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 f or all ground-state atoms from hydrogen:(Z = 1) through uranium (Z = 9 2). It is observed that (i) the logarithmic derivative of rho(r) alway s attains its absolute minimum at the nucleus for Z=1-92, which extend s a previous result for Z less than or equal to 54, (ii) the second de rivative of rho(r) presents pairs of local minima and maxima, the numb er of which never decreases with increasing nuclear charge, and (iii) the occurrence of new local maxima and minima in rho''(r) always corre sponds to the addition of an electron in a new subshell. The regularit y in the behavior of the local characteristics of rho''(r) not only su ggests an alternative way of studying the atomic shell structure by me ans of the one-particle density, but also provides further evidence of the hierarchical arrangement of the atomic charge density.