  We have developed models of the fission barrier (barrier heights and
transition state spectra) that reproduce reasonably well the measured fission
cross section of $^{235}$U from neutron energy of 1 keV to 2 MeV. From these
models we have calculated the fission cross section of the 77 eV isomer of
$^{235}$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 $^{235}$U at keV neutron energies. We have
also calculated the cross section for the population of the isomer by inelastic
neutron scattering form the $^{235}$U ground state. We find that the isomer is
strongly populated, and for $E_n = 1 MeV$ the $(n,n'\gamma)$ cross section
leading to the population of the isomer is of the order of 0.5 barn. 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 $^{235}$U.
With these same models the fission cross sections of $^{233}$U and $^{237}$U
can be reproduced approximately using only minor adjustments to the barrier
heights. With the significant lowering of the outer barrier that is expected
for the outer barrier the general behavior of the fission cross section of
$^{239}$Pu can also be reproduced.
