E2strengths and transition radii difference of one-phonon2+states of92Zr from electron scattering at low momentum transfer

Abstract

Background: Mixed-symmetry ${2}^{+}$ states in vibrational nuclei are characterized by a sign change between dominant proton and neutron valence-shell components with respect to the fully symmetric ${2}^{+}$ state. The sign can be measured by a decomposition of proton and neutron transition radii with a combination of inelastic electron and hadron scattering [C. Walz et al., Phys. Rev. Lett. 106, 062501 (2011)]. For the case of ${}^{92}$Zr, a difference could be experimentally established for the neutron components, while about equal proton transition radii were indicated by the data.Purpose: Determination of the ground-state (g.s.) transition strength of the mixed-symmetry ${2}_{2}^{+}$ state and verification of the expected vanishing of the proton transition radii difference between the one-phonon ${2}^{+}$ states in ${}^{92}$Zr.Method: Differential cross sections for the excitation of one-phonon ${2}^{+}$ and ${3}^{\ensuremath{-}}$ states in ${}^{92}$Zr have been measured with the ($e,{e}^{\ensuremath{'}}$) reaction at the S-DALINAC in a momentum transfer range $q\ensuremath{\simeq}0.3--0.6$ fm${}^{\ensuremath{-}1}$.Results: Transition strengths $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})=6.18(23)$, $B(E2;{2}_{2}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})=3.31(10)$, and $B(E3;{3}_{1}^{\ensuremath{-}}\ensuremath{\rightarrow}{0}_{1}^{+})=18.4(1.1)$ Weisskopf units are determined from a comparison of the experimental cross sections to quasiparticle-phonon model (QPM) calculations. It is shown that a model-independent plane wave Born approximation (PWBA) analysis can fix the ratio of $B(E2)$ transition strengths to the ${2}_{1,2}^{+}$ states with a precision of about 1$%$. The method furthermore allows to extract their proton transition radii difference. With the present data $\ensuremath{\Delta}R=\ensuremath{-}0.12(51)$ fm is obtained.Conclusions: Electron scattering at low momentum transfers can provide information on transition radii differences of one-phonon ${2}^{+}$ states even in heavy nuclei. Proton transition radii for the ${2}_{1,2}^{+}$ states in ${}^{92}$Zr are found to be identical within uncertainties. The g.s. transition probability for the mixed-symmetry state can be determined with high precision limited only by the available experimental information on the $B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+}$) value.