Abstract
The nucleus of $^{235}\mathrm{U}$ has a low-lying isomeric state of energy about 76.7 eV. Excitation cross sections of the nucleus from the ground state to the isomeric state by inelastic electron scattering are calculated on the level of the Dirac distorted-wave Born approximation. The cross sections are about six orders of magnitude higher than known values based on the Dirac plane-wave Born approximation, emphasizing the vital importance of wave function distortion in the nuclear excitation. In addition, we find that even with low-energy electrons on the order of 100 eV, relativistic effects are significant without which the excitation cross sections drop by an order of magnitude.
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