Inelastic Scattering of Deuterons from the Magnesium Isotopes

Natural and enriched magnesium targets were bombarded with 15-Mev deuterons from the University of Pittsburgh cyclotron. The reaction products were magnetically analyzed and detected by a scintillator or by nuclear emulsions. Angular distributions were obtained for the deuterons inelastically scattered from the ${\mathrm{Mg}}^{24}$ 1.37-, ${\mathrm{Mg}}^{25}$ 1.61-, and ${\mathrm{Mg}}^{26}$ 1.83-Mev states. The results are compared to the predictions of the plane-wave Born approximation theory and of the inelastic diffraction scattering model. The curves obtained from the Born approximation give better over-all correspondence with the experimental points. The inelastic diffraction scattering model, however, allows one to extract directly the effective values of the nuclear deformation parameter $\beta$. One obtains $\left|\beta \right|=0.20, 0.19, \mathrm{and} 0.17$ for ${\mathrm{Mg}}^{24}$, ${\mathrm{Mg}}^{25}$, and ${\mathrm{Mg}}^{26}$, respectively. The spectra of deuterons inelastically scattered from ${\mathrm{Mg}}^{25}$ and ${\mathrm{Mg}}^{26}$ were also observed, at ${\theta }_{\mathrm{lab}}\approx 12°, 30°, \mathrm{and} 60°$. The only large cross sections in ${\mathrm{Mg}}^{25}$ were those for the 1.61-Mev (${\frac{7}{2}}^{+}$) level and for a level near 3.4 Mev. The strength of the reaction to the latter level suggests that it is the $\frac{9}{2^{+}}$ member of the ground-state rotational band which, in analogy with ${\mathrm{Al}}^{25}$, should appear at approximately this energy. The results tend to confirm the selection rule that favors collective excitations over single-particle excitation in inelastic scattering. In ${\mathrm{Mg}}^{26}$ strong scattering was observed only from the first two excited states. A previously unreported ${\mathrm{Mg}}^{26}$ state was found at the excitation energy of 3.614±0.020 Mev.