EXACT NUMERICAL VALUES OF DIAGONAL MATRIX ELEMENTS nl, AS n≤8and-7≤k≤4, AND THE SYMMETRY OF APPELL'S FUNCTION F2(1, 1)

Abstract

This article deals with the connection between diagonal matrix elements <rk> for 3H- and DH-atoms and the property of Appell's function F2(1, 1) mirror-like symmetry with respect to the center j0=-1/2 under the substitution j↦-j-1, j∈ℤ. Exact numerical values for <rk>nl of a 3H-atom, as n≤8 and -7≤k≤4, in the form of regular rational fractions are first given, i.e. practically for all the D. I. Mendeleev table.