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

2021/07/03 by Cong Wang, Wang, Cong
Physics and Astronomy · #Atomic Physics (physics.atom-ph) #FOS: Physical sciences #physics.atom-ph

paper · pdf · doi:10.48550/arxiv.2107.01415

26 pages, 2 figures

arxiv created 2021/07/03 · arxiv updated 2021/07/06

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.

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