Semiempirical Calculation of the Differential Energy Expended per Ion Pair for Fission Fragments inH2

Abstract

High and low limits for the variation of ${w}_{\mathrm{ff}}$, the differential energy expended per ion pair, are calculated for the average-energy ${\mathrm{Cf}}^{252}$ fission fragment in ${\mathrm{H}}_{2}$. The electronic and nuclear stopping cross sections are obtained from the "unified" range theory for heavy ions constructed by Lindhard and co-workers and from recent experimental energy-distance data. Published experimental data of primary ionization cross sections for protons in hydrogen over the appropriate recoil energies yield the high limit. The low limit is obtained when protons are considered to expend energy in the creation of an ion pair at the same rate for their whole trajectory as they do at very high energies. The variation of ${w}_{\mathrm{ff}}$ with fission-fragment energy can be calculated if total ionization cross sections of the stopping-medium knocked atoms and energy-distance curves of the incident particles are known.