Proton recoil energy and angular distribution of neutron radiativeβ−decay

Abstract

We analyze the proton recoil energy and angular distribution of the radiative ${\ensuremath{\beta}}^{\ensuremath{-}}$ decay of the neutron to leading order in the large baryon mass expansion by taking into account the contributions of the proton-photon correlations. We show that the account for the proton-photon correlations does not contradict the description of the radiative corrections to the lifetime of the neutron and the proton recoil energy spectrum of the neutron ${\ensuremath{\beta}}^{\ensuremath{-}}$ decay in terms of the functions $(\ensuremath{\alpha}/\ensuremath{\pi}){g}_{n}({E}_{e})$ and $(\ensuremath{\alpha}/\ensuremath{\pi}){f}_{n}({E}_{e})$, where ${E}_{e}$ is the electron energy. In addition we find that the contributions of the proton-photon correlations in the radiative ${\ensuremath{\beta}}^{\ensuremath{-}}$ decay of the neutron to the proton recoil asymmetry $C$ are of order ${10}^{\ensuremath{-}4}$. They make the contributions of the radiative corrections to the proton recoil asymmetry $C$ symmetric with respect to a change ${A}_{0}\ensuremath{\leftrightarrow}{B}_{0}$, where ${A}_{0}$ and ${B}_{0}$ are the correlation coefficients of the neutron ${\ensuremath{\beta}}^{\ensuremath{-}}$ decay.