Magnetic electron scattering and valence nucleon radial wave functions

Abstract

Cross sections have been measured for elastic electron scattering from the magnetization distributions of ${}_{}{}^{49}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$, ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$, ${}_{}{}^{87}{}_{}{}^{}\mathrm{Sr}$, ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Bi}$. Particular emphasis has been placed on the multipole distribution of the highest order possible, which dominates the magnetic form factor at momentum transfer values $q$ between 1.7 and 3.0 ${\mathrm{fm}}^{-1\mathrm{}}$. The data for the $1f_{\frac{7}{2}}$ shell nuclei ${}_{}{}^{49}{}_{}{}^{}\mathrm{Ti}$, ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$ and for the $1g_{\frac{9}{2}}$ shell nuclei ${}_{}{}^{87}{}_{}{}^{}\mathrm{Sr}$, ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}$ are interpreted in terms of occupation probability and radial extension of the odd proton or neutron wave function. An accuracy of 1% is obtained for the valence orbit rms radii for both protons and neutrons. Corrections due to two-body magnetization currents and core polarization effects are investigated and found to be small. A detailed comparison of the experimental results with different types of density-dependent Hartree-Fock calculations is made in both momentum space and configuration space. It is found that the best available theory predicts the rms valence radii to within 2%. Comparisons are made between the present results and information on radial wave functions obtained from isotone shifts, proton scattering, and transfer reactions.