Deviations from Born-Oppenheimer mass scaling in spectroscopy and ultracold molecular physics

Jesse J Lutz,Jeremy M Hutson

doi:10.1016/j.jms.2016.08.007

Abstract

We investigate Born-Oppenheimer breakdown (BOB) effects (beyond the usual mass scaling) for the electronic ground states of a series of homonuclear and heteronuclear alkali-metal diatoms, together with the Sr2 and Yb2 diatomics. Several widely available electronic structure software packages are used to calculate the leading contributions to the total isotope shift for commonly occurring isotopologs of each species. Computed quantities include diagonal Born-Oppenheimer corrections (mass shifts) and isotopic field shifts. Mass shifts dominate for light nuclei up to and including K, but field shifts contribute significantly for Rb and Sr and are dominant for Yb. We compare the ab initio mass-shift functions for Li2, LiK and LiRb with spectroscopically derived ground-state BOB functions from the literature. We find good agreement in the values of the functions for LiK and LiRb at their equilibrium geometries, but significant disagreement with the shapes of the functions for all 3 systems. The differences may be due to contributions of nonadiabatic terms to the empirical BOB functions. We present a semiclassical model for the effect of BOB corrections on the binding energies of near-threshold states and the positions of zero-energy Feshbach resonances.

Highlights

The Born-Oppenheimer approximation (BOA) lies at the heart of chemical and molecular physics
We have investigated electronic structure calculations of bonding contributions to breakdown of the Born-Oppenheimer approximation for a range of molecules important in ultracold physics
These include the homonuclear and heteronuclear alkali-metal dimers and the Sr2 and Yb2 molecules. We have considered both isotopic mass shifts and isotopic field shifts

Summary

Introduction

The Born-Oppenheimer approximation (BOA) lies at the heart of chemical and molecular physics. Quantitative investigations of such deviations go back at least to the theoretical work of Kolos and Wolniewicz on H2 [1, 2], which stimulated reinterpretation of the experimental spectrum by Herzberg [3] They are important for H+3 [4], and they have been characterized spectroscopically for hydrides such as HeH+ [5], BeH+ [6], HF [7, 8, 9], HCl [10, 9], HBr and HI [9], AgH [11, 12], LiH [13], BeH [14] and MgH [15] and for CO [16], Li2 [17, 18, 19], LiK [20], and LiRb [21]. For molecules without such light nuclei, the deviations have been hard to detect [22, 23, 24], indications of them have been seen in K2 [25], Rb2 [22, 26], and I2 [27, 28]

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