Effects of an induced three-body force in the incident channel of (d,p) reactions

TL;DR

This paper investigates the impact of induced three-body forces in (d,p) reactions, showing that their inclusion modifies nucleon optical potentials and affects transfer reaction calculations.

Contribution

It introduces a method to estimate the first order effects of induced three-body terms in (d,p) reactions, refining the treatment of deuteron breakup.

Findings

Induced three-body terms can be approximated as modifications to two-body optical potentials.

The adiabatic approximation simplifies the inclusion of these three-body effects.

Results vary with different optical potential parameterizations at various energies.

Abstract

A widely accepted practice for treating deuteron breakup in $A(d,p)B$ reactions relies on solving a three-body $A+n+p$ Schr\"odinger equation with pairwise $A$-$n$, $A$-$p$ and $n$-$p$ interactions. However, it was shown in [Phys. Rev. C \textbf{89}, 024605 (2014)] that projection of the many-body $A+2$ wave function into the three-body $A+n+p$ channel results in a complicated three-body operator that cannot be reduced to a sum of pairwise potentials. It contains explicit contributions from terms that include interactions between the neutron and proton via excitation of the target $A$. Such terms are normally neglected. We estimate the first order contribution of these induced three-body terms and show that applying the adiabatic approximation to solving the $A+n+p$ model results in a simple modification of the two-body nucleon optical potentials. We illustrate the role of these terms for the case of $^{40}$Ca($d,p$)$^{41}$Ca transfer reactions at incident deuteron energies of 11.8, 20 and 56 MeV, using several parameterisations of nonlocal optical potentials.