Energy dependence of isospin mixing in compound-statistical reactions

Abstract

The ${}_{}{}^{69}{}_{}{}^{}\mathrm{Ga}$ compound nucleus was formed at excitation energies ranging from 17 to 22 MeV in the reactions ${}_{}{}^{65}{}_{}{}^{}\mathrm{Cu}+\alpha$ and ${}_{}{}^{68}{}_{}{}^{}\mathrm{Zn}+p$ and energy spectra of the emitted protons and $\alpha$ particles were measured between 30 and 150°. The extent of isospin mixing between the $T_{>}$ and $T_{<}$ states of the compound nucleus was determined by comparison of the quantity $\frac{\sigma (p,p^{\prime })\sigma (\alpha ,{\alpha }^{\prime })}{\sigma (p,\alpha )\sigma (\alpha ,p)}$ with theory and the fractional mixing was found to increase from 0 to 0.3 over the above energy range. The mixing width shows a corresponding increase from 0.2 to 16 keV. The independence hypothesis was verified at all energies by measurements of the $\alpha$ and $\mathrm{np}$ exit channels. The various spectra were compared with the spin-dependent statistical theory. It was not possible to fit the data for various energies with energy-independent parameters in the Fermi gas model level density expression suggesting that this expression is inadequate.