It is well-known that the traditional treatment of radiative corrections that utilizes the true'' neutrino momentum $\vec{p}_\nu$ in the differential decay rate formula could lead to a $\sim \alpha/\pi$ systematic error in certain observables due to the mistreatment of 4-body kinematics. I investigate the theory structure of one of the proposed solutions, the\(\nu'\)-formalism'', in the non-recoil limit appropriate for neutron and nuclear beta decays. I derive an elegant master formula for the 4-body phase space and use it to re-analyze the spectrum-dependent outer'' radiative corrections to the beta decay of a polarized spin-half nucleus; a complete set of analytic expressions is provided for readers to straightforwardly obtain the final numerical results. I compare it to therecoil formalism'' where the energy of the recoil nucleus is fixed.