Theoretical evaluations of the fission cross section of the 77 eV isomer of ${}^{235}\mathrm{U}$

We have developed models of the fission barrier (barrier heights and transition state spectra) that reproduce reasonably well the measured fission cross section of ${}^{235}\mathrm{U}$ from a neutron energy of from 1 keV to 2 MeV. From these models we have calculated the fission cross section of the 77 eV isomer of ${}^{235}\mathrm{U}$ over the same energy range. We find that the ratio of the isomer cross section to that of the ground state lies between about 0.45 and 0.55 at low neutron energies. The cross sections become approximately equal above 1 MeV. The ratio of the neutron capture cross section to the fission cross section for the isomer is predicted to be about a factor of 3 larger for the isomer than for the ground state of ${}^{235}\mathrm{U}$ at keV neutron energies. We have also calculated the cross section for the population of the isomer by inelastic neutron scattering from the ${}^{235}\mathrm{U}$ ground state. We find that the isomer is strongly populated, and for $E_n=1\mathrm{}$ MeV the ${(n,n}^{\prime }\gamma )$ cross section leading to the population of the isomer is of the order of 0.5 b. Thus, neutron reaction network calculations involving the uranium isotopes in a high neutron fluence are likely to be affected by the 77 eV isomer of ${}^{235}\mathrm{U}.$ With these same models the fission cross sections of ${}^{233}\mathrm{U}$ and ${}^{237}\mathrm{U}$ can be reproduced approximately using only minor adjustments to the barrier heights. With the significant lowering of the outer barrier that is expected the general behavior of the fission cross section of ${}^{239}\mathrm{Pu}$ can also be reproduced.