Studies of quantum self-frictional atomic potentials and nuclear attraction forces in standard convention

•The physical nature of quantum self-frictional atomic potentials and nuclear attraction forces are presented.•The quantum self-frictional potentials and nuclear attraction forces as a function of the distance from nucleus is analyzed.•Model calculations have demonstrated high efficiency of the present approach.

This paper is devoted to examine a physical nature of quantum self-frictional atomic potentials and nuclear attraction forces. Using analytical formulas for the L(pl∗)-generalized Laguerre polynomials (L(pl∗)-GLPs) and ψ(pl∗)-generalized exponential type orbitals (ψ(pl∗)-GETOs) in standard convention, the self-frictional atomic potentials and nuclear attraction forces are investigated, where pl∗=2l+2-α∗ and α∗ is the integer (α∗ = α  , -∞<α⩽2-∞<α⩽2) or noninteger (α∗ ≠ α, −∞ < α∗ < 3) self-frictional quantum number. We notice that the L(pl∗)-GLPs, the origin of which is the quantum self-frictional fields, are the radial parts of the ψ(pl∗)-GETOs. The dependence of the quantum self-frictional potentials and nuclear attraction forces as a function of the distance from nucleus is analyzed. The relationships presented are valid for the arbitrary values of quantum numbers and scaling parameters.