TY - JOUR
T1 - Boundary solutions of the two-electron Schrädinger equation at two-particle coalescences of the atomic systems
AU - Liverts, E. Z.
AU - Amusia, M. Ya
AU - Krivec, R.
AU - Mandelzweig, V. B.
PY - 2006
Y1 - 2006
N2 - 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 correlation function hyperspherical harmonic method wave functions. The asymptotic solutions of the proper two-electron Schrödinger 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 ln R. 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.
AB - 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 correlation function hyperspherical harmonic method wave functions. The asymptotic solutions of the proper two-electron Schrödinger 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 ln R. 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.
UR - http://www.scopus.com/inward/record.url?scp=33144483469&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.73.012514
DO - 10.1103/PhysRevA.73.012514
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AN - SCOPUS:33144483469
SN - 1050-2947
VL - 73
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
IS - 1
M1 - 012514
ER -