Relativistic Coulomb Sturmian matrix elements and the Coulomb Green’s function of the second-order Dirac equation.

Matrix elements with respect to a discrete ‘‘Sturmian’’ basis set of the operator r1/2gr1/2, where g is the Coulomb Green’s function of the ‘‘second-order’’ Dirac equation, are investigated. Closed expressions, involving Gaussian hypergeometric functions, can be obtained for the matrix elements. This calculation illustrates contour integration techniques capable of yielding closed expressions for a number of overlap integrals associated with the relativistic Kepler problem. [ABSTRACT FROM AUTHOR]