(p,n) Reaction on Deformed NucleiMg25andMg26

Abstract

The ${\mathrm{Mg}}^{25}(p,n){\mathrm{Al}}^{25}$ and ${\mathrm{Mg}}^{26}(p,n){\mathrm{Al}}^{26}$ reactions to individual levels have been investigated to assess the applicability of a strong-coupling deformed isospin model in describing the "inelastic" ($p,n$) charge-exchange reaction. For nuclei in the rotational region, the model predicts a simple splitting of the quadrupole strength [obtained from the ${0}^{+}\ensuremath{\rightarrow}{2}^{+}$, $\ensuremath{\Delta}T=0$, ${\mathrm{Mg}}^{26}(p,n)$ transition] among the members of the $K=\frac{5}{2}$ ground-state band in the ${\mathrm{Mg}}^{25}(p,n){\mathrm{Al}}^{25}$ reaction. The measured cross section, excitation function, and angular distribution for the ${\frac{5}{2}}^{+}\ensuremath{\rightarrow}{\frac{7}{2}}^{+}$ transition in ${\mathrm{Mg}}^{25}(p,n)$ are in fair agreement with the predictions of the deformed isospin model. The evidence for a quadrupole contribution to the ${\frac{5}{2}}^{+}$ ground state and ${\frac{9}{2}}^{+}$ excited state in ${\mathrm{Mg}}^{25}(p,n)$ is inconclusive because of the presence of a large contribution to the cross section from spin-flip with charge exchange. As in a previous experiment, the measured ${0}^{+}\ensuremath{\rightarrow}{2}^{+}$, $\ensuremath{\Delta}T=0$ cross section is much larger than the theoretical prediction of the deformed isospin optical model. However, the ${0}^{+}\ensuremath{\rightarrow}{2}^{+}(p,{n}^{\ensuremath{'}})$ cross sections are correlated with the analogous ${0}^{+}\ensuremath{\rightarrow}{2}^{+}(p,{p}^{\ensuremath{'}})$ cross sections. In the ${\mathrm{Mg}}^{26}(p,n){\mathrm{Al}}^{26}$ reaction, the measured ${0}^{+}\ensuremath{\rightarrow}{2}^{+}$, $\ensuremath{\Delta}T=0$ cross section is three times the ${0}^{+}\ensuremath{\rightarrow}{0}^{+}$ isobaric cross section. On the other hand, the ${0}^{+}\ensuremath{\rightarrow}{0}^{+}$, $\ensuremath{\Delta}T=0$; ${0}^{+}\ensuremath{\rightarrow}{1}^{+}$, ${0}^{+}\ensuremath{\rightarrow}{3}^{+}$, and ${0}^{+}\ensuremath{\rightarrow}{5}^{+}$, $\ensuremath{\Delta}T=1$ cross sections are comparable, indicating that charge exchange with spin-flip and with $\ensuremath{\Delta}l=0,2,4$ are almost as important as monopole charge exchange in the ${\mathrm{Mg}}^{26}(p,n){\mathrm{Al}}^{26}$ reaction. The observation of $K=\frac{5}{2}$ to $K=\frac{1}{2}$ band transitions, which are comparable to $K=\frac{5}{2}$ to $K=\frac{5}{2}$ transitions in ${\mathrm{Mg}}^{25}(p,n)$, would seem to indicate that single-particle transitions are relatively more important when compared with the analogous ($p,{p}^{\ensuremath{'}}$) scattering, and thus that an appreciable fraction of the $K=\frac{5}{2}$ to $K=\frac{5}{2} ({J}^{\ensuremath{\pi}}={\frac{7}{2}}^{+} or {\frac{9}{2}}^{+})$ transition strength goes via single-particle matrix elements. It is concluded that a microscopic strong-coupling calculation, in which the charge-exchange part of the two-body interaction includes spin-flip and angular-momentum transfers up to $\ensuremath{\Delta}l=4$, is needed to explain the measurements.