitude of fluctuations. In a few a r t i c l e s 3-5) h o w e v e r , the e x i s t e n c e of 104
s t a t i s t i c a l fluctuations in the total r e a c t i o n c r o s s s e c t i o n s for (n,p) and ( n , a ) r e a c t i o n s has been reported. We have t r i e d to find m o r e evidence for the existence of f l u c t u a t i o n s in the total c r o s s sections of n e u t r o n induced r e a c t i o n s and to e s t a b l i s h the A - d e p e n d e n c e of the p e r i o d of fluctuations and t h e i r amplitude dependence on the n u m b e r of f i n a l states. In the p r e s e n t work fine r e s o l u t i o n m e a s u r e -
Volume 10, number 1
PHYSICS LETTERS
m e n t s of the total r e a c t i o n c r o s s s e c t i o n s for the r e a c t i o n s F19(n,2n)F18~ Mg24(n,p)Na 24 and Fe56(n,p)Mn56 a r e r e p o r t e d for n e u t r o n e n e r g i e s around 14 MeV. F o r these e x p e r i m e n t s p l a t e s of m a g n e s i u m and i r o n 3 x 10 x 10 m m each were used and teflone p l a t e s 1 m m thick and 28 m m in d i a m e t e r were mounted r a d i a l l y around the n e u t r o n s o u r c e on a r i n ~ - s h a p e d h o l d e r , as des c r i b e d p r e v i o u s l y 3). N e u t r o n s of e n e r g y f r o m 14.13 to 14.78 MeV in the case of m a g n e s i u m and i r o n and f r o m 13.94 to 14.82 MeV in the case of teflone t a r g e t s were obtained by the a n g u l a r v a r i a t i o n of the d i r e c t i o n of the beam. The e n e r g y s p r e a d due to the finite g e o m e t r y of the e x p e r i ment was of the o r d e r of a few keV while the total
o.,, o
tttitt!tttt!tttt t tt tt
-
;
o,.o.
t
-; -1o
15 May 1964
e n e r g y s p r e a d was about 50 keY 6). The r e l a t i v e m e a s u r e m e n t s of the c r o s s sections were p e r f o r m e d by the activation method u s i n g a 3" × 3" NaI(T1) s c i n t i l l a t i o n c r y s t a l . The e x p e r i m e n t a l r e s u l t s a r e shown in fig. 1. The e x p e r i m e n t a l data were i n t e r p r e t e d in t e r m s of the E r i c s o n t h e o r y of s t a t i s t i c a l f l u c tuations. The a n a l y s i s of the r e s u l t s shows that f l u c t u a t i o n s of the total r e a c t i o n c r o s s sections a r e v i s i b l e in the e n e r g y r a n g e studied for all r e actions except for the Fe56(n,p)Mn56. The width and the amplitude of the fluctuations for a p a r t i c u l a r r e a c t i o n do not change a p p r e c i a b l y in the m e a s u r e d i n t e r v a l . Qualitatively the e x p e r i m e n t al r e s u l t s c o m p a r e well to the t h e o r y of s t a t i s t i c a l fluctuations as p r e s e n t e d by E r i c s o n 1,2). The p e r i o d of fluctuations i . e . the width of the c o h e r e n c e i n t e r v a l F d e c r e a s e s with i n c r e a s i n g atomic n u m b e r and r a n g e s from about 200 keV for f l u o r i n e to about 120 keV for both the r e a c t i o n s Mg24(n,p)Na24 and A127(n,~)Na 24. In the case of the r e a c t i o n Fe56(n,p)Mn56 f l u c t u a t i o n s , if existent, were e x p e r i m e n t a l l y undetectable in our case (period l e s s than 80 keV). A f u r t h e r inf e r e n c e f r o m fig. 1 c o n c e r n s the a m p l i t u d e s of the f l u c t u a t i o n s , which as i s well known, a r e r e duced by the n u m b e r of open outgoing channels. This is p a r t i c u l a r l y d i s c e r n i b l e f r o m the comp a r i s o n of the fluctuations in the r e a c t i o n A127(n, ~)Na 24 and Mg24(n,p)Na 24. The extent of the quantitative a g r e e m e n t b e tween theory and e x p e r i m e n t is shown in t a b l e s 1 and 2. The t h e o r e t i c a l v a l u e s of the c o h e r e n c e e n e r g y ~i m a x
=~-', giMi j" r=V'~ri
•
11)/
"
""
' 14'0
I
I 14"2
1
I 14"4
Fig. I
I
I !4'6
I 1"1'8
o
-~ ~2~2
2 ~u~-E/)
(~ici e (u
_.l ,_%2
dEi
Pc(U )
have been obtained by using the t h e o r e t i c a l p e n e t r a b i l i t i e s of Mani, Melkanoff and I o r i for n e u t r o n s 7) and p r o t o n s 8) and those of Huizenga and Igo for alphas 9), while the level d e n s i t y p a r a m e t e r s used have been listed in table 1. As seen f r o m table 1 t h e r e e x i s t s a f a i r a g r e e m e n t between the e x p e r i m e n t a l and the t h e o r e t i c a l v a l u e s of the coherence e n e r g y F. Another t e s t for the m e a n i n g f u l n e s s of these r e s u l t s i s p r e s e n t e d in table 2. In the p r e s e n t worl~ we have d e l i b e r a t e l y t r i e d to adjust the s t a t i s t i c a l model p a r a m e t e r s so as to obtain a g r e e m e n t with the e x p e r i m e n t a l values of the c o h e r e n c e e n e r g y F and then to use these p a r a m e t e r s to calculate some c r o s s sections for n e u t r o n induced r e a c t i o n s for these nuclei. We 105
Volume 10, number 1
PHYSICS LETTERS
15 May 1964
Table 1 Reaction
a (MeV-1)
Fn,
F19(n, 2n)F18
20.54-21.42
3.5
120
Mg24{n,p)Na 24
22.00- 22.65
3.5
A127(n, c0Na24
21.34 -21.99
Fe56(n, p)Mn56
21.99 -22.64
Fp
Fa
Ftheor_E Fi
Fexp.
Theor.
Exp:
11
152
283
220
2.1
3.1
74
33
36
143
160
5.7
5.1
4
82
15
28
125
130
6.3
5.8
8
6.3
-
96.1
0.3
Table 2
Reaction
F19(n,p)O 19 F19(n, ~.)N16
Theoretical Average values calRatio of experi- culated with v(n,p)/v(n,a) mental parameters cross sec- of table 1 tions (rob) (rob) Exp. Theor. 15 57
45 635
Mg24(n, p)Na24
200
213
A127(n,p)Mg27 A127(n, ~)Na24
73 115
116 218
Fe56(n, p)Mn56
116
65
0.263 0.071 -
-
0.635 0.532 -
-
have chosen this d i r e c t i o n r a t h e r than the opposite for the following r e a s o n s : (i) the c a l c u l a t i o n of F viz. T c o m p r i s e s the u s e of l e s s p a r a m e t e r s than the c a l c u l a t i o n of the total c r o s s s e c t i o n s ; (ii) a d j u s t i n g the s t a t i s t i c a l model p a r a m e t e r s to fit the c o h e r e n c e p e r i o d r a t h e r than the c r o s s s e c t i o n s we have avoided the c o m p a r i s o n of the s t a t i s t i c a l t h e o r y with q u a n t i t i e s which m a y include d i r e c t effects. It is obvious f r o m table 2 that the s t a t i s t i c a l t h e o r y in its s i m p l e f o r m i s not adequate to exp l a i n proton or alpha e m i s s i o n f r o m f l u o r i n e . It is a l m o s t c e r t a i n that c l u s t e r effects in the s t r u c t u r e of f l u o r i n e i n v a l i d a t e the s u p p o s i t i o n s of the s t a t i s t i c a l theory. The a g r e e m e n t between theor e t i c a l e s t i m a t e s and e x p e r i m e n t a l r e s u l t s for the other r e a c t i o n s listed in table 2 i s a c c e p t a b l e , e s p e c i a l l y if the r a t i o s of (n,p) vs. {n,~ ) e m i s s i o n p r o b a b i l i t i e s a r e compared. T h i s c o m p a r i s o n has to be r e g a r d e d in view of the fact that it would be u n r e a s o n a b l e to expect a b e t t e r a g r e e m e n t u s i n g a set of p a r a m e t e r s p r e v i o u s l y adjusted to fit a
106
Half-life of the compound..... nucleus (in 10.20 sec)
F (keV)
Excitation energy (MeV)
-
7
different set of data. It i s however i m p o r t a n t to note that the s a m e c o n s i s t e n t set of p a r a m e t e r s (with a ~-A) which s a t i s f i e s the e x p e r i m e n t a l values of the coherence e n e r g i e s gives an a c ceptable fit to the e x p e r i m e n t a l c r o s s sections, T h e r e i s little doubt that a m o r e c a r e f u l choice of p a r a m e t e r s would p e r m i t an even b e t t e r a g r e e m~nt, but would not change the e s s e n t i a l f e a t u r e s of t a b l e s 1 and 2. Recently Agodi and P a p p a l o r d o 1 0 ) h a v e i n t e r p r e t e d fluctuations in n e u t r o n induced r e a c t i o n s at low e n e r g y 4 , 5 , 1 0 ) by a s s u m i n g ' s t a t i s t i c a l fluctuations in the level d e n s i t i e s in the r e g i o n of n o n - o v e r l a p p i n g states of the compound nucleus. In our case the excitation of the compound n u c l e u s was c o n s i d e r a b l y higher and well inside the continuum r e g i o n (F >D) except p e r h a p s in the c a s s of F 20, and this kind of r e a s o n i n g could not be applied. The a u t h o r s a r e indebted to Mr. I. B a s a r and Mr. K. Kova~evi~ for c a r r y i n g out p a r t of the n u m e r i c a l work. 1) T.Ericson, Adv. Phys. 9 (1960) 425. 2) T.Ericson, Phys. Rev. Letters 5 (1960) 430. 3) N.Cindro, P.Kuli~i6 and P.Strohal, Physics Letters 6 (1963) 205. 4) G. Calvi, R. Potenza, R. Ricamo and D. Vinciguerra, Nuclear Phys. 39 (1962) 621. 5) J. Konijn and A. Lauber, Nuclear Phys. 48 (1963) 191. 6) B.Antolkovi6, M.Pai6, K. Prelec and P.Toma~, Glasnik m a t . - f i z . i astron. 15 (1960) 61; B. Antolkovi6, Thesis, University of Zagreb. 7) G.S. Mani, M.A. Melkanoff and I. Iori, Rep. CEA No. 2380. 8) G.S.Mani, M.A.Melkanoff and I. Icri, Rep. CEA No. 2379. 9) J.R.Huizengaand G.Igo, Nuclear Phys. 29 {1963) 462. 10) A.Agodi and G.Pappalardo, Nuclear Phys. 47 (1963} 129.