New Representation of theα→·p→Operator in the Solution of Dirac-Type Equations by the Linear-Expansion Method

The solution of Dirac-type equations by the linear expansion technique suffers from variational instability due to difficulties in obtaining accurate matrix representations of the $\overrightarrow{\alpha }·\overrightarrow{\mathrm{p}}$ operator in conventional basis sets. A new matrix representation of $\overrightarrow{\alpha }·\overrightarrow{\mathrm{p}}$ is proposed which resolves the problem. The method has been successfully applied in numerical calculations.