Bound-state β decay of a neutron in a strong magnetic field

Abstract

The \ensuremath{\beta} decay of a neutron into a bound $({\mathit{pe}}^{\ensuremath{-}})$ state and an antineutrino in the presence of a strong uniform magnetic field ($B\ensuremath{\gtrsim}{10}^{13}$ G) is considered. The \ensuremath{\beta} decay process is treated within the framework of the standard model of weak interactions. A Bethe-Salpeter formalism is employed for description of the bound $({\mathit{pe}}^{\ensuremath{-}})$ system in a strong magnetic field. For the field strengths ${10}^{13}\ensuremath{\lesssim}B\ensuremath{\lesssim}{10}^{18}$ G the estimate for the ratio of the bound-state decay rate ${w}_{b}$ and the usual (continuum-state) decay rate ${w}_{c}$ is derived. It is found that in such strong magnetic fields ${w}_{b}/{w}_{c}~0.1\text{\ensuremath{-}}0.4$. This is in contrast to the field-free case, where ${w}_{b}/{w}_{c}\ensuremath{\simeq}4.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ [J. N. Bahcall, Phys. Rev. 124, 495 (1961); L. L. Nemenov, Sov. J. Nucl. Phys. 15, 582 (1972); X. Song, J. Phys. G: Nucl. Phys. 13, 1023 (1987)]. The dependence of the ratio ${w}_{b}/{w}_{c}$ on the magnetic field strength B exhibits a logarithmiclike behavior. The obtained results can be important for applications in astrophysics and cosmology.