Approximations for the interparticle interaction energy in an exactly solvable two-electron model atom

Journal Article · Fri Jan 15 00:00:00 EST 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.014501· OSTI ID:21388840

Nagy, I ^[1]; Pipek, J ^[1]

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1. Department of Theoretical Physics, Institute of Physics, Technical University of Budapest, H-1521 Budapest (Hungary)

The capability of different ansatz kernels, denoted as K(r,r{sup '}), in the calculation of the electron-electron interaction energy is investigated here for an exactly solvable two-electron model atom proposed by Moshinsky. The model atom is in the spin-compensated, paramagnetic ground state. The exact expression for the interaction energy in this state, derived by the diagonal of the second-order density matrix, is used as a rigorous background for comparison. It is found that the form of K{sub M}(r,r{sup '})=2rho(r)rho(r{sup '})-gamma{sup p}(r,r{sup '})gamma{sup q}(r{sup '},r), expressed via the rho(r) density distributions and operator powers of the one-body density matrix gamma(r,r{sup '}), results in the exact value for the interparticle interaction energy of the two-electron model atom if and only if p=q=1/2. Approximate forms with p=qnot =1/2 and with pnot =q at (p+q)=1 give deviations from the exact expression.

• OSTI ID: 21388840
• Journal Information: Physical Review. A, Vol. 81, Issue 1; Other Information: DOI: 10.1103/PhysRevA.81.014501; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

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74 ATOMIC AND MOLECULAR PHYSICS
75 CONDENSED MATTER PHYSICS
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71 CLASSICAL AND QUANTUM MECHANICS
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APPROXIMATIONS
ATOMS
COMPARATIVE EVALUATIONS
DENSITY MATRIX
DISTRIBUTION
ELECTRON-ELECTRON COLLISIONS
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ELEMENTARY PARTICLES
ENERGY LEVELS
EVALUATION
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