Phenomenological refinement of $p$-$d$ elastic scattering descriptions towards the 3NF study in nuclei via the ($p,pd$) reaction

Abstract

The ($p,pd$) reaction is expected to be a powerful tool for probing three-nucleon forces (3NFs) in nuclear medium since it can be essentially regarded as the $p$-$d$ elastic scattering inside nuclei. One of the important points in the theoretical description of the ($p,pd$) reaction is to calculate the $p$-$d$ scattering in a nucleus quantitatively using effective interactions. This work aims to develop a phenomenological approach to improve the quantitativity of the $p$-$d$ scattering cross section in free space calculated with effective interactions. The $p$-$d$ elastic amplitude is decomposed into a 2N part, described using 2N effective interactions, and a residual part, which the 2N part cannot describe. The latter is approximated by a superposition of Legendre polynomials, with coefficients treated as adjustable parameters. These parameters are determined to reproduce experimental $p$-$d$ differential cross-section data at various incident energies. The obtained parameters exhibit smooth energy dependence, which is approximated by quadratic functions. The numerical results with the analytic energy dependence also reproduce the experimental data. The developed approach works well for improving the $p$-$d$ scattering cross section in a wide range of incident energies. This work can be regarded as the first step toward the description of ($p,pd$) reactions taking 3NF effect in nuclear medium into account.