Volume 29B, number 3 P H Y S I C S L E T T E R S 28 Apri l 1969

EVEN-ODD DIFFERENCES AND STRUCTURE THE FISSION BARRIERS

A. V. IGNATYUK and G. N. SMIR ENKIN Institute of Physics and Energetics, Obninsk, USSR

Received 3 Apri l 1969

O F

The possibi l i ty of the in te rpre ta t ion of the data on even and odd dif ferences of the f iss ion b a r r i e r s f rom the point of view of the double-act ing f iss ion pic ture is shown in this work.

A t p r e s e n t t h e r e a r e s o m e p a p e r s on s y s t e - m a t i z a t i o n of t h e o b s e r v e d f i s s i o n b a r r i e r [1]. T h e n u c l e u s m a s s a t t h e s a d d l e p o i n t , d e t e r - m i n e d f r o m t h e b a r r i e r h e i g h t s c o r r e s p o n d i n g to t h e l o w e s t t r a n s i e n t s t a t e a t t h e b a r r i e r s h o w s c h a r a c t e r i s t i c c h a n g e s d e p e n d i n g on w h e t h e r t h e r e a r e an e v e n o r odd n u m b e r of n u c l e o n s in a n u c l e u s . T h e o b t a i n e d d i f f e r e n c e of e n e r g y s u r - f a c e s of e v e n and odd n u c l e i o r t h e p a i r i n g e n e r - gy Af = 1.2 M e V e x c e e d s c o n s i d e r a b l y t he p a i r - i ng e n e r g y f o r t h e g r o u n d s t a t e s A o = 0.7 M e V of t h e h e a v y n u c l e i k n o w n f r o m t he b i n d i n g e n e r - g i e s of n u c l e i . G r i f f i n [2] c a m e to t h e s a m e c o n - c l u s i o n f o r t h e gap p a r a m e t e r c o n n e c t e d w i th t he p a i r i n g e n e r g y on t h e b a s i s of t h e f i s s i o n f r a g - m e n t s ' a n g u l a r a n i s o t r o p y a n a l y s i s . T h e d i f f e r - e n c e Af-A o i s u s u a l l y i n t e r p r e t e d a s a n i n c r e a s e of t h e p a i r i n g e n e r g y w i t h n u c l e u s d e f o r m a t i o n .

In t h i s w o r k we w a n t to a t t r a c t a t t e n t i o n to a n u m b e r of t he e f f e c t s w h i c h do no t a g r e e w i t h t h e h y p o t h e s i s of s i g n i f i c a n t d i f f e r e n c e A f - A o , and to show the p o s s i b i l i t y of t he i n t e r p r e t a t i o n of t h e w h o l e s e t of t h e d a t a on e v e n and odd d i f f e r - e n c e s of t h e b a r r i e r s f r o m t h e p o i n t of v i e w of n e w i d e a s a b o u t t h e t w o - h u m p e d f i s s i o n b a r - r i e r [3]. We s h a l l c o n s i d e r t h r e e c l a s s e s of e x - p e r i m e n t a l d a t a f o r Bf of t he h e a v i e s t n u c l e i - a c t i n i d e s : t he d i r e c t i n f o r m a t i o n a b o u t t h e t h r e s h o l d s of i n d u c e d f i s s i o n (fig. l a ) ; t h e s y s - t e m a t i z a t i o n of t h e r a t i o s of a v e r a g e n e u t r o n and f i s s i o n w i d t h s r n / r f = f ( B f - B n ) [4] (fig. l b ) , t h e s p o n t a n e o u s h a l f - t i m e s Tf [ 1]. T h e d a t a on t h r e s h o l d s o b s e r v e d a t t h e i n d u c e d f i s s i o n a r e u s u a l l y e x t r a c t e d f r o m t he two s o u r c e s : i) t he e n e r g y d e p e n d e n c e of f i s s i o n c r o s s - s e c - t i o n s in t he (n , f ) and (y , f ) r e a c t i o n s (in t h e h o g - g ing p o i n t b e f o r e go ing out on t h e p l a t e a u ) ; i i ) t h e c h a n n e l a n a l y s i s of 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 i s s i o n f r a g m e n t s . T h e v a l u e s of t he Bf , s h o w n in f ig . 1, w e r e found

100

IC

I

~I,AMeV~ 4 • • A N

°'0 2 Mev • I A

4 • 8 -2 -t 0 ! 2

B~- B,, MeV

~2 6

5

m o A | •

• •

• qP C1

232 2~ 240 244

A Fig. 1. a) The thresholds of the induced f i ss ion of the even--even O, oddm and odd--odd nuclei k . b) The r a - tio of the average neutron and f iss ion widths as the function of the Bf-B n difference. (The s igns a r e the

same as for a).

f o r t h e odd and o d d - o d d n u c l e i f r o m t h e f i s s i o n c r o s s s e c t i o n by f a s t n e u t r o n s ; f o r e v e n - e v e n n u c l e i t h e s e v a l u e s w e r e found f r o m the c h a n n e l a n a l y s i 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 (d ,p f ) , ( t , p f ) [5] and (7 , f ) [6] r e a c t i o n s . W e d r o p p e d c o n s i d e r a t i o n of t he d a t a on t h e (y , f ) c r o s s s e c - t i on [ 1], u s u a l l y u s e d f o r t he e v a l u a t i o n of t h e Bf , a s t h i s i n f o r m a t i o n s e e m s u n r e l i a b l e b e - c a u s e of t h e a b s e n c e of r e l i a b l e d a t a on t o t a l c r o s s - s e c t i o n w - r e a c t i o n b e l o w t h e b i n d i n g e n - e r g y of t h e n e u t r o n . In t h i s c a s e t h e r e i s a b i g d i s c r e p a n c y b e t w e e n t he o b s e r v e d and r e a l t h r e s h o l d s owing to a s m a l l r a d i a t i o n w i d t h F~, w h i c h c o m p e t e s w i t h t h e Ff [7]. 159

Volume 29B, number 3 P H Y S I C S L E T T E R S 28 April 1969

For l a rge d i f f e r ences Af-A o the fol lowing ef - f ec t s must be observed: 1) the d i f fe rence between the induced f i ss ion b a r r i e r s and the spontaneous h a l f - t i m e for odd and even -even nuclei on the one hand and the odd-odd and odd nuclei on the other one is on the ave r a ge the same; 2) the spl i t t ing of the F n / F f fami ly for the even- even and odd nuclei along the Bf-B n axis is equal to Af+Ao, and for the odd-odd and odd nuclei it equals Af-A o.

F r o m the expe r imen ta l data p r e sen t ed in fig. 1 one can see that a supposit ion about the d i f f e r - ence Af-A o of approx imate ly 0.5 MeV coinc ides with the obse rved spl i t t ing of Bf and F n / F f for the even -even and odd nuclei , but the analogous spl i t t ing for the odd and odd-odd nuclei is p r o b - ably absent. The same d i sc repancy o c c u r s in h a l f - t i m e s of the spontaneous f i ss ion ~f. The ra t io of the h a l f - t i m e s of spontaneous f i s s ion of the odd nuclei with r e s p e c t to the adjacent even- even nuclei f luctuates g r e a t l y f r o m 10 for 233U, 235U to 105 for 239pu, 241Am and 249Cf.

This leads to unnatura l ly g rea t dev ia t ions of the Af-A o d i f fe rence r e l a t ing to the a v e r a g e value of 0.5 MeV. It is impor tan t to note that two ha l f - t i m e s of the f i s s ion of odd-odd nuclei of 242Am and 254Es known at the p r e sen t t ime do not con- f i r m ' the double r a t i o ' expected at Af > A o.

We shall show that the d i f f icul t ies of the ex- p e r i m e n t a l data in t e rp re ta t ion ment ioned above can be r e m o v e d if we take into cons idera t ion the double-humped nature of the f iss ion b a r r i e r . Fo r this model the natura l ques t ion a r i s e s : which b a r r i e r s do we d e t e r m i n e in d i f ferent e x p e r i - ments ? Th is ques t ion was a l ready pa r t ly d i s - cussed by Strut insky and Bj~rnholm [3]. The ene rgy dependence of the f i s s ion c r o s s sect ion is de t e rmined by the b igges t of the two b a r r i e r s [3,8].

The angular d is t r ibut ion in the model of the double-ac t ing f i s s ion p i c tu re is de t e rmined by the second b a r r i e r (the b a r r i e r B in the t e r m i - nology of ref . [8]). So the r e s u l t s of the channel ana lys i s of the angular d i s t r ibu t ions of f r a g - ments in the (d, pf) [5] and (y,f) [6] r e a c t i o n s mus t be a t t r ibuted to the b a r r i e r B. The s i m u l - taneous ana lys i s of the f i ss ion c r o s s sect ion and angular d i s t r ibu t ions of f r agmen t s in the (7, f ) - r eac t ion shown in ref . [9] says that the f i r s t b a r - r i e r A is the highest and most pronounced in the c r o s s sect ion for the ma jo r i t y of heavy nuclei .

The d i f fe rence of the b a r r i e r heights 5AB can r e a c h 1 MeV. It is poss ib le to obtain an inde- pendent value of the 5AB ~ 0.5 t 0.8 MeV f r o m the ana lys i s of g r o s s - s t r u c t u r e of the f i s s ion

c r o s s sect ion of the 234U, 237Np, 240pu, 242pu nuclei by the r e sonance neutrons [ 10].

It s e e m s poss ib le to suppose, t he r e fo r e , that the b a r r i e r d i f fe rence of the odd and even-even nuclei de t e rmined f r o m the sys temat i za t ion of the Bf co r r e sponds not to an i n c r e a s e of the en- e rgy gap but s imply r e f l e c t s the ex i s tence of the b a r r i e r heights d i f ference . The spl i t t ing of the Bf shown in fig. la co r r e sponds to the d i f fe rence 5AB ~ 0.6 MeV. The d i sappearance of this d i f - f e r e n c e for the m o r e light nuclei cons ide red can be unders tood for these nucle i if we a s s u m e that B A = B B or B A < B B.

In this way it is poss ib le to i n t e r p r e t spli t t ing of the F n / F f depending on the Bf-Bn (fig. lb). Now it is easy to unders tand the absence of s y s - t emat i c spli t t ing of the Fn /F f for the odd and odd-odd nuclei if Af = A o. The same r e su l t may be obtained f rom the obse rved spli t t ing F n / F f for the even-even and odd nuclei , if the d i f f e r - ence of the b a r r i e r heights Af + A = 2.0 - 5AB = = 1.4 MeV is e l iminated. The obse rved t h r e s h - olds for the nucle i such as Th do not include the d i f f e rences 5AB and h e r e the expe r imen ta l value Af + n o ~ 1.4 MeV (fig. lb). The value of 5AB = = 0.6 MeV used h e r e must be cons idered , of course , as a rough e s t ima te for a set of nuclei . Note that the above mentioned conclusion is con- f i r m e d too by the analys is of the p a r a m e t e r K 2 in the angular d is t r ibut ion of f r a g m e n t s [11].

The even-odd d i f f e rences in the h a l f - t i m e s of spontaneous f i s s ion ~-f d i scussed above find, as is known, a na tura l in te rp re ta t ion f r o m the point of view of W h e e l e r ' s hypothesis [12] about con- se rva t ion of the quantum number K at the spon- taneous f i ss ion . This hypothesis , con t r a ry to the supposit ion about ' the big gap ' , does not lead to the sys t ema t i c d i f fe rence of the h a l f - t i m e s of spontaneous f i ss ion of the odd and odd-odd nu- c le i . This a g r e e s with the two exis t ing hal f - t i m e s of the odd-odd nuclei .

References

i. E.K. Hyde, I. Perlmann and G. T. Seaborg, The nu- clear properties of the heavy elements, vol. 1 (New Jersey, 1964); W.J. Swiatecki, Phys. Rev. i01 (1955) 97; V. E. Viola Jr. and B. D. Wilkins, Nucl. Phys. 82 (1966) 65.

2. J . J . Griffin, Phys. Rev. 132 (1963) 2204. 3. V. M. Strutinsky, Nucl. Phys. A95 (1968) 420;

V. M. Strutinsky and S. Bjornholm, Int. Syrup. on Nuclear Structure, Dubna 1966.

4. R. Vandenboseh and Y. R. Huizenga, Proc. 2nd U.N. Intern. Conf. Peaceful Uses At. Energy, Geneva 1958, 15 (1958) 284.

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5. H. C. Bri t t , F .A. Rickey J r . and A.W. Hall, P r e - pr int LA-DC-9562 (1968}.

6. N. S. Rabotnov, G.N. Smirenkin, A.S. Soldatov et al., Phys. Le t te rs 26B (1968) 218.

7. L.N. Usachev, N. S. Rabotnov and V. A. Pavl in- chuck, AE 17 (1964) 479.

8. J. E. Lynn, Int. Syrup. Nucl. Structure, Dubna 1968; H. Weidman, Z. f~lr Physik 214 (1968) 7.

9. S. P. Kapiza, N. S. Rabotnov, G.N. Smirenkin, A.S. Soldatov et al. , Zh. Eksp. Teor. Fiz. P i s 'ma 9

(1969) 128. 10. E. Migneco and G. Theobald, Nuel. Phys. Al12

(1968) 603; A. Fubint, J . Blons, A. Michaudon and D. Paya, Phys. Rev. Le t te rs 20 (1968) 1373; G. D. James and E. R. Rae, Nucl. Phys. Al18 (1968) 313.

11. G.N. Smirenkin, V. G. Nesterov and A. S. Tishin, Jadern. Fiz. 6 (1967) 921.

12. J .A .Whee l e r , Essays Niels-Bohr and the devel- opment of physics (London, 1955).

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