Rates of convergence of the partial-wave expansion beyond Kato's cusp condition II: evaluations for the prefactors on the ground state of the helium atom

Abstract

This article is a continuation of our previous work (Phys. Rev. A 88, 032511 (2013)). The prefactors for the partial-wave expansion of the helium atom are derived. Due to series of cancellations, the partial-wave increments of the energy converge as $L^{-2N-6}$. The origin of these cancellations is identified from alternative expressions of the partial-wave energies. There is some evidence that the assumptions of regularities for the exact wavefunction can be reduced.

26 pages, 2 figures