Hylleraas-CI approach to Dirac-Coulomb eigenvalue problem:
Ground states of helium-like atoms
Grezegorz Pestka
Instytut Fizyki, Uniwersytet Mikoaja Kopernika
Grudziadzka 5, PL-87-100 Torun, Poland
Tuesday, July 2, 2002 15:00-16:00,
Room 145, NIST North (820)
Gaithersburg
Tuesday, July 2, 2002 13:00-14:00,
Room 4550
Boulder
Abstract:
In the non-relativistic quantum mechanics the most accurate variational
approximations to the stationary-state energies and wave-functions of
many-electron systems have been obtained using trial functions which
explicitly depend on the interelectronic distance. The
interelectronic distance dependence of the wavefunction appears
to be necessary in order to
correctly describe the correlation cusp. Particularly accurate results for
two- and three-electron systems may be obtained using the so called
Hylleraas-CI approach in which the interelectronic distance dependence
is introduced to the
configuration interaction expansion of the wavefunction. Very recently
an extension of this approach to solving a relativistic Dirac-Coulomb
eigenvalue problem has been performed. In this work the method has been
further generalized and applied to evaluation of the ground state energies
of helium-like atoms described by the Dirac-Coulomb Hamiltonian with the
nuclear charges ranging from Z=1 to Z=110. The energies obtained are
equal to the eigenvalues of the Dirac-Coulomb Hamiltonian with the accuracy
of 8 significant figures (the highest accuracy ever achieved). In order
to impose the correct boundary conditions and to comply with the kinetic
balance condition which are necessary to assure the bound properties of the
variational ground-state energies, apart from the standard correlation
factors used in the non-relativistic formulations, some special correlation
factors have been introduced. The algorithm for the evaluation of the
resulting integrals has been already published. The approach may be
considered as a relativistic generalization of the Hylleraas-CI method.
Contact: J. S. SimsNote: Visitors from outside NIST must contact
Robin Bickel; (301) 975-3668;
at least 24 hours in advance.
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