Probability of α-particle emission during fission

i

2.J: 5 "]]

NuclearPhysicsA96 (1967) 588--592; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

PROBABILITY OF ~-PARTICLE E M I S S I O N D U R I N G F I S S I O N T H U P H O N G D O A N , C L A U D E C A R L E S and R A Y M O N D C H A S T E L

Laboratoire de Physique Nucl6aire, Fucultd des Sciences de Bordeaux Received 23 N o v e m b e r 1966 Abstract: The experimental results of Schmitt and Feather for thermal neutron fission of z35U, allow us to draw the curve of variation of intrinsic c~-particle emission probability versus the mass ratio of fragments. Taking account that this curve is valuable in the mass range 233--241, we find again the experimental rate of ternary z-particle production. We find that a similar shape exists at scission in binary fission and fight-particle ternary fission. We can also explain the correlation between symmetrical fission and light-particle ternary fission.

Experimental results show that the probability for the production of a light charged particle during fission (mostly a-particles) changes with the fissioning nucleus and with the excitation energy. Several theoretical studies have been published on this subject t - 3 ) and in spite of the important progress made in the understanding of the phenomenon, several questions remain unanswered. In this paper, we try to find a relation between the probability of a-particle production and some other fission parameters. To simplify the calculations Schmitt and Feather 1) assumed that the emission of a-particles is a two-step process; they computed the emission probability for an aparticle from a fragment of mass M P~(M) -

Yv(M-4) YB(M)

where Y T ( M - 4 ) and YB(M) are the respective probabilities to obtain the fragments of masses M - 4 and M in a fission associated with the emission of an a-particle ("tripartition") and a binary fission. Halpern 2) has studied the influence of the form of P~(M) on the mass distribution in tripartition in relation with the distribution in binary fission. Refs. 1,2) do not imply necessarily a two-step process. Likewise, the considerations that we develop in this paper do not imply suppositions about the development of this phenomenon in time. if we take P:,(Mx) and P~(M2) from the curves of Schmitt and Feather 1), we can calculate the value of P~ --- P~(M1)+P~(M2) for each pair of values of Mt and M 2 (masses of the two fragments from a binary fission). The results have been obtained for 23SU fission with thermal neutrons, these 588

s-PARTICLE EMISSION

589

results are the only ones that we have been able to use. We can thus obtain the variation o f P~ as a function of the parameter R = Me~Mr (with R > 1). We have obtained P,(R) (fig. l) for the tripartition o f z3sU by thermal neutrons. There are some comments to be made about this curve: the probability of ,sparticle emission shows two minima in the regions corresponding to closed shells (R ~ 1.2 to 1.3 and R ~ 1.6 to 1.7); in the regions where one o f the fragments is very deformed 4,5), the probability o f ,s-emission is the greatest. The function P,(R) has been calculated for a given fissioning nucleus and for a

P_R (~ uo.

3

R

I

;.2

I;

'

118

I;

;

F i g . l . P r o b a b i l i t y o f s - p a r t i c l e as a f u n c t i o n o f t h e m a s s r a t i o .

FB{R)

10

- -

2SSU + ? h e r r n o l

....

23SU+ n e u t r o n s 14

neutrons NIeV

, ,

ua

R

1.2

1;

116

Is

Fig. 2. Mass distributions in binary fission as a function of the mass ratio. given excitation energy. The different points in the curve are not k n o w n very precisely because the experimental results are not very accurate and it is difficult to exploit them. However, we think that the general trend is satisfactory and have therefore considered P~(R) as a universal function for the masses between 233 and 241. We c o m p u t e the ratio between tripartitions and the number o f binary fissions with the aid o f P=(R) and F~(R) ,S

Kf"'-F.(R)PR)dR 1

590

T.P. DOAN et al.

We have thus calculated the values of c¢/f for different masses and different excitation energies of the fissioning nucleus. The functions FB(R) (fig. 2) are obtained from the experimental results for the mass distributions of the fragments in binary fission for the nuclei studied. The functions FB(R) and P~(R) cannot be represented by a simple analytic expression, therefore, we have integrated numerically. We found the normalization constant K so as to give the experimental result corresponding to the TABLE 1

Values o f the ratio c¢/f for different fissioning nuclei Target nuclei

Calculated values

22~g

1 5-00

235 U

1 420

Experimental values

Incident particle

1 500 1

thermal neutrons ~)

1350-- 190 l

neutrons 14 MeV

496~- 64 b)

1

c)

4147_- 26 233 U

1 465

1 a) 445_1- 13 1

thermal neutrons

e)

405 _]- 30

1 2agpu

1 450

e)

411 _J= 26 1 a)

thermal neutrons

445 ± 35

1 24apu

1 520

4 4 0 ± 28 1

o) f)

thermal neutrons

370z~ 36 T h e result o f ref. s), which is obtained in a later experiment, seems m o r e precise t h a n the data o f ref. 7). a) Ref, 7). b) Ref. s). e) Ref. 9). a) Ref. 10). e) Ref. al). ~) Ref. 1~).

tripartition of 235U by thermal neutrons. We have used the same value of K to calculate the values of the ratio ~/f for different target nuclei. The results shown in table 1 are in very good agreement with the experimental values. The good agreement encouraged us to apply the same method to calculate the ratio c¢/f for the tripartition of 23SU by protons and to keep the same value of K. We show the results on fig. 3 with the experimental results of Thomas and Whetstone 6). Here

z-PARTICLE

591

EMISSION

also the agreement with the experimental results is satisfactory. We note that the different curves o f FB(R) are strongly modified with increasing excitation energy. Therefore, the agreement between the c o m p u t e d and the measured values of cq~fas a function of excitation energy seems to indicate that the curve P,(R) does not change. The shape of this curve shows that the probability of a-emission in tripartition is large for the symmetric fissions and also for the very asymmetric fissions. The change in FB(R) with excitation energy is small for very asymmetric fissions (R > 1.7). We see that the increase in e/f as a function o f excitation energy comes chiefly from symmetric fissions. If we assume that the probability for the emission o f these c~-particles depends upon the deformations, which seems reasonable, then we can compare this probability with the value of ~ (average n u m b e r o f p r o m p t neutrons). The fission of 10~3 F

~gNp

2~ z~ c a l c u l a t e d

values

o TD THOMAS a n d SL W H E T S T O N E . J n

E" MeV

o

B

15

20

2'5

Fig. 3. Yield of ~-particles from the fission of ~a~Npas a function of the excitation energy. The errors on the calculated points are from the error on the value of K.

252Cf obtained by Stein and Whetstone lo) shows that 9 as a function o f R presents two minima. This is very similar to our curve P~(R). These minima probably correspond to the complete shells. It seems important to have more precise experimental results in order to know the curve P,(R) better, but in the absence o f new experimental results, we nevertheless hope to make a correction to P,(R), which is dependent on the mass A o f the fissioning nucleus. This work allows us to draw the conclusion that the p h e n o m e n o n o f light-particle emission in tripartition is not essentially different from binary fission. In fact, the mass distribution in binary fission enables us to obtain results on tripartition in g o o d agreement with experiments. This work shows also the connection between symmetric

592

T.P. t)OAN et al.

f i s s i o n a n d t h e p r o b a b i l i t y o f c~-particle e m i s s i o n i n t r i p a r t i t i o n . I f f u r t h e r c o n f i r m a t i o n o f t h e s e i d e a s is o b t a i n e d , it m a y b e p o s s i b l e t o g e t i n t e r e s t i n g i n f o r m a t i o n o n t h e s c i s s i o n s t a g e i n t h e case o f s y m m e t r i c fission.

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13)

H. W. Schmitt and N. Feather, Phys. Rev. 134 B (1964) 565 I. Halpern, Symp. on the physics and chemistry of fission, Vol. 11, Salzburg (1965) p. 369 E. K. Hyde, The nuclear properties of the heavy elements, Vol. II1 V. V. Vladimirskii, JETP (Soy. Phys.) 5 (1957) 673 S. L. Whetstone Jr., Phys. Rev. 114 (1959) 581 T. D. Thomas and S. L. Whetstone Jr., Phys. Rev, 144 (1966) 1060 N. A. Perfilov, Z. I. Solov'eva and R. S. Filov, Atom. Energ. (USSR) 14 (1963) 575 L. V. Drapchinskii, S. S. Kovalenko, K. A. Petrzhak and I. I. Tyutyugin, Atom. Energ. (USSR) 16 (1964) 144 R. A. Nobles, Phys. Rev. 126 (1962) 1508 A. J. Druytter and M. N6ve de Mevergnies, Congr. Int. de physique nucl6aire, Vol. II, Paris (1964) p. 1114 and private communication K. W. Allen and J. T. Dewan, Phys. Rev. 80 (1950) 181 T. A. Mostovaya, Atom. Energ. (USSR) 10 (1961) 372 W. E. Stein and S. L. Whetstone Jr., Phys. Rev. 110 (1958) 476