The time-dependent fields experienced by a nucleus as it passes through a crystal can cause transitions to excited nuclear states. The transition rate is especially large when the speed of the nucleus satisfies a resonance condition. Previous estimates of the nuclear excitation rates have been based on symmetry arguments and experimental data for related processes. We present here a calculation of the nuclear excitation rate which does not rely on these simplifying approximations.Vsing nonrelativistic quantum mechanics, the excitation cross sections of highly stripped nuclei channeled along the Si (110) crystal axis have been calculated. The results are smaller than those given by previous estimates by several orders of magnitude. We note that there are similarly large discrepancies between different theoretical and experimental results for other phenomena involving coupled electronic and nuclear transitions. The reason for these disagreements is not clear. PACS number(s): 23.20.Lv, 23.20.Nx, 32.90.+a