Two-Body Electrodisintegration of $^3$He at High Momentum Transfer

TL;DR

This study models the $^3$He$(e,e'p)d$ reaction at high momentum transfer using advanced wave functions and a realistic Glauber approximation, achieving good agreement with experimental cross sections up to 700 MeV/c.

Contribution

It introduces a nucleon-nucleon scattering amplitude-based profile operator in the Glauber approximation, improving the treatment of final state interactions in three-nucleon electrodisintegration.

Findings

Predicted cross section matches experimental data up to 700 MeV/c missing momentum.

Underestimates data at around 1 GeV/c by a factor of two.

Longitudinal-transverse asymmetry is well reproduced.

Abstract

The $^3$He$(e,e^\prime p)$$d$ reaction is studied using an accurate three-nucleon bound state wave function, a model for the electromagnetic current operator including one- and two-body terms, and the Glauber approximation for the treatment of final state interactions. In contrast to earlier studies, the profile operator in the Glauber expansion is derived from a nucleon-nucleon scattering amplitude, which retains its full spin and isospin dependence and is consistent with phase-shift analyses of two-nucleon scattering data. The amplitude is boosted from the center-of-mass frame, where parameterizations for it are available, to the frame where rescattering occurs. Exact Monte Carlo methods are used to evaluate the relevant matrix elements of the electromagnetic current operator. The predicted cross section is found to be in quantitative agreement with the experimental data for values of the missing momentum $p_{\rm m}$ in the range (0--700) MeV/c, but underestimates the data at $p_{\rm m} \simeq 1$ GeV/c by about a factor of two. However, the longitudinal-transverse asymmetry, measured up to $p_{\rm m} \simeq$ 600 MeV/c, is well reproduced by theory. A critical comparison is carried out between the results obtained in the present work and those of earlier studies.