$${}^{5}$$He($${}^{3}$$He,$${}^{4}$$He)$${}^{4}$$He as a three-body reaction via a continuum resonance in the n+$${}^{4}$$He system

The $${}^{5}$$ 5 He($${}^{3}$$ 3 He,$${}^{4}$$ 4 He)$${}^{4}$$ 4 He reaction involving the unstable $${}^{5}$$ 5 He nucleus is a possible process in primordial nucleosynthesis to convert $${}^{3}$$ 3 He into $${}^{4}$$ 4 He in a neutron transfer reaction. Since experimental data for the reaction cross section are not available, a theoretical prediction is needed to estimate the relevance of this process in comparison to other reactions, e.g., $${}^{3}$$ 3 He($${}^{2}$$ 2 H,p)$${}^{4}$$ 4 He or $${}^{3}$$ 3 H($${}^{2}$$ 2 H,n)$${}^{4}$$ 4 He. In this work the cross section and the Maxwellian-averaged transition rate of the $${}^{5}$$ 5 He($${}^{3}$$ 3 He,$${}^{4}$$ 4 He)$${}^{4}$$ 4 He reaction are calculated using a post-form distorted-wave Born approximation in a simple cluster model. For that purpose the reaction is treated as a genuine process with three particles, $$\text{ n }+{}^{4}\text{ He }+{}^{3}\text{ He }$$ n + 4 He + 3 He , in the entrance channel proceeding through the $$3/2^{-}$$ 3 / 2 - resonance in the $$n-{}^{4}$$ n - 4 He scattering continuum.