Anomalous phosphine sensitivity coefficients as probes for a possible variation of the proton-to-electron mass ratio

Abstract

A robust variational approach is used to investigate the sensitivity of the rotation-vibration spectrum of phosphine (PH${}_3$) to a possible cosmological variation of the proton-to-electron mass ratio, $\mu$. Whilst the majority of computed sensitivity coefficients, $T$, involving the low-lying vibrational states acquire the expected values of $T\approx -1$ and $T\approx -1/2$ for rotational and ro-vibrational transitions, respectively, anomalous sensitivities are uncovered for the $A_1-A_2$ splittings in the ${\nu }_2/{\nu }_4$, ${\nu }_1/{\nu }_3$ and $2{\nu }_4^{\ell =0}/2{\nu }_4^{\ell =2}$ manifolds of PH${}_3$. A pronounced Coriolis interaction between these states in conjunction with accidentally degenerate $A_1$ and $A_2$ energy levels produces a series of enhanced sensitivity coefficients. Phosphine is expected to occur in a number of different astrophysical environments and has potential for investigating a drifting constant. Furthermore, the displayed behaviour hints at a wider trend in molecules of ${\mathbf{C}}_{3\mathrm{v}}(\mathrm{M})$ symmetry, thus demonstrating that the splittings induced by higher-order ro-vibrational interactions are well suited for probing $\mu$ in other symmetric top molecules in space, since these low-frequency transitions can be straightforwardly detected by radio telescopes.