Isomeric Cross-Section Ratios in (n, γ) Reactions

Isomeric cross-section ratios for ($n, \gamma$) reactions have been measured for the even-even target nuclei ${\mathrm{Te}}^{120}$, ${\mathrm{Te}}^{130}$, ${\mathrm{Ce}}^{138}$, ${\mathrm{Pt}}^{196}$, and ${\mathrm{Hg}}^{196}$. In addition, cross sections for ${\mathrm{Pt}}^{194}(n, \gamma ){\mathrm{Pt}}^{195m}$ and ${\mathrm{Pt}}^{192}(n, \gamma ){\mathrm{Pt}}^{193m}$ reactions have also been measured. It is found that isomeric cross-section ratios ($\frac{{\sigma }_{\mathrm{low}\mathrm{spin}}}{{\sigma }_{\mathrm{high}\mathrm{spin}}}$) tend to increase at the magic numbers of neutrons as well as protons. Away from the magic numbers, these ratios obey an empirical rule which states, "The isomeric cross-section ratios for various isotopes in the same element remain approximately the same provided the spins of the compound nuclei and the isomeric states are the same for all the isotopes." This rule applies to even-even target nuclei. On the basis of this new empirical rule, the cross sections for the production of some of the isomeric states have been estimated. Multiplicity factors (i.e., the number of $\gamma$ rays emitted per neutron capture by target nuclei) have been calculated for $A<\mathrm{}100\mathrm{}$, using capture $\gamma$-ray spectra of Groshev et al. Theoretical calculations of the isomeric cross-section ratios are performed using the spin dependence of the nuclear level density expression of Bloch. Experimental values of the isomeric cross-section ratios are compared with the theoretical values and the results are discussed.