Nuclear temperature effects in the scission-point model of nuclear fission

According to the scission-point model, the probability for a particular fission event can be expressed in terms of the collective potential and the collective kinetic energy at the scission point. Two additional assumptions make the scission-point model an easily calculable model: the assumption of equal collective kinetic energies for constant distances $d$ between the tips of the fragments, and the assumption that one is able to characterize the excitation energy of the fragments with a nuclear temperature $T$, independent of both the mass ratio and the charge ratio, and of the deformations of the fragments. It is pointed out that the latter assumption violates energy conservation. A modified, recursive procedure is proposed, resulting in an "energy conservation consistent" scission-point method. Mass and charge distributions for the fission of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ and ${}_{}{}^{252}{}_{}{}^{}\mathrm{Cf}$ compound systems have been calculated and compared with distributions following the "standard" scission-point method of Wilkins, Steinberg, and Chasman.