Quadrupole transitions in the bound rotational-vibrational spectrum of the deuterium molecular ion

TL;DR

This paper calculates highly precise energies and quadrupole transition probabilities for the deuterium molecular ion D₂⁺ across multiple vibrational and rotational states using advanced numerical methods.

Contribution

It provides the first detailed calculation of quadrupole transitions in D₂⁺ with unprecedented accuracy, extending previous studies on H₂⁺.

Findings

Energy levels computed with up to 13-digit accuracy for the lowest states.

Quadrupole transition probabilities calculated with six significant figures.

Results cover vibrational states v=0-3 and rotational states up to J=56.

Abstract

After the study of the three body molecular system H$_2^+$ ({\it J. Phys. B: At. Mol. Opt. Phys.} {\bf 45} 065101), its isotopomer, the deuterium molecular ion D$_2^+$ is studied. The three-body Schr\"odinger equation is solved using the Lagrange-mesh method in perimetric coordinates. Energies and wave functions for four vibrational states $v=0-3$ and bound or quasibound states for total orbital momenta from 0 to 56 are calculated. The 1986 fundamental constant $m_d=3670.483014\,m_e$ is used. The obtained energies have an accuracy from about 13 digits for the lowest vibrational state to at least 9 digits for the third vibrational excited state. Quadrupole transition probabilities per time unit between those states over the whole rotational bands were calculated. Extensive results are presented with six significant figures.