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On the sudden model for ternary fission
Volume 34B, number 7
ON T H E
PHYSICS LETTERS
SUDDEN
MODEL
FOR
12 April 1971
TERNARY
FISSION
U. FACCHINI and E. S A E T T A - M E N I C H E L L A C . I . S . E . , Segrate, Milatzo, Italy and Istituto di F i s i c a dell UniversitY, Milano, Italy
Received 25 February 1971 A description is given of the ternary fission mechanism by means of the "sudden model", which has been previously proposed by the authors in the case of binary fission.
It has been shown that the light p a r t i c l e e m i t ted in t e r n a r y f i s s i o n is r e l e a s e d f r o m the s p a c e between the h e a v i e r f r a g m e n t s at about the i n stant of s c i s s i o n [1]. Due to this fact t e r n a r y f i s sion is a p a r t i c u l a r l y i n t e r e s t i n g topic: the study of p e c u l i a r p r o p e r t i e s of t e r n a r y f i s s i o n , such as the angular d i s t r i b u t i o n and the e n e r g e t i c s p e c t r u m of the light p a r t i c l e , m a k e s it p o s s i b l e to i n v e s t i g a t e the d y n a m i c a l conditions of the nuc l e a r s y s t e m s at the s c i s s i o n point [2, 3]. The p u rp o s e of this l e t t e r is to give a d e s c r i p t i o n of the m e c h a n i s m of t e r n a r y f i s s i o n , by m e a n s of the f i s s i o n model r e c e n t l y p r o p o s e d by the au t h o rs [4]. In the y e a r s 1963-66 energy and m a s s s p e c t r a of the f r a g m e n t s in the c a s e of binary f i s s i o n w e r e a n a l y s e d [5, 6] by m e a n s of a s t a t i s t i c a l f o r m u l a given by E r i c s o n [7]. The r e m a r k a b l e r e s u l t of t h es e a n a l y s e s has been to evidence that at the m o m e n t of splitting, the two f i s s i o n f r a g me nts go through a potential b a r r i e r thinner and s h a r p e r than the Coulombian one [6, 8]. An i n t e r p r e t a t i o n of this b a r r i e r has been given [4, 8, 9] a s s u m i n g that the two f r a g m e n t s a r e f o r m e d in the compound nucleus and then blow up suddenly f r o m it; the b a r r i e r r e p r e s e n t s the p e c u l i a r e n e r g e t i c conditions for f o r m a t i o n and splitting of the two f r a g m e n t s . In the c a s e of 236U, for i n s t a n c e , the potential b a r r i e r has a top about 10 MeV above the Bohr saddle, and a t h i c k n e s s of the o r d e r of 2 fm when at 50 MeV below the top (fig. 1). At l a r g e r d i s t a n c e s t h e r e is a flat potential r eg io n , w h e r e r e s i d u a l a t t r a c t i v e n u c l e a r i n t e r a c t i o n s and Coulombian r e p u l sion balance each other (fig. 1). At the distance D ( s c i s s i o n point) the f r a g m e n t s s e p a r a t e ; the a n a l y s e s do not p r e d i c t the value of D, but only allow to e s t a b l i s h its l o w e r l i m i t which is of the o r d e r of 20-22 fm. 572
v
( 1,4eVl 200 C.N.S
Vb
~Fs 150
\\
i Coutombian ~ier
\~.
D i
r (Frn)
22
Fig. 1. Dynamical potential barrier acting between the two fission fragments. C. N.S. indicates the compound nucleas states. The potential is plotted versus r, the distance between the centres of the two fragments; the dotted line indicates that the potential in this region is not well defined. S represents the scission point. £FS represents the total kinetic energy of the fission fragments at the scission point in the case of binary fission. Vb is the potential energy of the binary fragments when they come out of the barrier. To d i s c u s s the p r o p e r t i e s of t e r n a r y f i s s i o n r e f e r e n c e is made for the sake of s i m p l i c i t y to the c a s e s when o~ p a r t i c l e s a r e e m i t t e d in the spontaneous f i s s i o n of 252Cf and in the f i s s i o n of 235U induced by t h e r m a l n e u t r o n s . A c c u r a t e a n a l y s i s of t h e s e r e a c t i o n s have been made r e c e n t ly be Boneh et al. [10] and Ben David [11]. T h e s e a u t h o r s , through the i n v e s t i g a t i o n of the c o r r e l a tions between the angular and the e n e r g e t i c d i s t r i b u t i o n of the ~ p a r t i c l e s , obtain the v a l u e s of D, the i n i t i al position, and the initial k i n et i c e n e r g y Cao of the o~ p a r t i c l e and the kinetic e n e r g y of the h e a v i e r f r a g m e n t s EFS at the s c i s -
Volume 34B, number 7
PHYSICS LETTERS
sion point. The obtained v a l u e s a r e given in t a b le 1. T h e s e v a l u e s and the ones given in the f o l l o w ing a r e a v e r a g e d o v e r the v a r i o u s couples of f r a g m e n t s and o v e r t h e i r k i n e ti c e n e r g y s p e c t r a . A r e m a r k a b l e r e s u l t f r o m t h e s e a n a l y s e s is the c o n f i r m a t i o n of the validity of H a l p e r n ' s [2] b a s i c co n cl u s i o n , i.e. that at s c i s s i o n the h e a v i e r f r a g m e n t s have a c o n s i d e r a b l e amount of k i n e ti c energy. The t o t al k i n et i c e n e r g y at infinity Eta , the sum of the total k i n e t i c e n e r g i e s of the a p a r t i c l e and of the two h e a v i e r f r a g m e n t s , is r e l a t e d to the v a l u e s e a o and eFS by the c o n s e r v a t i o n equation: eta =eao +EFS+Vst
,
(1)
Vst being the t o t al potential e n e r g y at the s c i s sion point. When a c o m p a r i s o n is m a d e between the v a l u e s of e t a and the c o r r e s p o n d i n g v a l u e s of the total kine t i c e n e r g y Cb of the f r a g m e n t s in b i n a r y f i s sion, it is found that e b is s m a l l e r then e t_ by 23 MeV. The v a l u e s of e t a - e b a r e c o l l e c t e ~ in ta bl e 1 [12, 13]. On the c o n t r a r y the d i f f e r e n c e between the final t o t al e x c i t a t i o n e n e r g i e s in b i n a r y Ub and t e r n a r y f i s s i o n Ut r e s p e c t i v e l y , is p o s i t i v e and about 6 MeV [12, 13]; the d i f f e r e n c e of the a v e r age f i s s i o n e n e r g i e s Qb - Q t is p o s i t i v e and of the o r d e r of 4 MeV [12]. The c o n s e r v a t i o n equation g i v e s : Vb-Vt = (eb-et)+(Ub-Ut)
"
(2)
L e t us now c o n s i d e r the p o s s i b l e m e c h a n i s m of t e r n a r y f i s s i o n , in the f r a m e work of the s u d den m o d e l . In the splitting p r o c e s s of b i n a r y f i s s i o n the f r a g m e n t s c o m e out of the b a r r i e r with a given potential e n e r g y Vb. T h i s potential Vb c o r r e sponds to the total k i n e ti c e n e r g y at infinity Vb = ~ b •
(3)
F r o m fig. 1, it can be seen that as soon as the two f r a g m e n t s m o v e a p a r t , they gain a c o n s i d e r a b l e amount of k i n e ti c e n e r g y , which can be e s t i m a t e d of the o r d e r of few tens of MeV at d i s t a n c e s of 20-25 fm ( s c i s s i o n point). In the c a s e of t e r n a r y f i s s i o n a few s i m p l i f y ing a s s u m p t i o n s a r e made: a) the p o t en t i al e n e r g y of the f r a g m e n t s a f t e r spli t t i n g is the s a m e as in b i n a r y f i s s i o n Vt = Vb ;
(4)
b) c o r r e s p o n d i n g l y , the t o t a l e x c i t a t i o n e n e r gy of the h e a v i e r f r a g m e n t s at splitting is the s a m e as in b i n a r y f i s s i o n ;
12 April 1971 Table 1 D (fm)
£ao (MeV)
EFS (MeV)
Cta-Eb (MeV)
236U
23
2
25.5
~ 2
252Cf
24
3
28.0
~ 3.5
D, £ao, £FS values are given assuming Y = 0. Ybeing the initial distance of the point of the light particle emission from the fission axis connecting the fission fragments. The starting point of the a particle is in the centre between the two heavier fragments. c) at the s c i s s i o n point, p a r t of the e x c i t a t i o n e n e r g y and n a m e l y the d i f f e r e n c e Ub - Ut, t u r n s into the a v e r a g e binding e n e r g y and the i n i t i al k i n et i c e n e r g y of the a p a r t i c l e . Noting that the a p a r t i c l e binding e n e r g y is equal to (Qb- Q ) we have: Ub - Ut = ( Q b - Q t ) + % ~ o .
(5)
U n d er t h e s e a s s u m p t i o n s , t e r n a r y f i s s i o n ap p e a r s to be a p a r t i c u l a r mode of the u s u a l b i n a r y f i s s i o n . The a p a r t i c l e is built up in the i n t e r a c tion r e g i o n between the two h e a v i e r f r a g m e n t s by m e a n s of the e x t e r n a l e x c i t e d n u cl eo n s. C o m p a r i n g eqs. (2) and (5), we have e a o = £tot - Cb "
(6)
Notwithstanding the v a r i o u s s i m p l i f i c a t i o n s and e r r o r s , the data c o l l e c t e d in table 1 show that the p r e d i c t e d v a l u e s of ( a o a r e in r e a s o n a b l e a g r e e m e n t with the e x p e r i m e n t a l v a l u e s of (c t eb). In the f r a m e work of the m o d el it is p o s s i b l e to i n v e s t i g a t e the d y n am i c conditions at the s c i s sion point. The i n i t i al potential e n e r g y Vt at this point t u r n s p a r t l y into the k i n et i c e n e r g y of the heavy f r a g m e n t s ; t h e r f o r e , it is: Yt : E F S + Vst •
(7)
The value of Vst depends am o n g o t h er things on the d i s t a n c e D and on the i n i t i al position of the p a r t i c l e . A s s u m i n g the a p a r t i c l e to be at a given point between the two h e a v i e r f r a g m e n t s and D of the o r d e r of 20-25 fm. eqs. (3) and (7) give d i r e c t l y v a l u e s of eFS of few tens of MeV in a g r e e m e n t with H a l p e r n ' s b a s i c conclusion [2]. P a r t i c u l a r l y , when a s s u m i n g that the h e a v i e r f r a g m e n t s and the a p a r t i c l e have the s a m e r e l a t i v e position at the s c i s s i o n point, as deduced f r o m the t r a j e c t o r y a n a l y s e s by Boneh et al. [10, 11], the s a m e v a l u e s of CFS given by t h e s e autho r s (table 1 ) a r e obtained f r o m eq. (7): in fact when eqs. (3), (4) and (6) a r e taken into account 573
Volume 34B, number
7
PHYSICS
LETTERS
eq. (7) becomes equivalent to eq. (1) used in trajectory analyses. An important remark: according to the proposed model there is no great difference in the splitting process of the different fissioning nuelides; the mechanism of light particle emission and the heavy fragment motion at the scission point should not depend, at least not to a great extent, on the mass of the fissioning nucleus. Therefore the properties of ternary fission shall be sensibly constant when various nuclides from
Pb and Cf are considered. A careful investigation of ternary fission for nuclides of different mass will prove the validity of the proposed model.
References [l] Tsien San-Tsiang,
J. Phys. Radium 9 (1948) 6.
*****
574
12 April 1971
[Z] I. Halpern, CERN Report 6812 (63), unpublished. [3] N. Feather, Physics and chemistry of fission, IAEA, Vienna (1969) 83. [4] U. Facchini and E. Saetta-Menichella, Acta Physica Polonica A38 (1970) 537; Energia Nucleare, to be published. [5] E. Erba and U. Facchini et al., Phys. Letters 6 (1963) 294. [6] E. Erba, U. Facchini and E. Saetta-Menichella, Nucl. Phys. 84 (1966) 595. Advan. Phvs. 9 (1960) 36. 171 T. Ericson, and E.Saetta181 U. Facchini, E. Gadioli-Erba Menichella, Phys. Letters 28B (1969) 534. Phys. Rev. Letters [91P. G. Sonna and E. Gadioli-Erba, 22 (1969) 406. 1101E. Nardi, Y. Boneh and 2. Fraenkel, Physics and chemistry of fission, IAEA, Vienna (1969) 143. IllI G. Ben David, Physics and chemistry of fission, IAEA, Vienna (1969) discussion, 129. 1121N. Feather, Phys.Rev. 170 (1968) 1118. Phys.Rev. C 2 (1970) iI31 E.Nardi and Z. Fraenkel, 1156.
ON T H E
PHYSICS LETTERS
SUDDEN
MODEL
FOR
12 April 1971
TERNARY
FISSION
U. FACCHINI and E. S A E T T A - M E N I C H E L L A C . I . S . E . , Segrate, Milatzo, Italy and Istituto di F i s i c a dell UniversitY, Milano, Italy
Received 25 February 1971 A description is given of the ternary fission mechanism by means of the "sudden model", which has been previously proposed by the authors in the case of binary fission.
It has been shown that the light p a r t i c l e e m i t ted in t e r n a r y f i s s i o n is r e l e a s e d f r o m the s p a c e between the h e a v i e r f r a g m e n t s at about the i n stant of s c i s s i o n [1]. Due to this fact t e r n a r y f i s sion is a p a r t i c u l a r l y i n t e r e s t i n g topic: the study of p e c u l i a r p r o p e r t i e s of t e r n a r y f i s s i o n , such as the angular d i s t r i b u t i o n and the e n e r g e t i c s p e c t r u m of the light p a r t i c l e , m a k e s it p o s s i b l e to i n v e s t i g a t e the d y n a m i c a l conditions of the nuc l e a r s y s t e m s at the s c i s s i o n point [2, 3]. The p u rp o s e of this l e t t e r is to give a d e s c r i p t i o n of the m e c h a n i s m of t e r n a r y f i s s i o n , by m e a n s of the f i s s i o n model r e c e n t l y p r o p o s e d by the au t h o rs [4]. In the y e a r s 1963-66 energy and m a s s s p e c t r a of the f r a g m e n t s in the c a s e of binary f i s s i o n w e r e a n a l y s e d [5, 6] by m e a n s of a s t a t i s t i c a l f o r m u l a given by E r i c s o n [7]. The r e m a r k a b l e r e s u l t of t h es e a n a l y s e s has been to evidence that at the m o m e n t of splitting, the two f i s s i o n f r a g me nts go through a potential b a r r i e r thinner and s h a r p e r than the Coulombian one [6, 8]. An i n t e r p r e t a t i o n of this b a r r i e r has been given [4, 8, 9] a s s u m i n g that the two f r a g m e n t s a r e f o r m e d in the compound nucleus and then blow up suddenly f r o m it; the b a r r i e r r e p r e s e n t s the p e c u l i a r e n e r g e t i c conditions for f o r m a t i o n and splitting of the two f r a g m e n t s . In the c a s e of 236U, for i n s t a n c e , the potential b a r r i e r has a top about 10 MeV above the Bohr saddle, and a t h i c k n e s s of the o r d e r of 2 fm when at 50 MeV below the top (fig. 1). At l a r g e r d i s t a n c e s t h e r e is a flat potential r eg io n , w h e r e r e s i d u a l a t t r a c t i v e n u c l e a r i n t e r a c t i o n s and Coulombian r e p u l sion balance each other (fig. 1). At the distance D ( s c i s s i o n point) the f r a g m e n t s s e p a r a t e ; the a n a l y s e s do not p r e d i c t the value of D, but only allow to e s t a b l i s h its l o w e r l i m i t which is of the o r d e r of 20-22 fm. 572
v
( 1,4eVl 200 C.N.S
Vb
~Fs 150
\\
i Coutombian ~ier
\~.
D i
r (Frn)
22
Fig. 1. Dynamical potential barrier acting between the two fission fragments. C. N.S. indicates the compound nucleas states. The potential is plotted versus r, the distance between the centres of the two fragments; the dotted line indicates that the potential in this region is not well defined. S represents the scission point. £FS represents the total kinetic energy of the fission fragments at the scission point in the case of binary fission. Vb is the potential energy of the binary fragments when they come out of the barrier. To d i s c u s s the p r o p e r t i e s of t e r n a r y f i s s i o n r e f e r e n c e is made for the sake of s i m p l i c i t y to the c a s e s when o~ p a r t i c l e s a r e e m i t t e d in the spontaneous f i s s i o n of 252Cf and in the f i s s i o n of 235U induced by t h e r m a l n e u t r o n s . A c c u r a t e a n a l y s i s of t h e s e r e a c t i o n s have been made r e c e n t ly be Boneh et al. [10] and Ben David [11]. T h e s e a u t h o r s , through the i n v e s t i g a t i o n of the c o r r e l a tions between the angular and the e n e r g e t i c d i s t r i b u t i o n of the ~ p a r t i c l e s , obtain the v a l u e s of D, the i n i t i al position, and the initial k i n et i c e n e r g y Cao of the o~ p a r t i c l e and the kinetic e n e r g y of the h e a v i e r f r a g m e n t s EFS at the s c i s -
Volume 34B, number 7
PHYSICS LETTERS
sion point. The obtained v a l u e s a r e given in t a b le 1. T h e s e v a l u e s and the ones given in the f o l l o w ing a r e a v e r a g e d o v e r the v a r i o u s couples of f r a g m e n t s and o v e r t h e i r k i n e ti c e n e r g y s p e c t r a . A r e m a r k a b l e r e s u l t f r o m t h e s e a n a l y s e s is the c o n f i r m a t i o n of the validity of H a l p e r n ' s [2] b a s i c co n cl u s i o n , i.e. that at s c i s s i o n the h e a v i e r f r a g m e n t s have a c o n s i d e r a b l e amount of k i n e ti c energy. The t o t al k i n et i c e n e r g y at infinity Eta , the sum of the total k i n e t i c e n e r g i e s of the a p a r t i c l e and of the two h e a v i e r f r a g m e n t s , is r e l a t e d to the v a l u e s e a o and eFS by the c o n s e r v a t i o n equation: eta =eao +EFS+Vst
,
(1)
Vst being the t o t al potential e n e r g y at the s c i s sion point. When a c o m p a r i s o n is m a d e between the v a l u e s of e t a and the c o r r e s p o n d i n g v a l u e s of the total kine t i c e n e r g y Cb of the f r a g m e n t s in b i n a r y f i s sion, it is found that e b is s m a l l e r then e t_ by 23 MeV. The v a l u e s of e t a - e b a r e c o l l e c t e ~ in ta bl e 1 [12, 13]. On the c o n t r a r y the d i f f e r e n c e between the final t o t al e x c i t a t i o n e n e r g i e s in b i n a r y Ub and t e r n a r y f i s s i o n Ut r e s p e c t i v e l y , is p o s i t i v e and about 6 MeV [12, 13]; the d i f f e r e n c e of the a v e r age f i s s i o n e n e r g i e s Qb - Q t is p o s i t i v e and of the o r d e r of 4 MeV [12]. The c o n s e r v a t i o n equation g i v e s : Vb-Vt = (eb-et)+(Ub-Ut)
"
(2)
L e t us now c o n s i d e r the p o s s i b l e m e c h a n i s m of t e r n a r y f i s s i o n , in the f r a m e work of the s u d den m o d e l . In the splitting p r o c e s s of b i n a r y f i s s i o n the f r a g m e n t s c o m e out of the b a r r i e r with a given potential e n e r g y Vb. T h i s potential Vb c o r r e sponds to the total k i n e ti c e n e r g y at infinity Vb = ~ b •
(3)
F r o m fig. 1, it can be seen that as soon as the two f r a g m e n t s m o v e a p a r t , they gain a c o n s i d e r a b l e amount of k i n e ti c e n e r g y , which can be e s t i m a t e d of the o r d e r of few tens of MeV at d i s t a n c e s of 20-25 fm ( s c i s s i o n point). In the c a s e of t e r n a r y f i s s i o n a few s i m p l i f y ing a s s u m p t i o n s a r e made: a) the p o t en t i al e n e r g y of the f r a g m e n t s a f t e r spli t t i n g is the s a m e as in b i n a r y f i s s i o n Vt = Vb ;
(4)
b) c o r r e s p o n d i n g l y , the t o t a l e x c i t a t i o n e n e r gy of the h e a v i e r f r a g m e n t s at splitting is the s a m e as in b i n a r y f i s s i o n ;
12 April 1971 Table 1 D (fm)
£ao (MeV)
EFS (MeV)
Cta-Eb (MeV)
236U
23
2
25.5
~ 2
252Cf
24
3
28.0
~ 3.5
D, £ao, £FS values are given assuming Y = 0. Ybeing the initial distance of the point of the light particle emission from the fission axis connecting the fission fragments. The starting point of the a particle is in the centre between the two heavier fragments. c) at the s c i s s i o n point, p a r t of the e x c i t a t i o n e n e r g y and n a m e l y the d i f f e r e n c e Ub - Ut, t u r n s into the a v e r a g e binding e n e r g y and the i n i t i al k i n et i c e n e r g y of the a p a r t i c l e . Noting that the a p a r t i c l e binding e n e r g y is equal to (Qb- Q ) we have: Ub - Ut = ( Q b - Q t ) + % ~ o .
(5)
U n d er t h e s e a s s u m p t i o n s , t e r n a r y f i s s i o n ap p e a r s to be a p a r t i c u l a r mode of the u s u a l b i n a r y f i s s i o n . The a p a r t i c l e is built up in the i n t e r a c tion r e g i o n between the two h e a v i e r f r a g m e n t s by m e a n s of the e x t e r n a l e x c i t e d n u cl eo n s. C o m p a r i n g eqs. (2) and (5), we have e a o = £tot - Cb "
(6)
Notwithstanding the v a r i o u s s i m p l i f i c a t i o n s and e r r o r s , the data c o l l e c t e d in table 1 show that the p r e d i c t e d v a l u e s of ( a o a r e in r e a s o n a b l e a g r e e m e n t with the e x p e r i m e n t a l v a l u e s of (c t eb). In the f r a m e work of the m o d el it is p o s s i b l e to i n v e s t i g a t e the d y n am i c conditions at the s c i s sion point. The i n i t i al potential e n e r g y Vt at this point t u r n s p a r t l y into the k i n et i c e n e r g y of the heavy f r a g m e n t s ; t h e r f o r e , it is: Yt : E F S + Vst •
(7)
The value of Vst depends am o n g o t h er things on the d i s t a n c e D and on the i n i t i al position of the p a r t i c l e . A s s u m i n g the a p a r t i c l e to be at a given point between the two h e a v i e r f r a g m e n t s and D of the o r d e r of 20-25 fm. eqs. (3) and (7) give d i r e c t l y v a l u e s of eFS of few tens of MeV in a g r e e m e n t with H a l p e r n ' s b a s i c conclusion [2]. P a r t i c u l a r l y , when a s s u m i n g that the h e a v i e r f r a g m e n t s and the a p a r t i c l e have the s a m e r e l a t i v e position at the s c i s s i o n point, as deduced f r o m the t r a j e c t o r y a n a l y s e s by Boneh et al. [10, 11], the s a m e v a l u e s of CFS given by t h e s e autho r s (table 1 ) a r e obtained f r o m eq. (7): in fact when eqs. (3), (4) and (6) a r e taken into account 573
Volume 34B, number
7
PHYSICS
LETTERS
eq. (7) becomes equivalent to eq. (1) used in trajectory analyses. An important remark: according to the proposed model there is no great difference in the splitting process of the different fissioning nuelides; the mechanism of light particle emission and the heavy fragment motion at the scission point should not depend, at least not to a great extent, on the mass of the fissioning nucleus. Therefore the properties of ternary fission shall be sensibly constant when various nuclides from
Pb and Cf are considered. A careful investigation of ternary fission for nuclides of different mass will prove the validity of the proposed model.
References [l] Tsien San-Tsiang,
J. Phys. Radium 9 (1948) 6.
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12 April 1971
[Z] I. Halpern, CERN Report 6812 (63), unpublished. [3] N. Feather, Physics and chemistry of fission, IAEA, Vienna (1969) 83. [4] U. Facchini and E. Saetta-Menichella, Acta Physica Polonica A38 (1970) 537; Energia Nucleare, to be published. [5] E. Erba and U. Facchini et al., Phys. Letters 6 (1963) 294. [6] E. Erba, U. Facchini and E. Saetta-Menichella, Nucl. Phys. 84 (1966) 595. Advan. Phvs. 9 (1960) 36. 171 T. Ericson, and E.Saetta181 U. Facchini, E. Gadioli-Erba Menichella, Phys. Letters 28B (1969) 534. Phys. Rev. Letters [91P. G. Sonna and E. Gadioli-Erba, 22 (1969) 406. 1101E. Nardi, Y. Boneh and 2. Fraenkel, Physics and chemistry of fission, IAEA, Vienna (1969) 143. IllI G. Ben David, Physics and chemistry of fission, IAEA, Vienna (1969) discussion, 129. 1121N. Feather, Phys.Rev. 170 (1968) 1118. Phys.Rev. C 2 (1970) iI31 E.Nardi and Z. Fraenkel, 1156.