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Boundary Solutions of the Two-electron Schrodinger Equation at Two-particle Coalescences of the Atomic Systems

E. Z. Liverts·M. Ya. Amusia·R. Krivec·V. B. Mandelzweig
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Abstract

The limit relations for the partial derivatives of the two-electron atomic wave functions at the two-particle coalescence lines have been obtained numerically using accurate CFHHM wave functions. The asymptotic solutions of the proper two-electron Schrodinger equation have been derived for both electron-nucleus and electron-electron coalescence. It is shown that the solutions for the electron-nucleus coalescence correspond to the ground and singly excited bound states, including triplet ones. The proper solutions at small distances $R$ from the triple coalescence point were presented as the second order expansion on R and lnR. The vanishing of the Fock's logarithmic terms at the electron-nucleus coalescence line was revealed in the frame of this expansion, unlike the case of electron-electron coalescence. On the basis of the obtained boundary solutions the approximate wave function corresponding to both coalescence lines have been proposed in the two-exponential form with no variational parameters.

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E. Z. Liverts, M. Ya. Amusia, R. Krivec, V. B. Mandelzweig. 2005-10-27. Boundary Solutions of the Two-electron Schrodinger Equation at Two-particle Coalescences of the Atomic Systems. https://doi.org/10.1103/physreva.73.012514

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