We identify the molecular ion NH${}^{+}$ as a potential candidate for probing variations in the fine-structure constant $\alpha$ and electron-to-proton mass ratio $\mu$. NH${}^{+}$ has an anomalously low-lying excited ${}^4{\Sigma }^{-}$ state, being only a few hundred cm${}^{-1}$ above the ground ${}^2\Pi$ state. Being a light molecule, this proximity is such that rotational levels of the respective states are highly intermixed for low angular momenta. We find that several low-frequency transitions within the collective rotational spectrum experience enhanced sensitivity to $\alpha$ and $\mu$ variation. This is attributable to the close proximity of the ${}^2\Pi$ and ${}^4{\Sigma }^{-}$ states, as well as the ensuing strong spin-orbit coupling between them. Suggestions that NH${}^{+}$ may exist in interstellar space and recent predictions that trapped-ion precision spectroscopy will be adaptable to molecular ions make NH${}^{+}$ a promising system for future astrophysical and laboratory studies of $\alpha$ and $\mu$ variation.

• Received 18 May 2011

DOI:https://doi.org/10.1103/PhysRevA.83.062514