Emission of a Neutrino Pair During Transitions of an Electron in the Field of the Nucleus of a Hydrogen-Like Atom in One Spatial Dimension

Abstract

The Dirac equation for a particle – an electron with negative charge equal in magnitude to the elementary charge e₁ in spacetime with one spatial dimension denoted as the z axis and in the field of a point-like charge (Ze₁) – the nucleus – with the one-dimensional potential φ₁ = – (Ze₁) |z| (a one-dimensional hydrogen-like atom) is solved. The two-component wave function and the quantum values of the energy are expressed in terms of the Airy function and its zeros. Using the contact Lagrangian of the weak interaction with Fermi constant G₁ = g₁ħc in such a space, where g₁ is some number, the probability of emission per unit time of a neutrino pair (Ze₁)^*→(Ze₁) + νν^– by the one-dimensional hydrogen-like atom, which turns out to be proportional to the square of the mass, is found. Prospects for the realization of the considered effect and its possible significance at various stages of the evolution of the Universe are discussed.