Two-electron wave functions in hyperspherical coordinates

Journal Article · Tue Apr 01 04:00:00 EST 1986 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.33.2212· OSTI ID:5892877

Hornos, J E; MacDowell, S W; Caldwell, C D

In order to investigate the potential precision of quantitative calculations using hyperspherical coordinates, we have reexamined this method in detail. By developing an analytic solution of the angular equation in the form of a series expansion in the variable x = tan(..cap alpha../2), we are able to isolate the numerical errors in the solution from those caused by the truncation of the angular momentum expansion and by the exclusion of radial coupling terms, which we then examine separately. This new method enables us to extend the calculation of the potential curves and channel functions to the large-R region and to obtain asymptotic expansions for the potential curves and radial couplings. From these we determine general expressions for the boundary conditions of the radial equation. Finally, we present the first nonadiabatic result for the ground-state energy of helium.

• Research Organization: Yale University, New Haven, Connecticut 06511
• OSTI ID: 5892877
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 33:4; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

640302* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory
74 ATOMIC AND MOLECULAR PHYSICS
ANIONS
CHARGED PARTICLES
DIFFERENTIAL EQUATIONS
ELECTRONIC STRUCTURE
ELEMENTS
ENERGY LEVELS
EQUATIONS
EVALUATION
FLUIDS
FUNCTIONS
GASES
GROUND STATES
HELIUM
HYDROGEN IONS
HYDROGEN IONS 1 MINUS
IONS
MANY-BODY PROBLEM
NONMETALS
PARTIAL DIFFERENTIAL EQUATIONS
RARE GASES
SCHROEDINGER EQUATION
THREE-BODY PROBLEM
WAVE EQUATIONS
WAVE FUNCTIONS