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Angular distribution of photofission fragments near threshold
Volume 26B, number 4
ANGULAR
PHYSICS
DISTRIBUTION NEAR
LETTERS
OF
22 January 1968
PHOTOFISSION
FRAGMENTS
THRESHOLD
N. S. R A B O T N O V , G . N . S M I R E N K I N , Ao S. S O L D A T O V and L. N. Y S A C H E V Institute of Physics and Energetics, Obninsk, USSR and S. P. K A P I T Z A and Yu. M. T S I P E N I U K Vavilov Institute f o r Physical Problems, Moscow, USSR Received 20 December 1967
The results of measurements of angular distributions of the photofission fragments for 232Th, 238U, 240Pu, 242pu and 239pu nuclei in the bremsstrahlung energy interval Emax = 5 - 8 MeV are r e ported and discussed. These results support the hypothesis about approximate conservation of the quantum number K at moderate excitation energies.
I n v e s t i g a t i o n s of t h e a n g u l a r d i s t r i b u t i o n s of t h e f r a g m e n t s of n u c l e a r f i s s i o n i n d u c e d by 7 q u a n t a at e x c i t a t i o n e n e r g i e s n e a r the f i s s i o n t h r e s h o l d p r o v i d e v a l u a b l e i n f o r m a t i o n about the c h a n n e l s t r u c t u r e of the f i s s i o n b a r r i e r . T h e f i s s i o n of h e a v y n u c l e i by d i p o l e r a d i a t i o n n e a r the t h r e s h o l d w a s s t u d i e d in d e t a i l by K a t z et al. [1]. In t h i s p a p e r we r e p o r t and d i s c u s s n e w d a t a on the a n g u l a r d i s t r i b u t i o n s of the p h o t o f i s s i ' o n f r a g m e n t s f o r 232Th, 238U, 2 3 9 p u , 2 4 0 p u and 2 4 2 p u in the u n d e r b a r r i e r e n e r g y r e gion, f o r w h i c h no e x p e r i m e n t a l r e s u l t s w e r e p u b l i s h e d up to now. T h e 12 MeV m i c r o t r o n was u s e d to p r o d u c e the b r e m s s t r a h l u n g b e a m in the e n e r g y i n t e r v a l E m a x = 5 - 8 MeV. T h e t r a c e s l e f t by the f i s s i o n f r a g m e n t s in g l a s s w e r e u s e d to d e t e c t the f i s s i o n e v e n t s [2]. T h e a v e r a g e c u r r e n t of the e l e c t r o n b e a m w a s about 50 g A and a 1 mm tungsten bremsstrahlung target was used
w h e r e E i s t h e e x c i t a t i o n e n e r g y , E~ t h e f i s s i o n t h r e s h o l d f o r g i v e n K, and Ekcurv the p a r a m e t e r d e s c r i b i n g the c u r v a t u r e of the b a r r i e r ' s top. Fig. 1 s h o w s the r e s u l t s of e x p e r i m e n t s f o r e v e n - e v e n n u c l e i . T h e a n i s o t r o p y of d i p o l e p h o t o f i s s i o n (i.e. t h e c o e f f i c i e n t b) w i l l b e c o m e z e r o w h e n the p r o b a b i l i t i e s of the f i s s i o n t h r o u g h the
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[3]. D i p o l e p h o t o a b s o r p t i o n d o m i n a t e s in the p r o c e s s of c o m p o u n d - n u c l e u s f o r m a t i o n at t h e e n e r g i e s in q u e s t i o n . T h e d i f f e r e n t i a l f i s s i o n c r o s s s e c t i o n i s t h e n p r o p o r t i o n a l to a + b sin20. T h e r a t i o b / a i s d e t e r m i n e d by the c o m p e t i t i o n of t h e c h a n n e l s w i t h K = 0 and K = 1 (K is the p r o j e c t i o n of the n u c l e a r s p i n on the f i s s i o n axis). The e n e r g y d e p e n d e n c e of the a v e r a g e f i s s i o n w i d t h is d e t e r m i n e d by the h e i g h t and f o r m of the f i s s i o n barrier for a given channel / Ekf-E ,
218
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Fig. 1. The measured value of b/a as a function of energy. Photofission cross sections taken from ref. 1 are also shown for 232Th and 238U. E is the average excitation energy of the fissioning nuclei and Tf the observable fission threshold.
Volume 26B, number 4
PHYSICS LETTERS
channels with d i f f e r e n t K b e c o m e equal. This o c c u r s when the e x c i t a t i o n e n e r g y is e i t h e r 1 ) h ig h e r than the t h r e s h o l d s f o r both K - v a l u e s or 2) c o n s i d e r a b l y l o w e r than the lowest b a r r i e r . Hence b/a as a function of E m u s t have a m a x i mum in b et ween t h e s e l i m i t s . C a lc u l a t in g the p e n e t r a b i l i t i e s of the b a r r i e r s one can show that the position of the m a x i m u m is d e t e r m i n e d by the value of the l o w e s t t h r e s h o l d . That b v a n i s h e s fo r low e n e r g y is hard to o b s e r v e . This conclusion a g r e e s q u a l i t a t i v e l y with the e x p e r i m e n t a l data which i n d i c a t e the p r e s e n c e of the m a x i m u m f o r the n u c l e i 240pu and 242pu; only "the r i g h t - h a n d s i d e " of the m a x i m u m , the a n i s o tropy plateau at low e n e r g i e s , is o b s e r v a b l e f o r 232Th and 238U. The value of K m a y be d e t e r m i n e d in two a l t e r n a t i v e ways: (a) K m a y be a good quantum n u m b e r in the c o m p o u n d - n u c l e u s s t a t e s at e x c i tation e n e r g i e s n e a r the f i s s i o n t h r e s h o l d and (b) K may be fixed when a n u c l e u s p a s s e s o v e r the saddle point. T h e s e two p o s s i b i l i t i e s r e s u l t in two d i f f e r e n t r e l a t i o n s b e t w e e n the e n e r g y d e pendence b/a(E) and af(E). Let Tf be the e n e r g y at which the f i s s i o n and r a d i a t i o n widths b e c o m e equal. Below the n e u t r o n e m i s s i o n t h r e s h o l d Tf may be c a l l e d an " o b s e r v a b l e f i s s i o n t h r e s h o l d " . The d i f f e r e n c e AEf = E f - Tf v a r i e s usually b e tween a few hundred keV and n e a r l y 1 MeV. It is e a s y to show f r o m the e n e r g y dependence of the d i f f e r e n t i a l and t o t al f i s s i o n c r o s s s e c t i o n s that in the c a s e (a) the e n e r g y v a l u e E c r i t , w h e r e the f i s s i o n a n i s o t r o p y b e g i n s to d e c r e a s e f r o m the m a x i m u m v a l u e , is a p p r o x i m a t e l y equal to Tf, but in the c a s e (b) E c r i t would be AEf higher than Tf. E x p e r i m e n t a l data (see fig. 1) a r e in f a i r a g r e e m e n t with (a), s i n c e the r e l a t i o n E c r i t = Tf a p p r o x i m a t e l y holds, w h i le for (b) the e s t i m a t e d d i f f e r e n c e b e t w e e n t h e s e two v a l u e s would have been about 500-600 keV. The k i n e m a t i c s of the 239pu photofission is s o m e w h a t m o r e c o m p l i c a t e d . The a n i s o t r o p y m u s t a l s o b eg i n to v a n i s h at E f or at the o b s e r v able t h r e s h o l d Tf. F u r t h e r m o r e , if the d i f f e r ence b e t w e e n the t h r e s h o l d s for two channels with d i f f e r e n t K is l a r g e , t h e r e w i l l be no p o s s i bility f o r the a n i s o t r o p y to change its sign u n d e r the b a r r i e r if (b) holds, but this can happen in c a s e (a) if the t h r e s h o l d d i f f e r e n c e is f a v o r a b l e for one K - v a l u e and the r a t i o of the compoundnucleus f o r m a t i o n c r o s s s e c t i o n s f o r a n o th e r K value. The r e a l t h r e s h o l d Ef may be d e t e r m i n e d e x p e r i m e n t a l l y f r o m the e n e r g y dependence of the c r o s s s e c t i o n of the 238pu(n, f) reaction. The threshold observed from photofission experiments is about 5.6 MeV. A n a l y s i s of n e u t r o n data y i e l d s E f ~ 6.5 MeV [4].
22 January 1968
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5.5B.
&O
6.5 E MeV Fig. 2. Energy dependence of the anisotropy for the 239Pu photofission and the 238pu(n, f) reaction. The neutron data are taken from ref. 4. In the upper part of the figure the energy dependence of the cross sections as m e a s u r e d in refs. i and 4 is shown. The shaded regions indicate approximately the positions of the observable and the real fission thresholds for the compound nucleus 239Pu; E n is the neutron binding - - - ~
energy in 239Pu. In fig. 2 it is shown that both the data, which can decide b et w een (a) and (b), support the f i r s t one: the a n i s o t r o p y begins to drop at about Tf, and this point i s n e a r l y 1 MeV l o w e r t h a n E f ; f u r t h e r m o r e the a n i s o t r o p y changes its sign f ar below the b a r r i e r . Thus our r e s u l t s d e m o n s t r a t e that the e x p e c t e d c o n s e q u e n c e s of the l a r g e t h r e s h o l d diff e r e n c e b e t w e e n the channels with d i f f er en t K can be o b s e r v e d e x p e r i m e n t a l l y . F u r t h e r m o r e , t h e s e r e s u l t s support the hypothesis about the e x i s t e n c e of the a p p r o x i m a t e c o n s e r v a t i o n law of the quantum n u m b e r K at m o d e r a t e e x c i t a t i o n e n e r g i e s .
References 1. L.Katz, A . P . B e a r g and F.Brown, Proe. Second Int. Conf. on the Peaceful uses of atomic energy, Vol. 15, (UN Geneva 1958) p. 198. 2. V. P. Perelygyn, S. P. Tretiakova and I. Zvara, Pribory Tekhn. Eksp. No. 4 (1964) p. 78; Instr. and Exp. Techn. (1965) 796. 3. N.S.R, abotnov, G.N. Smirenkin, A. S. Soldatov, L.N. Usaehev, S.P. Kapitza and Yu. M. Tsipeniuk, in: Physics and Chemistry of Fission, Vol. 1 (IAEA Vienna 1965) p. 135. 4. P.E. Vorotnikov, S.N. Dubrovina, G.A. Otroshchenko, and V.A. Shigin, Yadernaja Fiz. 3 (1966) 479. 219
ANGULAR
PHYSICS
DISTRIBUTION NEAR
LETTERS
OF
22 January 1968
PHOTOFISSION
FRAGMENTS
THRESHOLD
N. S. R A B O T N O V , G . N . S M I R E N K I N , Ao S. S O L D A T O V and L. N. Y S A C H E V Institute of Physics and Energetics, Obninsk, USSR and S. P. K A P I T Z A and Yu. M. T S I P E N I U K Vavilov Institute f o r Physical Problems, Moscow, USSR Received 20 December 1967
The results of measurements of angular distributions of the photofission fragments for 232Th, 238U, 240Pu, 242pu and 239pu nuclei in the bremsstrahlung energy interval Emax = 5 - 8 MeV are r e ported and discussed. These results support the hypothesis about approximate conservation of the quantum number K at moderate excitation energies.
I n v e s t i g a t i o n s of t h e a n g u l a r d i s t r i b u t i o n s of t h e f r a g m e n t s of n u c l e a r f i s s i o n i n d u c e d by 7 q u a n t a at e x c i t a t i o n e n e r g i e s n e a r the f i s s i o n t h r e s h o l d p r o v i d e v a l u a b l e i n f o r m a t i o n about the c h a n n e l s t r u c t u r e of the f i s s i o n b a r r i e r . T h e f i s s i o n of h e a v y n u c l e i by d i p o l e r a d i a t i o n n e a r the t h r e s h o l d w a s s t u d i e d in d e t a i l by K a t z et al. [1]. In t h i s p a p e r we r e p o r t and d i s c u s s n e w d a t a on the a n g u l a r d i s t r i b u t i o n s of the p h o t o f i s s i ' o n f r a g m e n t s f o r 232Th, 238U, 2 3 9 p u , 2 4 0 p u and 2 4 2 p u in the u n d e r b a r r i e r e n e r g y r e gion, f o r w h i c h no e x p e r i m e n t a l r e s u l t s w e r e p u b l i s h e d up to now. T h e 12 MeV m i c r o t r o n was u s e d to p r o d u c e the b r e m s s t r a h l u n g b e a m in the e n e r g y i n t e r v a l E m a x = 5 - 8 MeV. T h e t r a c e s l e f t by the f i s s i o n f r a g m e n t s in g l a s s w e r e u s e d to d e t e c t the f i s s i o n e v e n t s [2]. T h e a v e r a g e c u r r e n t of the e l e c t r o n b e a m w a s about 50 g A and a 1 mm tungsten bremsstrahlung target was used
w h e r e E i s t h e e x c i t a t i o n e n e r g y , E~ t h e f i s s i o n t h r e s h o l d f o r g i v e n K, and Ekcurv the p a r a m e t e r d e s c r i b i n g the c u r v a t u r e of the b a r r i e r ' s top. Fig. 1 s h o w s the r e s u l t s of e x p e r i m e n t s f o r e v e n - e v e n n u c l e i . T h e a n i s o t r o p y of d i p o l e p h o t o f i s s i o n (i.e. t h e c o e f f i c i e n t b) w i l l b e c o m e z e r o w h e n the p r o b a b i l i t i e s of the f i s s i o n t h r o u g h the
I'I
t
jn!'
'
JI . u .
.
! .
m~arni
/
,o
/0
[
I.O
[3]. D i p o l e p h o t o a b s o r p t i o n d o m i n a t e s in the p r o c e s s of c o m p o u n d - n u c l e u s f o r m a t i o n at t h e e n e r g i e s in q u e s t i o n . T h e d i f f e r e n t i a l f i s s i o n c r o s s s e c t i o n i s t h e n p r o p o r t i o n a l to a + b sin20. T h e r a t i o b / a i s d e t e r m i n e d by the c o m p e t i t i o n of t h e c h a n n e l s w i t h K = 0 and K = 1 (K is the p r o j e c t i o n of the n u c l e a r s p i n on the f i s s i o n axis). The e n e r g y d e p e n d e n c e of the a v e r a g e f i s s i o n w i d t h is d e t e r m i n e d by the h e i g h t and f o r m of the f i s s i o n barrier for a given channel / Ekf-E ,
218
LO
5.o r,, ---"
E
i
I
7.o ~o r~6.o ---'-
E
zo 5.o
~o ---"-
~o E.,ox
MeV
Fig. 1. The measured value of b/a as a function of energy. Photofission cross sections taken from ref. 1 are also shown for 232Th and 238U. E is the average excitation energy of the fissioning nuclei and Tf the observable fission threshold.
Volume 26B, number 4
PHYSICS LETTERS
channels with d i f f e r e n t K b e c o m e equal. This o c c u r s when the e x c i t a t i o n e n e r g y is e i t h e r 1 ) h ig h e r than the t h r e s h o l d s f o r both K - v a l u e s or 2) c o n s i d e r a b l y l o w e r than the lowest b a r r i e r . Hence b/a as a function of E m u s t have a m a x i mum in b et ween t h e s e l i m i t s . C a lc u l a t in g the p e n e t r a b i l i t i e s of the b a r r i e r s one can show that the position of the m a x i m u m is d e t e r m i n e d by the value of the l o w e s t t h r e s h o l d . That b v a n i s h e s fo r low e n e r g y is hard to o b s e r v e . This conclusion a g r e e s q u a l i t a t i v e l y with the e x p e r i m e n t a l data which i n d i c a t e the p r e s e n c e of the m a x i m u m f o r the n u c l e i 240pu and 242pu; only "the r i g h t - h a n d s i d e " of the m a x i m u m , the a n i s o tropy plateau at low e n e r g i e s , is o b s e r v a b l e f o r 232Th and 238U. The value of K m a y be d e t e r m i n e d in two a l t e r n a t i v e ways: (a) K m a y be a good quantum n u m b e r in the c o m p o u n d - n u c l e u s s t a t e s at e x c i tation e n e r g i e s n e a r the f i s s i o n t h r e s h o l d and (b) K may be fixed when a n u c l e u s p a s s e s o v e r the saddle point. T h e s e two p o s s i b i l i t i e s r e s u l t in two d i f f e r e n t r e l a t i o n s b e t w e e n the e n e r g y d e pendence b/a(E) and af(E). Let Tf be the e n e r g y at which the f i s s i o n and r a d i a t i o n widths b e c o m e equal. Below the n e u t r o n e m i s s i o n t h r e s h o l d Tf may be c a l l e d an " o b s e r v a b l e f i s s i o n t h r e s h o l d " . The d i f f e r e n c e AEf = E f - Tf v a r i e s usually b e tween a few hundred keV and n e a r l y 1 MeV. It is e a s y to show f r o m the e n e r g y dependence of the d i f f e r e n t i a l and t o t al f i s s i o n c r o s s s e c t i o n s that in the c a s e (a) the e n e r g y v a l u e E c r i t , w h e r e the f i s s i o n a n i s o t r o p y b e g i n s to d e c r e a s e f r o m the m a x i m u m v a l u e , is a p p r o x i m a t e l y equal to Tf, but in the c a s e (b) E c r i t would be AEf higher than Tf. E x p e r i m e n t a l data (see fig. 1) a r e in f a i r a g r e e m e n t with (a), s i n c e the r e l a t i o n E c r i t = Tf a p p r o x i m a t e l y holds, w h i le for (b) the e s t i m a t e d d i f f e r e n c e b e t w e e n t h e s e two v a l u e s would have been about 500-600 keV. The k i n e m a t i c s of the 239pu photofission is s o m e w h a t m o r e c o m p l i c a t e d . The a n i s o t r o p y m u s t a l s o b eg i n to v a n i s h at E f or at the o b s e r v able t h r e s h o l d Tf. F u r t h e r m o r e , if the d i f f e r ence b e t w e e n the t h r e s h o l d s for two channels with d i f f e r e n t K is l a r g e , t h e r e w i l l be no p o s s i bility f o r the a n i s o t r o p y to change its sign u n d e r the b a r r i e r if (b) holds, but this can happen in c a s e (a) if the t h r e s h o l d d i f f e r e n c e is f a v o r a b l e for one K - v a l u e and the r a t i o of the compoundnucleus f o r m a t i o n c r o s s s e c t i o n s f o r a n o th e r K value. The r e a l t h r e s h o l d Ef may be d e t e r m i n e d e x p e r i m e n t a l l y f r o m the e n e r g y dependence of the c r o s s s e c t i o n of the 238pu(n, f) reaction. The threshold observed from photofission experiments is about 5.6 MeV. A n a l y s i s of n e u t r o n data y i e l d s E f ~ 6.5 MeV [4].
22 January 1968
I0"" /0"~
l Q3
g.~
rJ I I
50
,~s ~
5.5B.
&O
6.5 E MeV Fig. 2. Energy dependence of the anisotropy for the 239Pu photofission and the 238pu(n, f) reaction. The neutron data are taken from ref. 4. In the upper part of the figure the energy dependence of the cross sections as m e a s u r e d in refs. i and 4 is shown. The shaded regions indicate approximately the positions of the observable and the real fission thresholds for the compound nucleus 239Pu; E n is the neutron binding - - - ~
energy in 239Pu. In fig. 2 it is shown that both the data, which can decide b et w een (a) and (b), support the f i r s t one: the a n i s o t r o p y begins to drop at about Tf, and this point i s n e a r l y 1 MeV l o w e r t h a n E f ; f u r t h e r m o r e the a n i s o t r o p y changes its sign f ar below the b a r r i e r . Thus our r e s u l t s d e m o n s t r a t e that the e x p e c t e d c o n s e q u e n c e s of the l a r g e t h r e s h o l d diff e r e n c e b e t w e e n the channels with d i f f er en t K can be o b s e r v e d e x p e r i m e n t a l l y . F u r t h e r m o r e , t h e s e r e s u l t s support the hypothesis about the e x i s t e n c e of the a p p r o x i m a t e c o n s e r v a t i o n law of the quantum n u m b e r K at m o d e r a t e e x c i t a t i o n e n e r g i e s .
References 1. L.Katz, A . P . B e a r g and F.Brown, Proe. Second Int. Conf. on the Peaceful uses of atomic energy, Vol. 15, (UN Geneva 1958) p. 198. 2. V. P. Perelygyn, S. P. Tretiakova and I. Zvara, Pribory Tekhn. Eksp. No. 4 (1964) p. 78; Instr. and Exp. Techn. (1965) 796. 3. N.S.R, abotnov, G.N. Smirenkin, A. S. Soldatov, L.N. Usaehev, S.P. Kapitza and Yu. M. Tsipeniuk, in: Physics and Chemistry of Fission, Vol. 1 (IAEA Vienna 1965) p. 135. 4. P.E. Vorotnikov, S.N. Dubrovina, G.A. Otroshchenko, and V.A. Shigin, Yadernaja Fiz. 3 (1966) 479. 219