## LSU Historical Dissertations and Theses

1990

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Physics and Astronomy

A. R. P. Rau

#### Abstract

The present study focusses on presenting a global picture to theoretically describe the singly- and doubly-excited states of molecular hydrogen. The non-iterative eigenchannel R-matrix method and multichannel quantum defect theory have been combined for understanding the physics of the wide range of energy and internuclear distances in a unified manner. In this dissertation ab initio calculations for $\sp{1}\Sigma\sb{g}$, $\sp3\Sigma\sb{g}$, $\sp1\Sigma\sb{u}$ and $\sp3\Sigma\sb{u}$ symmetries of hydrogen molecule are performed to test the present approach. The body-frame quantum defects are expected to be mild on energy, but found to be strongly dependent on both energy and internuclear distances in this problem. The energy-independent $\Gamma\sp\prime$ and $\Lambda$ matrices in the eigenchannel R-matrix formulation are interpolated for the internuclear distance variance. The streamlined treatment of eigenchannel R-matrix theory is also adapted for fine energy meshes of calculation. Seven bound states per each symmetry are calculated simultaneously in addition to the doubly excited states based on same matrices $\Gamma\sp\prime$ and $\Lambda$ in non-iterative eigenchannel R-matrix formulation. The global picture for each symmetry is presented, and this tells the interactions between singly- and doubly-excited states. The interactions of the doubly-excited states affect the potential curves of the bound states, and result in many double minimum potentials.

140

COinS