# Amplitude for neutron-proton conversion from first principles

I'm reading Dodelson's Modern Cosmology, and in one of the exercises on Big Bang nucleosynthesis it is quoted without reference that the amplitude for neutron-to-proton conversion is given by

$$|\mathcal{M}|^2 _{n+\nu_e \rightarrow p^ + e^-} = 32G_F ^2(1+3g_A ^2)m_p^2 p_\nu p_e$$ with $$g_A$$ the axial-vector coupling of the nucleon.

Does anyone know a reference for a derivation of this amplitude from first principles?