Dipole transitions in the bound rotational-vibrational spectrum of the heteronuclear molecular ion HD$^+$

TL;DR

This paper accurately calculates the energy levels and dipole transition probabilities for the heteronuclear molecular ion HD$^+$, providing detailed data for vibrational and rotational states using a precise numerical method.

Contribution

It introduces high-precision calculations of energies and dipole transitions for HD$^+$ using the Lagrange-mesh method, covering multiple vibrational and rotational states.

Findings

Energies computed with up to 12-digit accuracy for the lowest vibrational state.

Dipole transition probabilities provided with six significant figures.

Comprehensive data for vibrational states v=0-3 and rotational states up to J=47.

Abstract

The non-relativistic three-body Schr\"odinger equation of the heteronuclear molecular ion HD$^+$ is solved in perimetric coordinates using the Lagrange-mesh method. Energies and wave functions of the four lowest vibrational bound or quasibound states $v=0-3$ are calculated for total orbital momenta from 0 to 47. Energies are given with an accuracy from about 12 digits for the lowest vibrational level to at least 9 digits for the third vibrational excited level. With a simple calculation using the corresponding wave functions, accurate dipole transition probabilities per time unit between those levels are given over the whole $v=0-3$ rotational bands. Results are presented with six significant figures.