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

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 $12\le A\le 120$ 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 $A\ge 12$: ${\hat{\sigma }}_{GT}=109/A^{0.65}$. 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.

14 pages, 10 figures

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• Electron capture in stars
• Charge-exchange scattering to the isobaric analog state at medium energies as a probe of the neutron skin
• Constraints for stellar electron-capture rates on ${}^{86}$Kr via the ${}^{86}$Kr($t$,${}^3$He$+\gamma$)${}^{86}$Br reaction and the implications for core-collapse supernovae
• Experimental Constraint on Stellar Electron-Capture Rates from the ${}^{88}\text{Sr}(t,{}^3\text{He}+\gamma ){}^{88}\text{Rb}$ reaction at 115 MeV/u