Long-range interactions between polar bialkali ground-state molecules in arbitrary vibrational levels

TL;DR

This paper calculates long-range van der Waals interaction coefficients between identical heteronuclear alkali-metal diatomic molecules in various vibrational levels, providing data crucial for understanding ultracold molecular collisions.

Contribution

It extends previous work by computing isotropic $C_6$ coefficients for multiple species and vibrational levels using a sum-over-state approach with experimental and quantum-chemical data.

Findings

Validates Moelwyn-Hughes approximation for different vibrational levels.

Provides $C_6$ coefficients for ten alkali-metal diatomic species.

Results relevant for ultracold collision studies.

Abstract

We have calculated the isotropic $C\_6$ coefficients characterizing the long-range van der Waals interaction between two identical heteronuclear alkali-metal diatomic molecules in the same arbitrary vibrational level of their ground electronic state $X^1\Sigma^+$. We consider the ten species made up of $^7$Li, $^{23}$Na, $^{39}$K, $^{87}$Rb and $^{133}$Cs. Following our previous work [M.~Lepers \textit{et.~al.}, Phys.~Rev.~A \textbf{88}, 032709 (2013)] we use the sum-over-state formula inherent to the second-order perturbation theory, composed of the contributions from the transitions within the ground state levels, from the transition between ground-state and excited state levels, and from a crossed term. These calculations involve a combination of experimental and quantum-chemical data for potential energy curves and transition dipole moments. We also investigate the case where the two molecules are in different vibrational levels and we show that the Moelwyn-Hughes approximation is valid provided that it is applied for each of the three contributions to the sum-over-state formula. Our results are particularly relevant in the context of inelastic and reactive collisions between ultracold bialkali molecules, in deeply bound or in Feshbach levels.