Decomposition of the two-electron-atom eigenvalue problem

Journal Article · Sat Dec 31 23:00:00 EST 1994 · Physical Review A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.51.257· OSTI ID:7061597

Pont, M; Shakeshaft, R ^[1]

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1. Physics Department, University of Southern California, Los Angeles, California 90089-0484 (United States)

Following Bhatia and Temkin [Rev. Mod. Phys. 36, 1050 (1964)] we decompose the Hamiltonian of a two-electron atom (or ion) with a fixed nucleus in terms of Euler angles, and thereby reduce the energy-eigenvalue problem to a set of coupled equations involving only three lengths, the distance of the electrons from each other and the distances from the nucleus. However, our equations differ from those of Bhatia and Temkin since we use a different expansion of the wave function. When the total orbital-angular-momentum quantum number [ital L] is zero or one our equations are the same as those derived by Hylleraas [Z. Phys. 48, 469 (1928)] and Breit [Phys. Rev. 35, 569 (1930)]. We give the transformation relating the generalized Hylleraas-Breit equations to the equations of Bhatia and Temkin. Our derivation is facilitated by a special factorization of one-particle angular-momentum operators.

• OSTI ID: 7061597
• Journal Information: Physical Review A; (United States), Journal Name: Physical Review A; (United States) Vol. 51:1; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

664100* -- Theory of Electronic Structure of Atoms & Molecules-- (1992-)
74 ATOMIC AND MOLECULAR PHYSICS
ANGULAR MOMENTUM OPERATORS
ATOMIC MODELS
COORDINATES
EIGENFUNCTIONS
EIGENVALUES
ENERGY LEVELS
FUNCTIONS
HAMILTONIANS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
QUANTUM OPERATORS
WAVE FUNCTIONS