Nodal surfaces of helium atom eigenfunctions
Abstract
Using a rapidly convergent composite basis of FrankowskiPekeris and Frankowski functions, we have accurately calculated the nodal surfaces of lowlying excited states of the helium atom to investigate Bressanini and Reynolds’ conjecture [D. Bressanini and P. J. Reynolds, Phys. Rev. Lett. 95, 110201 (2005)] that these nodal surfaces are rigorously independent of the interelectronic angle θ_{12} . We find that in fact there is a slight dependence of the nodal surfaces on θ_{12} , but it is so small that the assumption of strict independence may well yield extremely useful approximations in fixednode quantum Monte Carlo calculations. We explain how Kato’s cusp conditions determine the qualitative features of these nodal surfaces, which can accurately be modeled using the familiar ansatz of a symmetric or antisymmetric linear combination of products of hydrogenic orbitals, with some adjustments of the parameters. We explain why a similar near independence of the nodal surfaces on the angular variables can be expected for the ground and singly excited states of the lithium atom, but generally not for larger atoms.
 Publication:

Physical Review A
 Pub Date:
 June 2007
 DOI:
 10.1103/PhysRevA.75.060101
 Bibcode:
 2007PhRvA..75f0101S
 Keywords:

 03.65.Ge;
 02.70.Ss;
 Solutions of wave equations: bound states;
 Quantum Monte Carlo methods