EGAS41 - Swansea University

41 st EGAS CP 199 Gdańsk 2009
Adiabatically and nonadiabatically corrected potential for H 2
M. Selg
Institute of Physics of the University of Tartu, Riia 142, 51014 Tartu, Estonia
E-mail: matti@fi.tartu.ee
Due to its simplicity, H 2 is an ideal specimen for testing ab initio and other theoretical
methods. Thus, a good-quality Born-Oppenheimer potential (BOP) is available for the
ground state of H 2 , its adiabatic, relativistic and radiative corrections also being accurately
determined [1]. Unfortunately, an adequate theory for nonadiabatic corrections is still
lacking, and one can only rely on various semi-empirical approaches to include these
corrections and make a direct comparison with the experimental data.
In this report, a new method will be demonstrated, which enables to ascertain all
corrections to the initial BOP simultaneously. To this end, an inverse perturbational
approach was used, based on repeated very accurate solution of the Schrödinger equation.
The problem was solved step-by-step, building a parametrized auxiliary potential and
trying to fit its discrete energy spectrum with the experimental data. Exact match with
the most acknowledged rotationless spectrum for H 2 [2] was achieved with only 4 cycles
of computations. By constructing such a pseudo-potential, one artificially removes the
dependence of nonadiabatic corrections on level energies (E vJ ) replacing them with an
effective mean value (E). However, the mentioned state-dependence is a higher-order
effect, which can be taken into account by slightly shifting the centrifugal energy (if
J ≠ 0). Simple analytic formulas for the shift have been derived, which can be used for
a wide range of vibrational and rotational quantum numbers. Good agreement with the
available astrophysical data was achieved.
References
[1] L. Wolniewicz, J. Chem. Phys. 99, 1851-1868 (1993)
[2] I. Dabrowski, Can. J. Phys. 62, 1639-1664 (1984)
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