Unified nuclear potential for heavy-ion elastic scattering, fusion, fission, and ground-state masses and deformations

Abstract

We develop a unified nuclear potential for the description of large-scale nuclear collective motion and find that it satisfactorily reproduces experimental data for heavy-ion elastic scattering, fusion, fission, and ground-state masses. Obtained by generalizing the modified liquid-drop model so that two semi-infinite slabs of constant-density nuclear matter have minimum energy at zero separation, this potential is given in terms of a double volume integral of a Yukawa-plus-exponential folding function. For heavy nuclear systems the resulting heavy-ion interaction potential is similar to the proximity potential of Swiatecki and co-workers. However, for light nuclear systems our potential lies slightly below the proximity potential at all nuclear separations. For heavy nuclei fission barriers calculated with our Yukawa-plus-exponential model are similar to those calculated with the liquid-drop model. However, for light nuclei the finite range of the nuclear force and the diffuse nuclear surface lower the fission barriers relative to those calculated with the liquid-drop model. Use of a Wigner term proportional to $\frac{|N\ensuremath{-}Z|}{A}$ in the nuclear mass formula resolves the major part of the anomaly between nuclear radii derived from elastic electron scattering on the one hand and from ground-state masses and fission-barrier heights on the other.NUCLEAR REACTIONS $^{4}\mathrm{He}$+$^{12}\mathrm{C}$, $^{16}\mathrm{O}$+$^{28}\mathrm{Si}$, $^{84}\mathrm{Kr}$+$^{208}\mathrm{Pb}$; calculated heavy-ion interaction potential. $^{16}\mathrm{O}$+$^{28}\mathrm{Si}$, $E=37.7, 81.0, 215.2$ MeV; calculated elastic-scattering angular distribution. $^{32}\mathrm{S}$+$^{27}\mathrm{Al}$, $^{35}\mathrm{Cl}$+$^{62}\mathrm{Ni}$, $^{16}\mathrm{O}$+$^{208}\mathrm{Pb}$; calculated compound-nucleus cross section. Calculated fission-barrier heights and ground-state masses for nuclei throughout Periodic Table. Nuclear potential energy of deformation, liquid-drop model, droplet model, modified liquid-drop model, Yukawa-plus-exponential model, proximity potential, Woods-Saxon potential, double-folding potential, optical model, ingoing-wave boundary condition, single-particle corrections, Strutinsky's method.