Abstract
A solution of the Dirac equation for an electron in the field of a point nucleus (Ze) has been obtained as an eigenfunction of the Schrodinger Hamiltonian and the spin projection operator Σ3. With the use of this solution, the probability W(ν) of the emission of a neutrino per unit time from a hydrogen-like atom, \((Ze)* \to (Ze) + \nu \bar \nu\), has been calculated for the first time in the first order of the parameter Ze ≪ 1. The probability W(ν) appears to be rather small, and the corresponding lifetime τ(ν) = [W(ν)]–1 is much larger than the age of the Universe; correspondingly, this process cannot affect the balance of low-energy neutrinos. The smallness of W(ν) is due not only to the presence of the obvious “weak” factor (Gmp2)2(m/mp)4 in the expression for W(ν), but also primarily to the “electromagnetic” factor (Zα)12, which can be revealed only in a particular calculation. It has been argued within quantum electrodynamics with the mentioned wavefunctions that photon emission, (Ze)* → (Ze) + γ, can be absent (analysis of photon emission requires the further development of the method), whereas axion emission, (Ze)* → (Ze) + a, can occur, although the last two effects have not been considered in detail.
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