Total (p,π+) cross sections on light nuclei near the pion Coulomb barrier

Angle-integrated ($p$,${\pi }^{+}$) cross sections on ${}_{}{}^9{}_{}{}^{}\mathrm{Be}$, ${}_{}{}^{10}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$, ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$, and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ have been measured over the energy range $0.5\lesssim T_p-T_{\mathrm{threshold}}\lesssim 10$ MeV by detecting ${\mu }^{+}$ decays. By combining the present results with higher energy measurements we show that, for $1p$-shell targets, the energy dependence of the ($p$,${\pi }^{+}$) reaction from $T_{\pi }\approx 0.5 \mathrm{to}\approx 50$ MeV can be explained in terms of pion phase space and barrier penetration.