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 ${\mathrm{fm}}^{\ensuremath{-}1}$. The data for the $1{f}_{\frac{7}{2}}$ shell nuclei $^{49}\mathrm{Ti}$, $^{51}\mathrm{V}$ and for the $1{g}_{\frac{9}{2}}$ 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.NUCLEAR REACTIONS $^{49}\mathrm{Ti}$, $^{51}\mathrm{V}$, $^{59}\mathrm{Co}$, $^{87}\mathrm{Sr}$, $^{93}\mathrm{Nb}$, $^{209}\mathrm{Bi}$$(e,e)$; ${E}_{0}=175\ensuremath{-}325$ MeV, $\ensuremath{\theta}=155\ifmmode^\circ\else\textdegree\fi{}$; ${E}_{0}=500$ MeV, $\ensuremath{\theta}=39\ensuremath{-}73\ifmmode^\circ\else\textdegree\fi{}$; measured $\ensuremath{\sigma}({E}_{0},\ensuremath{\theta})$; deduced magnetization distribution parameters, rms radii of neutron and proton $1{f}_{\frac{7}{2}}$ and $1{g}_{\frac{9}{2}}$ orbits.