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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.

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