Isospin and the Bohr Independence Hypothesis

Abstract

The influence of isospin on statistical nuclear decay at approximately 20 MeV is investigated for two composite systems ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}$ and ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}$ by measurement of the cross sections and the energy spectra of protons and α particles emitted from the two composite systems. The composite system ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}$ was formed at an excitation energy of 19.7 MeV in the ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}+p$ and ${}_{}{}^{62}{}_{}{}^{}\mathrm{Ni}+\alpha$ reactions, while the composite system ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}$ was formed at an excitation energy of 19.5 MeV in the ${}_{}{}^{63}{}_{}{}^{}\mathrm{Cu}+p$ and ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}+\alpha$ reactions. In both systems the experimental cross-section ratio $\frac{\sigma (\alpha ,{\alpha }^{\prime })\sigma (p,p^{\prime })}{\sigma (\alpha ,p)\sigma (p,\alpha )}$ exceeded the value of approximately unity predicted by the Bohr independence hypothesis and the statistical theory of compound-nuclear decay including angular momentum. The cross-section ratios were 2.2 ± 0.2 and 1.3 ± 0.1 for the ${}_{}{}^{66}{}_{}{}^{}\mathrm{Zn}$ and ${}_{}{}^{64}{}_{}{}^{}\mathrm{Zn}$ composite systems, respectively. The major part of the deviation of these ratios from unity in both the composite systems is ascribed to an isospin selection rule acting in the $T_{>}$ states of both composite systems which causes these states to decay preferentially by proton emission. Other factors which might enhance these ratios, such as direct reactions and reduced moments of inertia, are considered and are found to change the above ratios by a relatively small amount.