Forbidden "ortho"--"para" electric dipole transitions in H$_2^+$ ion

TL;DR

This paper systematically calculates forbidden electric dipole transitions between ortho and para states in H$_2^+$, revealing extremely low transition rates but suggesting potential for laser spectroscopy induction.

Contribution

First systematic calculation of electric dipole forbidden ortho-para transitions in H$_2^+$, providing transition rates and lifetimes for the first time.

Findings

Transition rate from ortho to para ground states is 4.9×10^{-14} s^{-1}.

Lifetime of the ortho state is approximately 6.4×10^5 years.

The Einstein coefficient for a specific transition is comparable to quadrupole transition values in H$_2^+$.

Abstract

We present the first systematic calculation of the electric dipole forbidden transitions in the homonuclear molecular ion 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 $4.9\!\times\!10^{-14}$ s$^{-1}$ that corresponds to the lifetime of $6.4\!\times\!10^5$ yr. The Einstein coefficient $A_{nn'}$ for the $(v\!=\!1,N\!=\!1,J\!=\!1/2)\!\to\!(v\!=\!0,N\!=\!0,J\!=\!1/2)$ transition is equal to $0.12\!\times\!10^{-9}$ s$^{-1}$, which is of "comparable" order with the values for quadrupole transitions in H$_2^+$. It gives hope that the "ortho"--"para" transitions in H$_2^+$ can be induced by the laser spectroscopy.