Accurate prediction of H$_3$O$^+$ and D$_3$O$^+$ sensitivity coefficients to probe a variable proton-to-electron mass ratio

TL;DR

This study uses advanced theoretical calculations to accurately predict the sensitivity coefficients of specific molecular transitions in H3O+ isotopologues, enabling tests of the proton-to-electron mass ratio's stability over cosmological timescales.

Contribution

It provides the first high-precision ab initio predictions of sensitivity coefficients for H3O+ ions, enhancing their use in probing fundamental constant variations.

Findings

Sensitivity coefficients are comparable to ammonia and methanol.

Theoretical results agree with approximate models.

New transitions show potential for cosmological tests.

Abstract

The mass sensitivity of the vibration-rotation-inversion transitions of H$_3{}^{16}$O$^+$, H$_3{}^{18}$O$^+$, and D$_3{}^{16}$O$^+$ is investigated variationally using the nuclear motion program TROVE~\citep{TROVE:2007}. The calculations utilize new high-level \textit{ab initio} potential energy and dipole moment surfaces. Along with the mass dependence, frequency data and Einstein A coefficients are computed for all transitions probed. Particular attention is paid to the $\Delta|k|=3$ and $\Delta|k-l|=3$ transitions comprising the accidentally coinciding $|J,K\!=\!0,v_2\!=\!0^+\rangle$ and $|J,K\!=\!3,v_2\!=\!0^-\rangle$ rotation-inversion energy levels. The newly computed probes exhibit sensitivities comparable to their ammonia and methanol counterparts, thus demonstrating their potential for testing the cosmological stability of the proton-to-electron mass ratio. The theoretical TROVE results are in close agreement with sensitivities obtained using the nonrigid and rigid inverter approximate models, confirming that the \textit{ab initio} theory used in the present study is adequate.