Neutron Evaporation and Energy Distribution in Individual Fission Fragments

Abstract

Using the isotopic probability distributions of fragments as given by a model for the fission process and those of products as calculated from published product charge distribution parameters, a new procedure is developed for obtaining the number of neutrons $\overline{\ensuremath{\nu}}(Z,N)$ evaporated from individual fragments of $^{235}\mathrm{U}({n}_{\mathrm{th}},F)$. Following neutron evaporation as a cascade process and applying Weisskopf's evaporation theory to each step of the cascade, the excitation energy carried by the individual fragments is solved for from the $\overline{\ensuremath{\nu}}(Z,N)$ data. This procedure also gives an estimate of the fission $\ensuremath{\gamma}$ energy from individual fragments without an a priori assumption. The kinetic energy for each fragment is calculated from the total fission energy obtained using a mass formula and the computed excitation energy. Isobaric, isotopic, and isotonic averages of the parameters are presented.The distributions of $\overline{\ensuremath{\nu}}(Z,N)$ versus $N$ for a given $Z$ show shell effects at neutron magic numbers $N=50 \mathrm{and} 82$. The maximum in isobaric average excitation energy for fragment pairs is found to occur a few mass units away from the point of symmetry, similar to such a trend observed in experimental $\overline{\ensuremath{\nu}}(A)$ for fragment pairs. The isotopic probability distributions given by the model do not take cognizance of any specific shell effects. However, from the minima in $\overline{\ensuremath{\nu}}(Z)$ and $\overline{\ensuremath{\nu}}(N)$ distributions in the region of magic numbers and the occurrence of peaks in the complementary regions, it is concluded that in fission events when a magic-number fragment is involved, the major part of the excitation energy is carried by the complementary fragment. The isobaric average kinetic energy distribution in the present work reproduces many of the fine structures in the experimental curve; however, the dip at the point of maximum excitation energy is not noticed in the latter. The fission-neutron spectrum in the laboratory frame is calculated from the spectra of evaporated neutrons from individual fragments and compared with the Watt spectrum. Average fission parameters obtained in the present work are in good agreement with experimental results.