Transverse electron scattering form factors at low momentum transfer: Sensitivity to in-medium modifications of vector mesons?

Abstract

Form factor measurements of $M2$ and $M4$ transitions to the lowest ${J}^{\ensuremath{\pi}}{=2}^{\ensuremath{-}}$ and ${4}^{\ensuremath{-}}$ states, respectively, in ${}^{48}\mathrm{Ca}$ with inelastic electron scattering at $180\ifmmode^\circ\else\textdegree\fi{}$ are reported for momentum transfers $q\ensuremath{\simeq}0.4\ensuremath{-}0.8{\mathrm{fm}}^{\ensuremath{-}1}.$ These form factors complement previous measurements at higher $q$ which have been treated by Lallena [Phys. Rev. C 48, 344 (1993)], as a test case to derive information on in-medium modifications of the $\ensuremath{\rho}$-meson mass. He deduced within the random-phase approximation (RPA) an effective mass ${m}_{\ensuremath{\rho}}^{*}\ensuremath{\simeq}0.9\ensuremath{-}0.95{m}_{\ensuremath{\rho}}$ assuming simultaneous scaling of the $\ensuremath{\pi}$ coupling constant (Brown-Rho scaling). The validity of the analysis is critically assessed by comparing the measured form factors to second random-phase approximation (SRPA) calculations with a $\ensuremath{\pi}+\ensuremath{\rho}$ exchange interaction. The dependence of the form factors on the choice of the interaction and corrections such as mesonic exchange currents (MEC) are found to be of comparable magnitude to effects from a dropping of ${m}_{\ensuremath{\rho}},$ and in-medium effects hence cannot be clearly inferred from the data. To quantify the latter would require first the construction of an interaction which is capable of describing simultaneously and optimally a large variety of low-energy nuclear properties in ${}^{48}\mathrm{Ca}.$ Remaining discrepancies in such a description could then be studied with the aim to single out in-medium effects of the type advocated by Lallena.