On the Theory of the Recoil in Beta-Decay

On the basis of the Fermi theory of $\beta$-decay a formula for the recoil spectrum is derived, and the average values of the momentum and energy of the recoil are calculated. Some properties of the recoil spectrum are discussed in the case when the $\beta$-decay is followed by $\gamma$-ray emission. It is shown that the average recoil energy is independent of a possible angular correlation between successive $\beta$- and $\gamma$-rays. Finally the influence of a finite mass of the neutrino and the neglect of the kinetic energy of the recoil in the energy balance is discussed.