Adiabatic versus Faddeev for (d,p) and (p,d) reactions

TL;DR

This study compares the finite range adiabatic wave approximation with the exact Faddeev method for (d,p) and (p,d) reactions, assessing their accuracy across various energies and nuclei to guide their application.

Contribution

It provides a systematic comparison between ADWA and Faddeev methods, identifying conditions where ADWA is sufficiently accurate for reaction analysis.

Findings

ADWA agrees within ~5% of Faddeev at 20-40 MeV beam energies.

Differences increase at very low and high energies.

ADWA performs best with small angular momentum transfer and loosely bound systems.

Abstract

The finite range adiabatic wave approximation provides a practical method to analyze (d,p) or (p,d) reactions, however until now the level of accuracy obtained in the description of the reaction dynamics has not been determined. In this work, we perform a systematic comparison between the finite range adiabatic wave approximation and the exact Faddeev method. We include studies of $^{11}$Be(p,d)$^{10}$Be(g.s.) at $E_p=$5, 10 and 35 MeV; $^{12}$C(d,p)$^{13}$C(g.s.) at $E_d=$7, 12 and 56 MeV and $^{48}$Ca(d,p)$^{49}$Ca(g.s.) at $E_d=$19, 56 and 100 MeV. Results show that the two methods agree within $\approx 5%$ for a range of beam energies ($E_d \approx 20-40$ MeV) but differences increase significantly for very low energies and for the highest energies. Our tests show that ADWA agrees best with Faddeev when the angular momentum transfer is small $\Delta l=0$ and when the neutron-nucleus system is loosely bound.