Beta decay of 252Cf on the way to scission from the exit point

Upon increasing significantly the nuclear elongation, the beta-decay energy grows. This paper investigates within a simple yet partly microscopic approach, the transition rate of the beta decay of the 252Cf nucleus on the way to scission from the exit point for a spontaneous fission process. A rather crude classical approximation is made for the corresponding damped collective motion assumed to be one dimensional. Given these assumptions, we only aim in this paper at providing the order of magnitudes of such a phenomenon. At each deformation the energy available for beta decay, is determined from such a dynamical treatment. Then, for a given elongation, transition rates for the allowed (Fermi) beta decay are calculated from pair correlated wave functions obtained within a macroscopic-microscopic approach and then integrated over the time corresponding to the whole descent from exit to scission. The results are presented as a function of the damping factor (inverse of the characteristic damping time) in use in our classical dynamical approach. For instance, in the case of a descent time from the exit to the scission points of about $10^{- 20}$ second, one finds a total rate of beta decay corresponding roughly to 20 events per year and per milligram of 252Cf. The inclusion of pairing correlations does not affect much these results.