Theoretical study of the capture of stable $^{39}$K and neutron-rich radioactive $^{46}$K by $^{181}$Ta

TL;DR

This paper uses empirical models to analyze capture cross sections of stable and neutron-rich potassium isotopes with tantalum, revealing differences in their reaction dynamics and the influence of neutron transfer channels.

Contribution

It provides a theoretical analysis comparing capture cross sections of $^{39}$K and $^{46}$K with $^{181}$Ta, highlighting the suppression in neutron-rich isotope reactions and the role of transfer channels.

Findings

${}^{39}$K + ${}^{181}$Ta cross sections align with the universal fusion function.

${}^{46}$K + ${}^{181}$Ta cross sections are overestimated by the ECC model.

Capture cross sections of ${}^{46}$K are suppressed above the Coulomb barrier.

Abstract

The empirical coupled-channel (ECC) model and the universal fusion function (UFF) prescription are used to analyse the data of capture cross sections for reactions ${}^{39}$K$+{}^{181}$Ta and ${}^{46}$K$+{}^{181}$Ta reported recently by A. Wakhle {\it et al.} [Phys. Rev. C 97, 021602(R) (2018)]. The results of the ECC model are in good agreement with the data of ${}^{39}$K$+{}^{181}$Ta while, for ${}^{46}$K$+{}^{181}$Ta, the predictions of the ECC model overestimate the above-barrier capture cross sections. Comparing the reduced data of these two reactions, it is found that the above-barrier cross sections of ${}^{39}$K$+{}^{181}$Ta are consistent with the UFF and are larger than those of ${}^{46}$K$+{}^{181}$Ta. This implies that the capture cross sections of ${}^{46}$K$+{}^{181}$Ta are suppressed at energies above the Coulomb barrier. Furthermore, at sub-barrier energies, the reduced calculated capture cross sections of ${}^{39}$K$+{}^{181}$Ta are a little larger than those of ${}^{46}$K$+{}^{181}$Ta, which is owing to the coupling to the positive $Q$-value two-neutron transfer channel.