The Rate of Decay of Fission Products

Abstract

There are two ways to describe the total β- and γ-radiation emitted by the fission products. The first, more accurate method describes it as the sum of radiations emitted by the differnt fission products. The second, less accurate method considers the fission products as a sort of statistical assembly and tries to arrive at once at the total radiation from all the fission products together. While this second method is unquestionably less complete taht the first one, it is so much simpler that it is much preferable in most practical calculations. Its validity is limited, of course, to times during which the radiation is emitted by many nuclei. at very long times after irradiation, when most of the radiation is caused by a few surviving species of nuclei, the first method is definitely preferable.

By considering the fission products as a sort of statistical assembly, calculations have been made of the β-disintegrations per second and of the total energy emitted per second at any time after fission has taken place (cf. Fig. 6). The results are in good agreement with experiment. The theoretical work is based on the assumption that the mass of a nucleus of mass number A and charge Z is given by a(Z_o(A)—Z) ²+b. Empirical values for a and b are used. Use is also made of an approximate empirical relationship between half-life and disintegration energy. A further basic hypothesis which is important for the results at very short times after fission has taken place is that, in the most probable way of splitting, the chain lengths of the light and heavy fragments are equal and that there is not much deviation from this most probable mode of fission. (See L. E. Glendenin, C. D. Coryell, R. R. Edwards, and M. H. Feldman, CL-LEG-1. A tenta-tive explanation has been given recently by R. D. Present, Phys. Rev. 72, 7 (1947).) The average number of β-disintegrations per fission is found to be 6; the average energy of all radiations (β, γ, and neutrino) of the fission products is 21.5 ±3 Mev. Apparently, about half of this energy escapes in the form of neutrinos and a quarter is emitted in the form of /3 and in the form of γ rays.

A few remarks are made concerning the possible origin of delayed neutrons. It is also pointed out that the spread of the kinetic energy of a given pair of fission fragments cannot be easily explained on the basis of differences of chain length which result in differences in excitation energy of the fragments. It is possible that fluctuations in the production of fission neutrons are at least partly responsible for the kinetic energy spread.