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 − states in 92 Zr have been measured with the (e, e ) reaction at the S-DALINAC in a momentum transfer range q 0.3 − 0.6 fm −1 . Results: Transition strengths B(E2; 2 + 1 → 0 + 1 ) = 6.18(23), B(E2; 2 + 2 → 0 + 1 ) = 3.31(10) and B(E3; 3 − 1 → 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 ∆R = −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 → 0 + 1 ) value.
Abstract. The one-quadrupole phonon excitation of mixed symmetry, the 2 + 1,ms state, is a fundamental building block of nuclear structure. This article gives a summary of our recent experimental research on this excitation mode in the A = 90 and A = 130 mass regions.
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