Momentum density and spatial form of correlated density matrix in model two-electron atoms with harmonic confinement
- Departamento de Fisica de Materiales, Facultad de Ciencias Quimicas, Universidad del Pais Vasco, Centro Mixto UPV-CSIC, and Donostia International Physics Center (DIPC), 20018 San Sebastian (Spain)
The detailed nature of the correlated first-order density matrix for the model atoms in the title for arbitrary interparticle interaction u(r{sub 12}) is studied. One representation with contracted information is first explored by constructing the momentum density {rho}(p) in terms of the wave function of the relative motion, say {psi}{sub R}(r{sub 12}), which naturally depends on the choice of u(r{sub 12}). For u(r{sub 12})=e{sup 2}/r{sub 12}, the so-called Hookean atom, and for the inverse square law u(r{sub 12})={lambda}/r{sub 12}{sup 2}, plots are presented of the above density {rho}(p) in momentum space. The correlated kinetic energy is recovered from averaging p{sup 2}/2m, m denoting the electron mass, with respect to {rho}(p). The second method developed is in coordinate space and expands the density matrix {gamma}(r{sub 1},r{sub 2}) in Legendre polynomials, using relative coordinate r{sub 1}-r{sub 2}, center-of-mass coordinate (r{sub 1}+r{sub 2})/2 and the angle, {theta} say, between these two vectors. For the Moshinsky atom in which u(r{sub 12})=(1/2)kr{sub 12}{sup 2} only the s term (l=0) contributes to the Legendre polynomial expansion. The specific example we present of the inverse square law model is shown to be characterized by the low-order terms (s+d) of the Legendre expansion. The Wigner function is finally calculated analytically for both Moshinsky and inverse square law models.
- OSTI ID:
- 21015970
- Journal Information:
- Physical Review. A, Vol. 76, Issue 3; Other Information: DOI: 10.1103/PhysRevA.76.032510; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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