RESOLUTION OF A CONVERGENCE PROBLEM IN DIRECT-POTENTIAL-FIT DATA ANALYSES USING THE HERMAN-ASGHARIAN HAMILTONIAN

Abstract

The effective radial Schrodinger equation based on the Herman-Asgharian}, {\bf 19}, 305 (1966).} Hamiltonian for a diatomic molecule in a $^1\Sigma$ state has the form \vspace{-2mm} \begin{equation} -,\frac{\hbar^2}{2\mu} [1 + \beta(r)] \frac{d^2\psi_{v,j}(r)}{dr^2 } + \left{ \left[V_{\mathrm{CN}}(r) + \Delta V_{\mathrm{ad}}(r) \right] + \frac{ \hbar^2}{2\mu,r^2} [1 + \alpha(r)] [J(J+1)] \right} \psi_{v,j}(r) = E_{v,J} \psi_{v,j}(r) \label{eq:HAham} \end{equation} in which $,\beta(r),$ and $,\alpha(r),$ represent the effects of non-adiabatic corrections to the radial and angular kinetic energy operators, respectively, and $,\Delta V_{\mathrm{ad} }(r),$ is the adiabatic correction to the ``clamped nuclei'' potential energy function function $,V_{ \mathrm{CN}}(r),$. An internal convergence problem encountered when utilizing wavefunction propagator methods for direct-potential-fit diatomic data analyses using this Hamiltonian is described and corrected. Improved Hamiltonian parameters for the ground states of GaH and ArH$^+$ will be reported.