Self-friction power series and their use for evaluation of atomic nuclear attraction integrals with noninteger indices of Slater orbitals and Coulomb–Yukawa-like potentials

Using complete orthogonal [Formula: see text]-Self-Friction Polynomials ([Formula: see text]-SFPs) introduced by one of the authors, the analytical and power series formulas for SF atomic nuclear attraction integrals over [Formula: see text]-noninteger Slater type orbitals ([Formula: see text]-NISTOs) and [Formula: see text]-noninteger Coulomb–Yukawa-like potentials ([Formula: see text]-NICYPs) are presented, where [Formula: see text] are the integer ([Formula: see text] or noninteger ([Formula: see text] SF quantum numbers and [Formula: see text]. As an application, the computer calculations for dependence of the atomic nuclear attraction integrals over [Formula: see text]-NISTOs and [Formula: see text]-NICYPs functions are presented.

COMBINED THEORY OF NONRELATIVISTIC AND QUASIRELATIVISTIC ATOMIC INTEGRALS OVER INTEGER AND NONINTEGER N-SLATER-TYPE ORBITALS

One- and two-electron nonrelativistic and quasirelativistic basic functions are introduced. The combined analytical relations in terms of these basic functions are derived for the non- and quasi-relativistic atomic integrals over integer and noninteger n-Slater-type orbitals. The relationships obtained are valid for the arbitrary values of principal quantum numbers and screening constants of Slater orbitals.