Transverse electron scattering response function of $^3$He with $\Delta$-isobar degrees of freedom

TL;DR

This paper calculates the transverse electron scattering response function of helium-3 including $4$-isobar effects, revealing significant contributions from $4$-isobar currents and their cancellation by relativistic one-body currents, and compares results with experimental data.

Contribution

First calculation of $^3$He transverse response including $4$-isobar degrees of freedom using the Lorentz integral transform method.

Findings

Large $4$-isobar current contributions are observed.

Relativistic one-body currents largely cancel $4$-isobar effects.

Results are consistent with experimental data.

Abstract

A calculation of the $^3$He transverse $(e,e')$ inclusive response function, $R_T$, which includes $\Delta$ degrees of freedom is performed using the Lorentz integral transform method. The resulting coupled equations are treated in impulse approximation, where the $NNN$ and $NN\Delta$ channels are solved separately. As NN and NNN potentials we use the Argonne V18 and UrbanaIX models respectively. Electromagnetic currents include the $\Delta$-isobar currents, one-body N-currents with relativistic corrections and two-body currents consistent with the Argonne V18 potential. $R_T$ is calculated for the breakup threshold region at momentum transfers near 900 MeV/c. Our results are similar to those of Deltuva {\it et al.} in that large $\Delta$-isobar current contributions are found. However we find that these are largely canceled by the relativistic contribution from the one-body N-currents. Finally a comparison is made between theoretical results and experimental data.