Isomer Ratios from (α, xn) Reactions on Silver

Abstract

Excitation functions have been measured for the ${\mathrm{Ag}}^{107}(\ensuremath{\alpha}, n){\mathrm{In}}^{110,110m}$ and ${\mathrm{Ag}}^{109}(\ensuremath{\alpha}, 3n){\mathrm{In}}^{110,110m}$ reactions with isotopically separated targets. The excitation functions for the high-spin metastable state peak in both reactions at higher bombarding energies than the low-spin ground state. In the case of the ${\mathrm{Ag}}^{107}(\ensuremath{\alpha}, n)$ reaction, the cross section for the formation of ${\mathrm{In}}^{110}$ peaks at a helium-ion energy of about 17 MeV and that for ${\mathrm{In}}^{110m}$ peaks at about 19.5 MeV. The isomer ratio, $\frac{{\ensuremath{\sigma}}_{m}}{({\ensuremath{\sigma}}_{m}+{\ensuremath{\sigma}}_{g})}$, determined for the ${\mathrm{Ag}}^{107}(\ensuremath{\alpha}, n)$ reaction varies from 0.13 at a helium-ion energy of 10.8 MeV to 0.81 at a helium-ion energy of 22.0 MeV. In the ${\mathrm{Ag}}^{109}(\ensuremath{\alpha}, 3n)$ reaction, this ratio varies from 0.68 at a helium-ion energy of 27.6 MeV to 0.87 at a helium-ion energy of 38.7 MeV. The experimental cross sections are based on measured half-lives of 70.2\ifmmode\pm\else\textpm\fi{}1.4 min and 5.2\ifmmode\pm\else\textpm\fi{}0.2 h for ${\mathrm{In}}^{110}$ and ${\mathrm{In}}^{110m}$, respectively. The isomer ratios were calculated theoretically for the above reactions and the effects of various parameters on the calculations were examined. The experimental isomer ratios for the ${\mathrm{Ag}}^{107}(\ensuremath{\alpha}, n)$ reaction for bombarding energies below 18 MeV agree within experimental uncertainties with calculated results based on either a Fermi-gas model with a rigid moment of inertia (${\ensuremath{\sigma}}^{2}=34.7t$) or a superconductor model. A superconductor model predicts only about a 20% reduction in the moment of inertia for ${\mathrm{In}}^{110}$ and such a small change could not be definitely established from the data. A marked increase in the experimental isomer ratios from the ${\mathrm{Ag}}^{107}(\ensuremath{\alpha}, n)$ reaction is observed near the onset of the ($\ensuremath{\alpha}, 2n$) reaction. This increase is probably due to a fractionation of the intermediate spin distribution for energies slightly exceeding the threshold of a second reaction. This effect is suggested also in the ${\mathrm{Ag}}^{109}(\ensuremath{\alpha}, 3n)$ reaction by the small experimental isomer ratios at bombarding energies where the ($\ensuremath{\alpha}, 2n$) competition is sizeable. These results indicate that values of $\ensuremath{\sigma}$ deduced from the isomer ratio technique are in error at energies where cross sections for a competing reaction are large.