Gamma-Ray Yields from Nuclear Reactions and Level Densities of Deformed Nuclei

Theoretical calculations of spin distributions of compound nuclei and subsequent neutron-evaporation products are made for 27-MeV alpha particles on ${}_{}{}^{178}{}_{}{}^{}\mathrm{Hf}$, 52-MeV alpha particles on ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}$, and 56-MeV ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ ions on ${}_{}{}^{165}{}_{}{}^{}\mathrm{Ho}$. The first two cases were chosen to match experimental work of Lark and Morinaga. We use our calculations as a basis for interpretation of their relative yield of ${}_{}{}^{180m}{}_{}{}^{}\mathrm{W}$, the $J=8^{-}$ isomer, and the $J=4^{+}$ state of the ground rotational band. We find these yields consistent with the simple assumption that after the last neutron is evaporated to form the excited ${}_{}{}^{180}{}_{}{}^{}\mathrm{W}$ nucleus all products with spin $J\gtrsim 10$ feed into the $8^{-}$ isomer and those with spin $J\lesssim 10$ contribute to the prompt radiation from the first $J=4^{+}$ level. Possible relationships between the course of the gamma-ray cascade and the nature of the Nilsson orbitals nearest the Fermi surface are discussed. Finally, the importance of measuring gamma-ray angular distributions in addition to integrated yields is stressed, and formulas of possible value for the analysis of such angular distributions are collected and presented.