Forbidden ortho-para electric dipole transitions in the H2+ ion

Abstract

We present a systematic calculation of the electric dipole forbidden transitions in the homonuclear molecular ion ${\mathrm{H}}_{2}^{+}$. We get that the transition rate from the ground ortho $(v=0,N=1,J=1/2)$ state to the ground para $(v=0,N=0,J=1/2)$ state is $4.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, which corresponds to the lifetime of $6.4\ifmmode\times\else\texttimes\fi{}{10}^{5}$ yr. The Einstein coefficient ${A}_{n{n}^{\ensuremath{'}}}$ for the $(v=1,N=1,J=1/2)\ensuremath{\rightarrow}(v=0,N=0,J=1/2)$ transition is equal to $0.12\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, which is of comparable order with the values for quadrupole transitions in ${\mathrm{H}}_{2}^{+}$. It gives hope that the ortho-para transitions in ${\mathrm{H}}_{2}^{+}$ can be explored by laser spectroscopy.