$^1$H, $^2$H and $^3$H nuclear magnetic dipole moment effects on the electron energy states

Abstract

The effect of nuclear magnetic dipole moment of hydrogen, deuterium and tritium isotopes on the electron atomic energy has been studied and analysed in this work. The electromagnetic Hamiltonian was rewritten in terms of the orbital angular momentum $L_e$ of the electron, the gyromagnetic ratio $\gamma _N$ of the nucleus and its total angular momentum $J_N$. The first-order energy correction has been derived, and this correction splits each $\ell$ state into $2J_N+1$ states. The energy corrections and the differences between the split states of the first two lowest energy states for each isotope were calculated and it is found that these two energy states are in the radiowave range.