Target-state dependence of cross sections for reactions on statically deformed nuclei

As part of an effort to understand how neutron-induced reactions on excited states in deformed nuclei differ from those on ground states, we have carried out coupled-channels calculations of the angle-integrated cross sections on the ground and excited states of several actinide nuclei with differing K values for the ground-state band (²³³U, K=5/2; ²³⁵U, K=7/2; ²³⁸U, $K=0$; and ²³⁹Pu, K=1/2). Of particular interest is the compound-nucleus formation cross section. We find that the ratio of the excited- to ground-state compound-formation cross sections is very close to unity in all cases (within ≈0.16em0ex0.1$%$) over the range studied (1 keV to 20 MeV). This result requires that sufficient levels be coupled to ensure convergence (approximately 14 levels for odd-A nuclei). These results are close to the predictions of the adiabatic model for scattering from statically deformed nuclei. This model yields compound-formation cross sections, as well as total cross sections, that are independent of both the K value of the band and the spin of the target state within the band. Our calculations show that the actual cross sections are surprisingly close to the adiabatic limit, even at very low incident energies. We find similar results for statically deformed rare-earth and s-d shell nuclei.