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Title:Is watson's "charge-modified" reduced mass always best for diatomic ions ?
Author(s):Le Roy, Robert J.
Contributor(s):Dattani, Nikesh S.
Subject(s):Theory and Computation
Abstract:Watson's landmark reformulation of the Born-Oppenheimer separation problem has been the basis of most combined-isotopologue analyses of diatomic spectroscopic data since 1980.\footnote{J.K.G.\ Watson, {\it J.\ Mol.\ Spectrosc.} {\bf 80}, 411 (1980)} One noteworthy feature of this work was his proposal that description of the dynamical behaviour of a diatomic ion with ($\pm$) charge $Q$, formed from atoms with isotopic masses of $M_1$ and $M_2$, should use a ``charge-modified'' reduced mass: $\,\mu_{\rm Wat}\equiv M_1\,M_2 /(M_1 + M_2 - Q\,m_e)\,$, in which $m_e$ is the electron mass, and this proposal seems to have been benignly accepted and adopted. The first quantitative test of this proposal was in the pioneering combined-isotopologue direct-potential-fit (CI-DPF) study of HeH$^+$ by Coxon and Hajigeorgiou in 1999,\footnote{J.A. Coxon and P. Hajigeorgiou, {\it J.\ Mol.\ Spectrosc.}\ {\bf 193}, 306 (1999).} where they compared the quality of fit for analyses that used different choices for the definition of the reduced masses of the various isotopologues, and found that the best choice seemed to be to use conventional two-body reduced masses for $\left(M_1 - \frac{1\,}{2\,} m_e\right)$ and $\left( M_2 - \frac{1}{2}\,m_e \right)$. This question was re-examined recently in the context of a CI-DPF study of CH$^+$, and a rather different conclusion was reached.\footnote{Y.-S. Cho and R.J.\ Le~Roy, {\it J.\ Chem.\ Phys.}\ {\bf 144}, 024311 (2016).} The present paper combines new CI-DPF studies of HeH$^+$ and BeH$^+$ with our recent CH$^+$ work, and attempts to draw some general conclusions on this matter.
Issue Date:2016-06-21
Publisher:International Symposium on Molecular Spectroscopy
Genre:Conference Paper/Presentation
Rights Information:Copyright 2016 by the authors
Date Available in IDEALS:2016-08-22

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