Diagonalisation of the Dirac Hamiltonian as a basis for a relativistic many-body procedure
Heully, Jean Louis ; Lindgren, Ingvar ; Lindroth, Eva ; Lundqvist, Stig and Martensson-Pendrill, Ann Marrie LU
(1986)
In Journal of Physics B: Atomic and Molecular Physics
19(18).
p.2799-2815
- Abstract
A diagonalisation procedure of the Foldy-Wouthuysen type is considered for the single-electron Dirac Hamiltonian as a basis for many-body applications. A modified procedure is suggested. In the diagonalisation procedure the Dirac equation is completely decoupled into two equations of the Pauli type. The expressions for positive- and negative-energy projection operators in the transformed basis are then trivial and, by performing the inverse transformation, projection operators for Dirac functions are obtained. Applying a similar transformation to the two-electron Dirac-Coulomb Hamiltonian leads to a diagonalised single-electron part and a non-diagonal two-electron interaction. In principle, the effect of the exchange of virtual,... (More)
A diagonalisation procedure of the Foldy-Wouthuysen type is considered for the single-electron Dirac Hamiltonian as a basis for many-body applications. A modified procedure is suggested. In the diagonalisation procedure the Dirac equation is completely decoupled into two equations of the Pauli type. The expressions for positive- and negative-energy projection operators in the transformed basis are then trivial and, by performing the inverse transformation, projection operators for Dirac functions are obtained. Applying a similar transformation to the two-electron Dirac-Coulomb Hamiltonian leads to a diagonalised single-electron part and a non-diagonal two-electron interaction. In principle, the effect of the exchange of virtual, transverse photons (Breit interactions) can also be included in the electron-electron interaction and transformed in a similar way. It is indicated how a diagonalisation procedure of this kind can be used as a basis for relativistic many-body calculations in the coupled cluster formulation in analogy with the corresponding non-relativistic procedure.
(Less)
- author
- Heully, Jean Louis
; Lindgren, Ingvar
; Lindroth, Eva
; Lundqvist, Stig
and Martensson-Pendrill, Ann Marrie
LU
- publishing date
- 1986
- type
- Contribution to journal
- publication status
- published
- in
- Journal of Physics B: Atomic and Molecular Physics
- volume
- 19
- issue
- 18
- article number
- 011
- pages
- 17 pages
- publisher
- IOP Publishing
- external identifiers
-
- scopus:34547149847
- ISSN
- 0022-3700
- DOI
- 10.1088/0022-3700/19/18/011
- language
- English
- LU publication?
- no
- id
- 1aedea75-c1e2-4fb6-b8fb-7bf29ebb3e4c
- date added to LUP
- 2025-08-30 07:18:46
- date last changed
- 2025-09-02 15:22:16
@article{1aedea75-c1e2-4fb6-b8fb-7bf29ebb3e4c,
abstract = {{<p>A diagonalisation procedure of the Foldy-Wouthuysen type is considered for the single-electron Dirac Hamiltonian as a basis for many-body applications. A modified procedure is suggested. In the diagonalisation procedure the Dirac equation is completely decoupled into two equations of the Pauli type. The expressions for positive- and negative-energy projection operators in the transformed basis are then trivial and, by performing the inverse transformation, projection operators for Dirac functions are obtained. Applying a similar transformation to the two-electron Dirac-Coulomb Hamiltonian leads to a diagonalised single-electron part and a non-diagonal two-electron interaction. In principle, the effect of the exchange of virtual, transverse photons (Breit interactions) can also be included in the electron-electron interaction and transformed in a similar way. It is indicated how a diagonalisation procedure of this kind can be used as a basis for relativistic many-body calculations in the coupled cluster formulation in analogy with the corresponding non-relativistic procedure.</p>}},
author = {{Heully, Jean Louis and Lindgren, Ingvar and Lindroth, Eva and Lundqvist, Stig and Martensson-Pendrill, Ann Marrie}},
issn = {{0022-3700}},
language = {{eng}},
number = {{18}},
pages = {{2799--2815}},
publisher = {{IOP Publishing}},
series = {{Journal of Physics B: Atomic and Molecular Physics}},
title = {{Diagonalisation of the Dirac Hamiltonian as a basis for a relativistic many-body procedure}},
url = {{http://dx.doi.org/10.1088/0022-3700/19/18/011}},
doi = {{10.1088/0022-3700/19/18/011}},
volume = {{19}},
year = {{1986}},
}