(p,n) Reaction on Deformed NucleiMg25andMg26

Abstract

The ${\mathrm{Mg}}^{25}\mathrm{}(p,n)\mathrm{}{\mathrm{Al}}^{25}$ and ${\mathrm{Mg}}^{26}\mathrm{}(p,n)\mathrm{}{\mathrm{Al}}^{26}$ 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 $0^{+}\to 2^{+}$, $\Delta T=0\mathrm{}$, ${\mathrm{Mg}}^{26}\mathrm{}(p,n)\mathrm{}$ transition] among the members of the $K=\frac{5}{2}$ ground-state band in the ${\mathrm{Mg}}^{25}\mathrm{}(p,n)\mathrm{}{\mathrm{Al}}^{25}$ reaction. The measured cross section, excitation function, and angular distribution for the ${\frac{5}{2}}^{+}\to {\frac{7}{2}}^{+}$ transition in ${\mathrm{Mg}}^{25}\mathrm{}(p,n)\mathrm{}$ 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 ${\mathrm{Mg}}^{25}\mathrm{}(p,n)\mathrm{}$ 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 $0^{+}\to 2^{+}$, $\Delta T=0\mathrm{}$ cross section is much larger than the theoretical prediction of the deformed isospin optical model. However, the $0^{+}\to 2^{+}(p,n^{\prime })$ cross sections are correlated with the analogous $0^{+}\to 2^{+}(p,p^{\prime })$ cross sections. In the ${\mathrm{Mg}}^{26}\mathrm{}(p,n)\mathrm{}{\mathrm{Al}}^{26}$ reaction, the measured $0^{+}\to 2^{+}$, $\Delta T=0\mathrm{}$ cross section is three times the $0^{+}\to 0^{+}$ isobaric cross section. On the other hand, the $0^{+}\to 0^{+}$, $\Delta T=0\mathrm{}$; $0^{+}\to 1^{+}$, $0^{+}\to 3^{+}$, and $0^{+}\to 5^{+}$, $\Delta T=1\mathrm{}$ cross sections are comparable, indicating that charge exchange with spin-flip and with $\Delta l=0,2,4\mathrm{}$ are almost as important as monopole charge exchange in the ${\mathrm{Mg}}^{26}\mathrm{}(p,n)\mathrm{}{\mathrm{Al}}^{26}$ 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 ${\mathrm{Mg}}^{25}\mathrm{}(p,n)\mathrm{}$, would seem to indicate that single-particle transitions are relatively more important when compared with the analogous ($p,p^{\prime }$) scattering, and thus that an appreciable fraction of the $K=\frac{5}{2}$ to $K=\frac{5}{2} (J^{\pi }={\frac{7}{2}}^{+} or {\frac{9}{2}}^{+})$ 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 $\Delta l=4\mathrm{}$, is needed to explain the measurements.