Theoretical study of pressure effects on fission fragment track registration lengths in apatite

Pressure effects on the track lengths of ²³⁵U fission fragments in an idealized 'random' fluoroapatite target are theoretically investigated by estimating changes in stopping power cross section due to pressure-induced changes in the electronic structure of the target material. Changes in the electronic density and mean ionization energy of compressed target atoms are evaluated through the Thomas-Fermi-Dirac-Weizsacker (TFDW) energy density functional for an atom confined within a spherical cavity whose radius is associated with the pressure exerted on the material. As a first approximation, chemical binding effects are neglected, treating the stopping contribution from target constituent atoms according to the material stoichiometry and assuming Bragg's additivity rule. Also, an approximate equation of state for apatite is used to estimate the pressure-induced changes in bulk density. Range calculations are performed for slow neutron induced fission of U235 with a light particle (A=96) at 93.1 MeV and a heavy particle (A=137) at 61.4 Mev at normal pressure using SRIM and compared with those obtained in this study for high pressures (2 GPa, 10 GPa and 105 GPa).