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A final state interaction model for the photodisintegration of the C12 into three α-particles
Volume 10, number 1
PHYSICS LETTERS
s e c t i o n to the (d,p) s t r i p p i n g one due to Butler is used in the calculation. The r e s u l t of the c a l c u l a t i o n is shown in fig. 1 for theO16(p,a)N 13 (ground state) r e a c t i o n . H e r e , we adopt the following v a l u e s of the " r a d i a l " r e duced widths; 00t = 0.62 and 00p00a = 4.76. The i n t e r f e r e n c e between the p i c k - u p and h e a v y - p a r t i c l e - s t r i p p i n g r e a c t i o n s is not taken into account in t h i s f i g u r e , b e c a u s e the i n t e r f e r e n c e i s found to provide only a s m a l l c o n t r i b u t i o n in our case. Next, we p r e s e n t in figs. 2a and 2b the calculated c r o s s s e c t i o n s for the N15(P,~0)C12 (ground state) and the N15(p,~I)C12 ( l s t excited state) r e a c t i o n s r e s p e c t i v e l y . The " r a d i a l " r e d u c e d withs a r e d e t e r m i n e d as follows; 00t = 0.89 and 00p00a = 0.93 for the N15(P,a0)C12 (ground state) r e a c tion and 00t = 0.61 and 00p 00a = 0.65 for the N15(p,al)C12 ( l s t e x c i t e d s t a t e ) r e a c t i o n . The d i f f e r e n t i a l c r o s s s e c t i o n s for the N15(p,a0)C12 r e a c t i o n and its i n v e r s e r e a c t i o n the C12(~,P0)N15 have been m e a s u r e d in wide r a n g e of incident e n e r g i e s . Since the e n e r g y - d e p e n d e n c e of the References 1) T. Honda and H. Ui, 2) T.Honda and H. Ui, 3) T.Honda, H.Horie, Phys. 31 (1964) No.
Nuclear Phys. 34 (1962) 593. Nuclear Phys. 34 (1962) 609. Y.Kudo and H.Ui, Prog. Theoret. 1.
A FINAL STATE PHOTODISINTEGRATION
15 May 1964
c r o s s section was a n a l y s e d in detail 1), f u r t h e r d i s c u s s i o n of it will not be needed. F r o m the p r e s e n t a n a l y s i s , the a - p a r t i c l e r e duced width for the ground state of 0 16 s e e m s to be l a r g e r than those for n e i g h b o u r i n g nuclei. It is to be noted, however, that in o r d e r to det e r m i n e the r e d u c e d - w i d t h u n a m b i g u o u s l y the e x p e r i m e n t a l data in a wider r a n g e of incident e n e r g y a r e n e c e s s a r y ; for the O16(p,a0)N13 (ground state) r e a c t i o n , the e x p e r i m e n t a l data a r e d e s i r e d at higher e n e r g i e s than that of Maxson 9). In the s a m e way a s developed h e r e , the a n a l y s i s i s now being p e r f o r m e d on the (p,a) r e action for other p - s h e l l n u c l e i , the r e s u l t of which will appear later.
4) T. Honda, Y. Kudo and H. Ui, Nuclear Phy,s. 44 (1963) 472. 5) A. M. Lane, Revs. Modern. Phys. 32 (1960) 519. 6) V.V. Balashov, V.G. Neudachin, Yu. F. Smirnov and N. P. Yudin, J. Exptl. Theor. Phys. 37 (1959) 1385. 7) Yu. F. Smirnov and D. Chlebowska, Nuclear Phys. 26 (1961) 306. 8) H. Horie, to be published. 9) D.R.Maxson, Phys. Rev. 123 (1961) 1304. 10) Nonaka, Suzuki, Kikuchi, Koike, Maki, Matsuda, Mikumo and Nagahara, to be published. 1D T.Hbnda and H. Ui, Prog. Theoret. Phys. 25 (1961) 613 and 635.
INTERACTION MODEL FOR THE OF THE C 12 I N T O T H R E E a-PARTICLES
J. L E T E S S I E R Facult~ des Sciences, Bordeaux, France* Received 8 April 1964
The p u r p o s e of this l e t t e r is to r e p o r t briefly** some r e s u l t s c o n c e r n i n g the role of the final state i n t e r a c t i o n s in p h e n o m e n a a s s o c i a t e d with the C12 p h o t o d i s i n t e g r a t i o n into t h r e e a - p a r t i c l e s . ~+ C 12 - , C 12. ~ 3a
(1)
* Postal address: Laboratoire de Physique Th~orique 351 Cours de la Lib6ration, Talence (Gironde), France. ** The detailed calculations are given in J. Letessier Thesis, Universitd de Bordeaux (unpublished). 102
W e wish especiall~ to see whether th~ models proposed by Watson ) and by Bonnevay ) can be used for interpreting the known experimental results concerning the above mentioned phenomena. The final state interaction conditions specified by Watson 1) seem to be well satisfied in our case. On the other hand we consider that the interaction between two of the produced a-particles, takes place via the f o r m a t i o n of a r e s o n a n c e in a given a n g u l a r m o m e n t u m state. Actually, in the C 12 c a s e , these a s s u m p t i o n s give r i s e to a m e c h a n i s m which can be r e p r e -
Volume 10, number 1
PHYSICS LETTERS
v
Pk
C12
Pi Fig. 1
s e n t e d by d i a g r a m s of the type d r a w n in fig. 1 and we s h a l l a s s u m e that two of the a l p h a ' s i n t e r a c t s t r o n g l y and p r o d u c e m a i n l y the 2 + e x c i t e d s t a t e of Be 8 s e t at 2.9 MeV. In the f r a m e w o r k of W a t s o n ' s m o d e l and taking, of c o u r s e , into account the s y m m e t r i z a t i o n b e tween a l l the p r o d u c e d a - p a r t i c l e s , the m a t r i x e l e m e n t of r e a c t i o n (1) i s :
A:5
~
p2(p~.p~,k)(Cl2*lV~l:2,P~,k)~
15 May 1964
The notations a r e the s a m e a s defined in ref. 2: s i = ( P - p i ) 2 , ~= ~is i= m2 + 3 : P i s t h e m o m e n t u m of the d e c a y i n g p a r t i c l e , hi i s the m o m e n t u m of the / - p a r t i c l e in the final s t a t e , q = ½ (4~:4). The a n a l y t i c p r o p e r t i e s of the s p e c t r a l function a(s ', (~) have been e x t e n s i v e l y studied by Bonn e v a y who h a s shown that t h e y a r e d o m i n a t e d by: 1. the two cuts {- oo,0} and { m - 1) 2 , + oo}, 2. the pole ob c o r r e s p o n d i n g to the two alpha r e sonant state (2 + e x c i t e d state of Be 8) and i t s c o m p l e x conjugate oto*, 3. the f i r s t two oil and (~2 l o g a r i t h m i c s i n g u l a r i t i e s induced by t h e s e p o l e s and t h e i r c o m p l e x conjugate otl*,ot2*. N e g l e c t i n g the two f a r a w a y u n p h y s i c a l c u t s {_ oo,0} and {(m - 1) 2, + oo} and a p p r o x i m a t i n g the c o n t r i b u t i o n s due to the oil", oil*, ot2 and ot2* l o g a r i t h m i c c u t s by e x p r e s s i o n s of the f o r m
(2)
~
f ( s ) log ( s - a 1 )
ivj, k w h e r e Pi is the z-particle' m o m e n t u m , Pi~,k and l a r e r e s p e c t i v e l y the r e l a t i v e l i n e a r and a n g u l a r m o m e n t u m of the j and k - p a r t i c l e s in t h e i r c e n t r e o f - m a s s s y s t e m , and V i s the final state i n t e r action o p e r a t o r . The m a t r i x e l e m e n t A h a s the f o r m g i v e n by eq. (2) b e c a u s e we have a s s u m e d the C 12. s t a t e to be a 0 + s t a t e * . In W a t s o n ' s m o d e l , the m a t r i x e l e m e n t (C 12. IV ]l,pj,k) i s e x p r e s s e d by a B r e i t - W i g n e r type f o r m u l a :
(C12* t V l l ' ~ ' k )
p2t j ,k : Wr- Wj,k-iTp2/+lj,k
(3)
'
with W r = Be 8 m a s s , Wj, k = e n e r g y o f j and k - 8* p a r t i c l e s in t h e i r c e n t r e - o f - m a s s s y s t e m , V-- Be half-width. On the o t h e r hand, following Bonnevay 2), one can w r i t e the a m p l i t u d e A ( s l , s 2 , s 3) of the r e a c tion (1), a s : 3
A ( S l , S 2 , S 3 ) = ~ goi(si,a ) . i=1
(4)
one g e t s : a~-
ds'+c.c.. (6) ot2 .s (The i n t e g r a t i o n path in ~ ) i s c h o s e n in such a jot2 way that it d o e s not c r o s s the cut {4, ~o}. ) The j u m p s of the e x a c t s p e c t r a l function a(s, ~) a c r o s s the cuts a s s o c i a t e d with a 1 and ot2 can be c a l c u l a t e d and we have d e t e r m i n e d the c o n s t a n t s A and B such that the a p p r o x i m a t e funct i o n s a(s',~) given by eq. (6) have the s a m e j u m p s in the neighbourhood of ~1 and ot2- R e p l a c i n g eq. (6) in eq. (5), one g e t s :
q~i(si'(r) = - - ~ 4
a(s',o)
ds'.
l+log(s-otl)+log
q21q oto ~-
Sr-Si-2i Yll + C ( a l ' a ° )
× [q log ( s i - 5 1 ) - qoto log ( s r - ~ l ) ] + D ( 5 2 , a l , a o ) × [q log (si+a2-8) - qotl log ( s t + a 2 - 8 ) ] with qao = ½(~sr-4 ) ,
The ~oi functions obey the following d i s p e r s i o n r e l a t i o n s: - - ?~ qZl
2i
ao = Re oto , (5)
._2 sr =w r ,
a l = Re a l , a2 = Re a 2 , ff
c(al,~o) : 2p(~l)q(~l ) Pt Ix(no)] q~o
q,21 (s,_si) and
* This simplifying hypothesis could be removed, but one is then led to an appreciably more complicated formula.
q 2l F= . 2 l + i ' ~qao
2l÷1 _
7
~qal
D((~2,~l ,°to) = B((~I ,otO) ~ ( ~ a
2) P [X((il)] -
17 J
103
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 -
PHYSICS LETTERS
s e c t i o n to the (d,p) s t r i p p i n g one due to Butler is used in the calculation. The r e s u l t of the c a l c u l a t i o n is shown in fig. 1 for theO16(p,a)N 13 (ground state) r e a c t i o n . H e r e , we adopt the following v a l u e s of the " r a d i a l " r e duced widths; 00t = 0.62 and 00p00a = 4.76. The i n t e r f e r e n c e between the p i c k - u p and h e a v y - p a r t i c l e - s t r i p p i n g r e a c t i o n s is not taken into account in t h i s f i g u r e , b e c a u s e the i n t e r f e r e n c e i s found to provide only a s m a l l c o n t r i b u t i o n in our case. Next, we p r e s e n t in figs. 2a and 2b the calculated c r o s s s e c t i o n s for the N15(P,~0)C12 (ground state) and the N15(p,~I)C12 ( l s t excited state) r e a c t i o n s r e s p e c t i v e l y . The " r a d i a l " r e d u c e d withs a r e d e t e r m i n e d as follows; 00t = 0.89 and 00p00a = 0.93 for the N15(P,a0)C12 (ground state) r e a c tion and 00t = 0.61 and 00p 00a = 0.65 for the N15(p,al)C12 ( l s t e x c i t e d s t a t e ) r e a c t i o n . The d i f f e r e n t i a l c r o s s s e c t i o n s for the N15(p,a0)C12 r e a c t i o n and its i n v e r s e r e a c t i o n the C12(~,P0)N15 have been m e a s u r e d in wide r a n g e of incident e n e r g i e s . Since the e n e r g y - d e p e n d e n c e of the References 1) T. Honda and H. Ui, 2) T.Honda and H. Ui, 3) T.Honda, H.Horie, Phys. 31 (1964) No.
Nuclear Phys. 34 (1962) 593. Nuclear Phys. 34 (1962) 609. Y.Kudo and H.Ui, Prog. Theoret. 1.
A FINAL STATE PHOTODISINTEGRATION
15 May 1964
c r o s s section was a n a l y s e d in detail 1), f u r t h e r d i s c u s s i o n of it will not be needed. F r o m the p r e s e n t a n a l y s i s , the a - p a r t i c l e r e duced width for the ground state of 0 16 s e e m s to be l a r g e r than those for n e i g h b o u r i n g nuclei. It is to be noted, however, that in o r d e r to det e r m i n e the r e d u c e d - w i d t h u n a m b i g u o u s l y the e x p e r i m e n t a l data in a wider r a n g e of incident e n e r g y a r e n e c e s s a r y ; for the O16(p,a0)N13 (ground state) r e a c t i o n , the e x p e r i m e n t a l data a r e d e s i r e d at higher e n e r g i e s than that of Maxson 9). In the s a m e way a s developed h e r e , the a n a l y s i s i s now being p e r f o r m e d on the (p,a) r e action for other p - s h e l l n u c l e i , the r e s u l t of which will appear later.
4) T. Honda, Y. Kudo and H. Ui, Nuclear Phy,s. 44 (1963) 472. 5) A. M. Lane, Revs. Modern. Phys. 32 (1960) 519. 6) V.V. Balashov, V.G. Neudachin, Yu. F. Smirnov and N. P. Yudin, J. Exptl. Theor. Phys. 37 (1959) 1385. 7) Yu. F. Smirnov and D. Chlebowska, Nuclear Phys. 26 (1961) 306. 8) H. Horie, to be published. 9) D.R.Maxson, Phys. Rev. 123 (1961) 1304. 10) Nonaka, Suzuki, Kikuchi, Koike, Maki, Matsuda, Mikumo and Nagahara, to be published. 1D T.Hbnda and H. Ui, Prog. Theoret. Phys. 25 (1961) 613 and 635.
INTERACTION MODEL FOR THE OF THE C 12 I N T O T H R E E a-PARTICLES
J. L E T E S S I E R Facult~ des Sciences, Bordeaux, France* Received 8 April 1964
The p u r p o s e of this l e t t e r is to r e p o r t briefly** some r e s u l t s c o n c e r n i n g the role of the final state i n t e r a c t i o n s in p h e n o m e n a a s s o c i a t e d with the C12 p h o t o d i s i n t e g r a t i o n into t h r e e a - p a r t i c l e s . ~+ C 12 - , C 12. ~ 3a
(1)
* Postal address: Laboratoire de Physique Th~orique 351 Cours de la Lib6ration, Talence (Gironde), France. ** The detailed calculations are given in J. Letessier Thesis, Universitd de Bordeaux (unpublished). 102
W e wish especiall~ to see whether th~ models proposed by Watson ) and by Bonnevay ) can be used for interpreting the known experimental results concerning the above mentioned phenomena. The final state interaction conditions specified by Watson 1) seem to be well satisfied in our case. On the other hand we consider that the interaction between two of the produced a-particles, takes place via the f o r m a t i o n of a r e s o n a n c e in a given a n g u l a r m o m e n t u m state. Actually, in the C 12 c a s e , these a s s u m p t i o n s give r i s e to a m e c h a n i s m which can be r e p r e -
Volume 10, number 1
PHYSICS LETTERS
v
Pk
C12
Pi Fig. 1
s e n t e d by d i a g r a m s of the type d r a w n in fig. 1 and we s h a l l a s s u m e that two of the a l p h a ' s i n t e r a c t s t r o n g l y and p r o d u c e m a i n l y the 2 + e x c i t e d s t a t e of Be 8 s e t at 2.9 MeV. In the f r a m e w o r k of W a t s o n ' s m o d e l and taking, of c o u r s e , into account the s y m m e t r i z a t i o n b e tween a l l the p r o d u c e d a - p a r t i c l e s , the m a t r i x e l e m e n t of r e a c t i o n (1) i s :
A:5
~
p2(p~.p~,k)(Cl2*lV~l:2,P~,k)~
15 May 1964
The notations a r e the s a m e a s defined in ref. 2: s i = ( P - p i ) 2 , ~= ~is i= m2 + 3 : P i s t h e m o m e n t u m of the d e c a y i n g p a r t i c l e , hi i s the m o m e n t u m of the / - p a r t i c l e in the final s t a t e , q = ½ (4~:4). The a n a l y t i c p r o p e r t i e s of the s p e c t r a l function a(s ', (~) have been e x t e n s i v e l y studied by Bonn e v a y who h a s shown that t h e y a r e d o m i n a t e d by: 1. the two cuts {- oo,0} and { m - 1) 2 , + oo}, 2. the pole ob c o r r e s p o n d i n g to the two alpha r e sonant state (2 + e x c i t e d state of Be 8) and i t s c o m p l e x conjugate oto*, 3. the f i r s t two oil and (~2 l o g a r i t h m i c s i n g u l a r i t i e s induced by t h e s e p o l e s and t h e i r c o m p l e x conjugate otl*,ot2*. N e g l e c t i n g the two f a r a w a y u n p h y s i c a l c u t s {_ oo,0} and {(m - 1) 2, + oo} and a p p r o x i m a t i n g the c o n t r i b u t i o n s due to the oil", oil*, ot2 and ot2* l o g a r i t h m i c c u t s by e x p r e s s i o n s of the f o r m
(2)
~
f ( s ) log ( s - a 1 )
ivj, k w h e r e Pi is the z-particle' m o m e n t u m , Pi~,k and l a r e r e s p e c t i v e l y the r e l a t i v e l i n e a r and a n g u l a r m o m e n t u m of the j and k - p a r t i c l e s in t h e i r c e n t r e o f - m a s s s y s t e m , and V i s the final state i n t e r action o p e r a t o r . The m a t r i x e l e m e n t A h a s the f o r m g i v e n by eq. (2) b e c a u s e we have a s s u m e d the C 12. s t a t e to be a 0 + s t a t e * . In W a t s o n ' s m o d e l , the m a t r i x e l e m e n t (C 12. IV ]l,pj,k) i s e x p r e s s e d by a B r e i t - W i g n e r type f o r m u l a :
(C12* t V l l ' ~ ' k )
p2t j ,k : Wr- Wj,k-iTp2/+lj,k
(3)
'
with W r = Be 8 m a s s , Wj, k = e n e r g y o f j and k - 8* p a r t i c l e s in t h e i r c e n t r e - o f - m a s s s y s t e m , V-- Be half-width. On the o t h e r hand, following Bonnevay 2), one can w r i t e the a m p l i t u d e A ( s l , s 2 , s 3) of the r e a c tion (1), a s : 3
A ( S l , S 2 , S 3 ) = ~ goi(si,a ) . i=1
(4)
one g e t s : a~-
ds'+c.c.. (6) ot2 .s (The i n t e g r a t i o n path in ~ ) i s c h o s e n in such a jot2 way that it d o e s not c r o s s the cut {4, ~o}. ) The j u m p s of the e x a c t s p e c t r a l function a(s, ~) a c r o s s the cuts a s s o c i a t e d with a 1 and ot2 can be c a l c u l a t e d and we have d e t e r m i n e d the c o n s t a n t s A and B such that the a p p r o x i m a t e funct i o n s a(s',~) given by eq. (6) have the s a m e j u m p s in the neighbourhood of ~1 and ot2- R e p l a c i n g eq. (6) in eq. (5), one g e t s :
q~i(si'(r) = - - ~ 4
a(s',o)
ds'.
l+log(s-otl)+log
q21q oto ~-
Sr-Si-2i Yll + C ( a l ' a ° )
× [q log ( s i - 5 1 ) - qoto log ( s r - ~ l ) ] + D ( 5 2 , a l , a o ) × [q log (si+a2-8) - qotl log ( s t + a 2 - 8 ) ] with qao = ½(~sr-4 ) ,
The ~oi functions obey the following d i s p e r s i o n r e l a t i o n s: - - ?~ qZl
2i
ao = Re oto , (5)
._2 sr =w r ,
a l = Re a l , a2 = Re a 2 , ff
c(al,~o) : 2p(~l)q(~l ) Pt Ix(no)] q~o
q,21 (s,_si) and
* This simplifying hypothesis could be removed, but one is then led to an appreciably more complicated formula.
q 2l F= . 2 l + i ' ~qao
2l÷1 _
7
~qal
D((~2,~l ,°to) = B((~I ,otO) ~ ( ~ a
2) P [X((il)] -
17 J
103
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 -