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

Abstract

A widely accepted practice for treating deuteron breakup in A(d, p)B reactions relies on solving a three-body A + n + p Schrödinger equation with pairwise A-n, A-p and n-p interactions. However, it was shown in [Phys. Rev. C 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.

Three-body optical potentials in $(d,p)$ reactions and their influence on indirect study of stellar nucleosynthesis

“…In general, applying the energy shift gives higher (d, p) cross sections than those obtained in standard ADWA with local optical potentials. Including φ 1 φ A |U (1) |φ d φ A brings these cross sections down due to increased absorption [4]. Interestingly, with a stronger imaginary part increasing the dynamical real (polarisation) part does not have any noticeable consequences for (d, p) cross sections.…”

“…It has been shown in [4] that projecting the many-body wave function of the A + n + p system onto a three-body channel results in a three-body Hamiltonian…”

“…We call them induced three-body effects (I3B). It has been shown in [4] that in the ADWA, the simplest term,…”

“…It has been possible to estimate the contribution of the leading terms of this operator within ADWA [3], which requires using nonlocal energy-dependent optical potentials taken at an energy shifted from the traditionally used value of E d /2 by n-p kinetic energy averaged over the short range of the n-p force. Adding the first-order term of the three-body optical operator in a leading order results in a doubling the dynamical part of this optical potential [4].…”

“…We assess these effects within the ADWA. In section II we summarise the ADWA threebody optical potential formalism of [3] and [4], arising due to neglecting the channels with target excitations. We will apply this formalism to (d, p) reactions, listed in section III, that could serve as indirect tools for measuring proton capture reactions of astrophysical interest.…”