The generalized Fermi interaction

Konopinski and Uhlenbeck have shown that the empirical β-ray spectra seem to require a modification of Fermi's original expression for the interaction leading to β decay‡. Their expression includes a derivative of the neutrino wave function. The purpose of the present paper is to investigate the most general type of such an interaction term and the possibility of introducing second-order derivatives. We have to deal with the transition§ neutron + neutrino → proton + electron or proton + anti-neutrino → neutron + positron. The whole system has the equations of motion where ψ1 and ψ2 are the wave functions of the initial and final states in configuration space, H1 and H2 are the Hamiltonians of the particles in the initial and final states, and A is a small interaction operator.