ITLApplied  Computational Mathematics Division
ACMD Seminar Series
Attractive Image NIST

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)
Tuesday, July 2, 2002 13:00-14:00,
Room 4550

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. Sims

Note: Visitors from outside NIST must contact Robin Bickel; (301) 975-3668; at least 24 hours in advance.

Privacy Policy | Disclaimer | FOIA
NIST is an agency of the U.S. Commerce Department.
Last updated: 2011-01-12.