Excitation of isovector giant resonances in pion single-charge exchange at 120, 165, and 230 MeV

We have measured doubly differential cross sections for the (${\pi }^{+}$,${\pi }^0$) and (${\pi }^{\mathrm{-}}$,${\pi }^0$) reactions at 120- and 230-MeV kinetic energies for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{60}{}_{}{}^{}\mathrm{Ni}$, and ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$. Nuclear-excitation energies up to 60 MeV were observed. We have extracted excitation energies, widths, and maximum cross sections for the isospin components of the isovector monopole resonance and the isovector dipole resonance. The excitation energies and widths from the present data and from earlier measurements at 165 MeV are compared and found to be in agreement. The cross sections for the isovector monopole and isovector dipole resonances show the same increase with bombarding energy in all targets. No isovector quadrupole strength is required to fit the experimental data. We compare the energy dependences of the isovector-resonance cross sections with those of isobaric-analog states, and to distorted-wave impulse approximation calculations.