THE LAPLACIAN OF THE INTRACULE AND EXTRACULE DENSITIES AND THEIR RELATIONSHIP TO THE SHELL STRUCTURE OF ATOMS

Numerical evidence of the monotonicity of both the intracule density I(r) and the extracule density E(R) in atoms are presented. However, it is found that their associated Laplacian fields NABLA2E(R) and NABLA2I(r) show a rich structure. Roots and extrema of these functions have been compared with the corresponding values of the Laplacian of the charge density NABLA2-rho(r). Radii corresponding to minima in NABLA2I(r) are found to match closely their corresponding values in NABLA2-rho(r). Linear relationships between the inverses of the roots of NABLA2E(R) and NABLA2I(r) and the nuclear charge Z are found. Calculations demonstrate that atomic shell structure is well resolved by the odd numbered zeros of NABLA2E(R) and by the radii corresponding to minima in NABLA2I(r).