Gamow-Teller Unit Cross Sections for (t,3He) and (3He,t) Reactions

TL;DR

This study investigates the proportionality of differential cross sections to Gamow-Teller transition strength for ($t$, $^{3}$He) and ($^{3}$He$, t$) reactions across various target masses, establishing a simple mass-dependent relation for unit cross sections.

Contribution

It provides a unified description of Gamow-Teller unit cross sections for ($t$, $^{3}$He) and ($^{3}$He$, t$) reactions, including new data and phenomenological models for mass dependence.

Findings

Unit cross sections follow a nearly identical A-dependent trend for A ≥ 12.

Simple phenomenological functions describe the mass dependence of the distortion and interaction factors.

Short-range approximations overestimate cross sections in theoretical calculations.

Abstract

The proportionality between differential cross sections at vanishing linear momentum transfer and Gamow-Teller transition strength, expressed in terms of the \textit{unit cross section} ($\hat{\sigma}_{GT}$) was studied as a function of target mass number for ($t$,$^{3}$He) and ($^{3}$He,$t$) reactions at 115 $A$MeV and 140 $A$MeV, respectively. Existing ($^{3}$He,$t$) and ($t$,$^{3}$He) data on targets with mass number $12\leq A\leq 120$ were complemented with new and reevaluated ($t$,$^{3}$He) data on proton, deuteron, $^{6}$Li and $^{12}$C targets. It was found that in spite of the small difference in beam energies between the two probes, the unit cross sections have a nearly identical and simple dependence on target mass number $A$, for $A\geq 12$: $\hat{\sigma}_{GT}=109/A^{0.65}$. The factorization of the unit cross sections in terms of a kinematical factor, a distortion factor and the strength of the effective spin-isospin transfer nucleus-nucleus interaction was investigated. Simple phenomenological functions depending on mass number $A$ were extracted for the latter two. By comparison with plane and distorted-wave Born approximation calculations, it was found that the use of a short-range approximation for knock-on exchange contributions to the transition amplitude results in overestimated cross sections for reactions involving the composite ($^{3}$He,$t$) and ($t$,$^{3}$He) probes.