NONCONVEXITY OF THE ATOMIC CHARGE-DENSITY AND SHELL STRUCTURE

The logarthmic derivative and the second derivative of the spherically averaged charge density rho(r), denoted as rho'(r)/rho(r) and rho''(r), respectively, are numerically studied in a Hartree-Fock framework for all ground-state atoms from hydrogen:(Z = 1) through uranium (Z = 92). It is observed that (i) the logarithmic derivative of rho(r) always attains its absolute minimum at the nucleus for Z=1-92, which extends a previous result for Z less than or equal to 54, (ii) the second derivative of rho(r) presents pairs of local minima and maxima, the number of which never decreases with increasing nuclear charge, and (iii) the occurrence of new local maxima and minima in rho''(r) always corresponds to the addition of an electron in a new subshell. The regularity in the behavior of the local characteristics of rho''(r) not only suggests an alternative way of studying the atomic shell structure by means of the one-particle density, but also provides further evidence of the hierarchical arrangement of the atomic charge density.