Inelastic Scattering of 42-MeV Alpha Particles byMg25

Abstract

Cross sections have been measured for elastic and inelastic scattering of 42-MeV $\alpha$ particles by ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$ in the range $\theta \left(\mathrm{lab}\right)=10\mathrm{}°-60\mathrm{}°$. Six inelastic $\alpha$ groups were identified at the following measured $-Q$ values: 1.59, 1.94, 2.55, 2.75 (doublet), 3.400 (doublet), and 4.05 MeV. The cross sections are analyzed in terms of the distorted-wave Born-approximation version of the extended optical model and the smoothed Fraunhofer inelastic diffraction model. A general discussion is given of the transition strengths of odd-mass nuclei within the context of the strong-coupling rotational model or modifications thereof, and application is made to the present results. The main conclusions are: Inelastic scattering within the ground-state band supports the rotational model in its simplest form. Comparison of the elastic cross sections from ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$, and ${}_{}{}^{26}{}_{}{}^{}\mathrm{Mg}$ indicates the presence of a quadrupole contribution to the elastic cross section from ${}_{}{}^{25}{}_{}{}^{}\mathrm{Mg}$, consistent with the strong-coupling prediction. The $\lambda =2\mathrm{}$ single-nucleon contribution to transitions into the lowest $K={\frac{1}{2}}^{+}$ band appears to be very small. The excitation corresponding to the known level at 4.057 MeV suggests that this level arises from coupling a $\gamma$ vibration to the ground-state band. The second $K={\frac{1}{2}}^{+}$ band may have the same origin, although other evidence indicates that there is at least a sizable admixture of a single-nucleon orbital to this band.