Search for three-nucleon force effects on the longitudinal response function ofHe4

Abstract

A detailed study of the $^{4}\mathrm{He}$ longitudinal response function ${R}_{L}(\ensuremath{\omega},q)$ is performed at different kinematics, with particular emphasis on the role of three-nucleon forces. The effects reported are the results of an $\mathrm{ab} \mathrm{initio}$ calculation where the full four-body continuum dynamics is considered via the Lorentz integral transform method. The contributions of the various multipoles to the longitudinal response function are analyzed, and integral properties of the response are discussed as well. The Argonne V18 nucleon-nucleon interaction and two three-nucleon force models (Urbana IX and Tucson-Melbourne\ensuremath{'}) are used. At lower momentum transfers ($q\ensuremath{\leqslant}200 \mathrm{MeV}/c$) three-nucleon forces play an important role. One even finds a dependence of ${R}_{L}$ on the three-nucleon force model itself, with differences of up to 10%. Thus a Rosenbluth separation of the inclusive electron scattering cross section of $^{4}\mathrm{He}$ at low momentum transfers would be of great value for differentiating among force models.