Charge vibrations in the liquid-drop model of fission

The two-spheroid liquid-drop model of fission developed by Nix and Swiatecki has been extended to include charge vibrations. Using the Myers-Swiatecki mass formula, the appropriate stiffness constants have been obtained in analytic form. The effective mass, M_Δ, associated with charge vibrations for fission shapes was deduced from eigenenergies for the giant dipole resonance calculated by Updegraff and Onley, assuming that the eigenenergy is given by

$\text{h}\text{?}\text{ω}{}_{\mathrm{dipole}}\text{=}\text{h}\text{?}\text{K}{}_{\mathrm{\Delta \Delta }}\text{M}{}_{\mathrm{\Delta }}$

,where K_ΔΔ is the stiffness for charge vibrations. To account for the experimental charge dispersion widths a highly constricted fission shape was chosen. The dependence of fragment deformation energy on mass increases more rapidly than in the Nix and Swiatecki treatment when the eigenvalues of two new normal modes have similar values; it is concluded that this, together with spherical closed-shell effects, may explain the discrepancy between the Nix and Swiatecki values and experimental data. Various other aspects of the effect of charge vibrations are discussed.