Systematic variation of fission barrier heights for symmetric and asymmetric mass divisions

The excitation functions and the mass yield curves for proton-induced fissions of ${}_{}{}^{233}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{236}{}_{}{}^{}\mathrm{U}$, ${}_{}{}^{237}{}_{}{}^{}\mathrm{Np}$, ${}_{}{}^{239}{}_{}{}^{}\mathrm{Pu}$, ${}_{}{}^{242}{}_{}{}^{}\mathrm{Pu}$, ${}_{}{}^{244}{}_{}{}^{}\mathrm{Pu}$, ${}_{}{}^{241}{}_{}{}^{}\mathrm{Am}$, and ${}_{}{}^{243}{}_{}{}^{}\mathrm{Am}$ targets were studied. The excitation functions for near-symmetrically divided fragments were found quite different in shapes and threshold energies from those of asymmetrically divided ones in all the fissioning systems studied. In order to obtain the fission barrier heights for symmetric and asymmetric mass division, the conventional Bohr-Wheeler type calculations for the competition between fission and neutron emission were performed. In the calculation, two independent fission channels, symmetric and asymmetric, were assumed, and fission barrier heights and level density parameters that could best reproduce the shapes of the excitation functions (incident energy dependence) of typical symmetric and asymmetric products were deduced. Barrier heights for symmetric and asymmetric mass divisions both decrease as the mass of fissioning nuclide ${\mathit{A}}_{\mathit{f}}$ increases, and they also exhibit slight dependence on the atomic number. Difference between the two barrier heights is 2.0–2.5 MeV in the region of ${\mathit{A}}_{\mathit{f}}$=236–245. From similar analysis of excitation function data reported in literature, it is found that the difference changes from a large positive value for N∼150, neutron number of the fissioning nuclide, to a large negative value for N∼126, and the two barrier heights become comparable at N=135–138.