Nonadiabatic corrections to electric quadrupole transition rates in H$_2$

TL;DR

This work derives and computes leading nonadiabatic corrections to electric quadrupole transition rates in H$_2$ using nonadiabatic perturbation theory (NAPT). The corrections are encapsulated in a single function $D^{(1)}(R)$ that augments the Born–Oppenheimer quadrupole moment $D^{(0)}(R)$, with the total moment expressed as $D(R) = D^{(0)}(R) + \frac{m}{m_n} D^{(1)}(R) D^{(0)}(R)$. High-precision curves for $D^{(0)}(R)$ and $D^{(1)}(R)$ are obtained via Ko{ ext}–Wolniewicz electronic structure using James–Coolidge and Heitler–London bases, revealing that $D^{(1)}(R)$ shares the same long-range asymptotic decay as $D^{(0)}(R)$ ($\sim R^{-6}$). Applying these results to the $v=1\rightarrow0$ band shows nonadiabatic corrections to E2 transition rates of roughly $0.4\%$–$12\%$, depending on the branch and $J$, with M1 channel contributions playing a role in certain cases. The findings improve the accuracy of H$_2$ transition rates and lifetimes, with potential extensions to HD and other diatomics and to related properties like polarizabilities and QED corrections.

Abstract

We derive formulas and perform calculations of nonadiabatic corrections to rates of electric quadrupole transitions in the hydrogen molecule. These corrections can be represented in terms of the quadrupole moment curve $D^{(1)}(R)$, similarly to the Born-Oppenheimer one, $D^{(0)}(R)$, derived originally by Wolniewicz. Numerical results change E2 transition rates for the fundamental band by as much as 0.4 - 12\% depending on rotational quantum numbers.

Figures (1)

• Figure 1: Top: Born-Oppenheimer approximated quadrupole operator $D^{(0)}(R)$ (orange; circles) and its leading-order mass correction $D^{(1)}(R)$ (blue; squares). Bottom: Their ratio, supporting the claim that their leading-order long-range asymptotics is the same ($\sim\!R^{-6}$) up to a constant relative factor of about 3.25(5).