Sensitivity of transfer cross sections to the bound-state wave functions

TL;DR

This paper investigates how transfer reaction cross sections are affected by the bound-state wave functions, using supersymmetric transformations to analyze the impact of nuclear interior differences on spectroscopic factors.

Contribution

It introduces a method to study the influence of nuclear interior wave functions on transfer cross sections by removing Pauli-forbidden states with supersymmetric transformations.

Findings

Spectroscopic factors for $^{17}$O decrease by about 30% with supersymmetric potentials.

Differences in spectroscopic factors for $^{16}$O are smaller.

Ambiguities in spectroscopic factor determination depend on the angular range of data fitting.

Abstract

We test the sensitivity of transfer reactions to the bound state wave functions within a distorted wave Born approximation formalism. Using supersymmetric transformations, we remove the Pauli-forbidden states from the two-body potentials and generate an equivalent supersymmetric partner. Wave functions from these potentials have the same asymptotics, but they differ in the nuclear interior. This allows us to study the influence of the nuclear interior on transfer cross sections. We apply the calculations to the $^{16}$O($d, p$)$^{17}$O and $^{12}$C($^7$Li, $t$)$^{16}$O reactions, which are typical examples of nucleon and $\alpha$ transfer, respectively. The spectroscopic factors for $^{17}$O are decreased by about 30\% when using supersymmetric potentials. For $^{16}$O, the differences are smaller. However, we show that ambiguities exist in the determination of the spectroscopic factors, due to the choice of the angular range where the fit is performed.