Rapid convergence of the Weinberg expansion of the deuteron stripping amplitude

TL;DR

This paper demonstrates that the Weinberg expansion converges rapidly for deuteron stripping amplitudes, simplifying calculations by showing the dominance of the first term in the expansion for certain nuclear reactions.

Contribution

It shows that the first Weinberg state term dominates the (d,p) transition amplitude, offering a simplified approach compared to full three-body calculations.

Findings

The first Weinberg state term dominates the transition amplitude.

Rapid convergence of the Weinberg expansion is observed.

Implications for simplifying future theoretical models.

Abstract

Theories of $(d,p)$ reactions frequently use a formalism based on a transition amplitude that is dominated by the components of the total three-body scattering wave function where the spatial separation between the incoming neutron and proton is confined by the range of the $n$-$p$ interaction, $V_{np}$. By comparison with calculations based on the CDCC method we show that the $(d,p)$ transition amplitude is dominated by the first term of the expansion of the three-body wave function in a complete set of Weinberg states. We use the \nuc{132}{Sn}(d,p)\nuc{133} {Sn} reaction at 30 and 100 MeV as examples of contemporary interest. The generality of this observed dominance and its implications for future theoretical developments are discussed.