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General formula for shape-resonance life times: the HeH(+) example

Peek J.M.

Polish Journal of Chemistry

1998

Vol. 72, nr 7S

1334-1342

Translational spectroscopy stimulated the investigation of shape resonances in the electronic ground state of HeH(+) a number of years ago. Subsequent spectroscopic studies have increased the accuracy of these experimental data. Theoretical investigations require an extremely accurate potential energy curve over an extended range of internuclear separation. The calculation by Kołos proved invaluable in identifying these states and continues to be the standard to which improvements are added. The accurate characterization of many isolated shape resonances may be necessary so convenient techniques are required. Test functions are often used to create a boundary condition that converts this problem in the continuum to a discrete state calculation. The resulting eigenvalue search is efficient and convenient to automate. The associated widths are usually found by other techniques. It is shown here that the eigenvalue calculation implies a width if one convenient and easily satisfied requirement is met. Two versions of this result are applied to selected experimantal data for HeH(+).