THE RADIAL HAMILTONIAN OPERATOR OF $HeH^{+}$

Abstract

Author Institution: Department of Chemistry, Dalhousie University; Department of Chemistry, University of British ColumbiaExperimental line positions for $^{3}HeH^{+}, ^{4}HeH^{+}, ^{3}HeD^{+}$, and $^{4}HeD^{+}$ have been employed in the determination of an effective non-adiabatic radial Hamiltonian operator for the ground $X^{1}\Sigma^{+}$ electronic state in compact analytic form. The procedure considers a Born-Oppenheimer potential and isotopically invariant Born-Oppenheimer breakdown functions for each atomic centre. The nuclear mass-independent potential is represented by the modified Morse $function^{1}$ $U^{BO}(R)= D_{r}[1 - e^{-\beta(R)(R-R_{e})}]^{2}$ where a Pad\'{e} approximant is adopted for $\beta(R)$. The spectroscopic data base, which samples the entire potential well, includes a number of transitions from quasibound levels. The experimental line positions are reproduced to within their experimental uncertainties and calculated quasibound level widths are in excellent agreement with experimental measurements. Results are compared to recent ab initio calculations. $^{1}$. J.A. Coxon and P.G. Hajigeorgiou, J. Mol. Spectrosc. 150, 1 (1991)