Systematics of isospin character of transitions to the21+and31−states inZr90,92,94,96

Differential cross sections for exciting the $2_1^{+}$ and $3_1^{\mathrm{-}}$ states of ${}_{}{}^{90,92,94,96}{}_{}{}^{}\mathrm{Zr}$ with 70-MeV ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ ions have been measured. Calculations of the cross sections have been performed using a deformed optical model potential (DOMP) with OMP deduced from fits to the elastic data, as well as a folding model with an effective nucleon-nucleon interaction with a Yukawa form factor obtained from fits to the elastic data and transition densities obtained from open-shell random phase approximation (RPA) calculations. The DOMP fits to the data yield values of ${\mathit{M}}_{\mathit{n}}$/${\mathit{M}}_{\mathit{p}}$ which are in good agreement with those predicted using the RPA. For the $2_1^{+}$ states, we find ${\mathit{M}}_{\mathit{n}}$/${\mathit{M}}_{\mathit{p}}$ increases from less than N/Z to greater than N/Z in going from ${}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$ to ${}_{}{}^{96}{}_{}{}^{}\mathrm{Zr}$. However, for the $3_1^{\mathrm{-}}$ states ${\mathit{M}}_{\mathit{n}}$/${\mathit{M}}_{\mathit{p}}$ remains less than N/Z for all cases, a result which is in disagreement with previous works. The folding model, with the RPA transition densities, provides good agreement with the $2_1^{+}$ measurements, but underpredicts the cross sections for the $3_1^{\mathrm{-}}$ states. A reanalysis of the earlier data from excitation of these states by (α,α’) reactions removes much of the apparent discrepancies between those measurements and other measurements, including the ones reported here. The localization of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ interaction is also discussed.