The shell structure of atoms and the Laplacian of the charge density J. Chem. Phys. 88, 4375 (1988); 10.1063/1.454711The Laplacian of the charge density and its relationship to the shell structure of atoms and ions 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 V1E(R) and V 2 I(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 V 2 p(r). Radii corresponding to minima in V 2 I(r) are found to match closely their corresponding values in V 2 p(r). Linear relationships between the inverses of the roots ofV 2 E(R) and V 2 I(r) and the nuclear charge Z are found. Calculations demonstrate that atomic shell structure is well resolved by the odd numbered zeros of V 2 E(R) and by the radiicorresponding to minima in V 2 I(r).
The β decay of 192,190 Pb has been studied using the total absorption technique at the ISOLDE (CERN) facility. The β-decay strength deduced from the measurements, combined with QRPA theoretical calculations, allow us to infer that the ground states of the 192,190 Pb isotopes are spherical. These results represent the first application of the shape determination method using the total absorption technique for heavy nuclei and in a region where there is considerable interest in nuclear shapes and shape effects.
The centre-of-mass or extracule and relative distance or intracule electron pair densities for the ground state of CO2 have been analysed by means of the radial, longitudinal and transverse reduced distribution functions. Calculations demonstrate that the independent-atom model (IAM) accounts for the chief characteristics of the distributions. The basis set dependence of the pair densities is illustrated by the moments of the distributions. Calculations with the 3-21G, 6-31G and 6-31G* basis sets show that augmenting the number of primitives of the various shells has a more profound effect than the addition of polarization functions. Finally analysis of increment electron-pair densities reveals that the 6-31G* basis favours small and intermediate distances with the respect to both the 3-21G and 6-31G basis set.
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