EGAS41 - Swansea University

41 st EGAS CP 42 Gdańsk 2009
The MBPT study of electrons correlation effects in open-shell
atoms using symbolic programming language MATHEMATICA
R. Juršėnas ∗ , G. Merkelis
Institute of Theoretical Physics and Astronomy of Vilnius University, A. Goštauto 12,
LT-01108 Vilnius, Lithuania
∗ Corresponding author: rjursenas@yahoo.com
Atomic Many-Body Perturbation Theory (mbpt) allows systematic study of correlation
effects in atoms and ions. In order to generate the atomic datum of high accuracy it is
necessary to include the third and higher orders of mbpt. However, the calculations of
correlation corrections in the third-order turns into a very complicated task due to the
large number of mbpt expansion terms. Especially difficult computational problem arises
for the open-shell atoms. Then one needs to calculate the matrix elements of n-particle
operators (n ≥ 2) in many-electron case.
In the present paper we develop technique for the generation of mbpt expansion
terms for open-shell atoms using symbolic programming language mathematica [1].
The generalised Bloch-equation is used [2] to determine correlation corrections for atomic
state wave function and energy levels. To demonstrate this technique, the expansion terms
(diagrams) of the second-order wave operator and effective operator [2] are generated
with authors produced package NCoperators (which is based on mathematica). The
special attention is paid to the angular reduction of the expansion terms because for the
open-shell atoms the efficiency of calculations depends on the way the valence electrons
(the electrons in the open-shells) are considered [3]. In the present paper the second
quantisation method, keeping in mind tensorial properties of creation and annihilation
operators for valence electrons, is used.
References
[1] S. Wolfram, The Mathematica Book (Wolfram Media/Cambridge University Press,
Champaign, Illinois 1999, 4th edition)
[2] I. Lindgren, J. Morrison, Atomic Many-Body Theory (Springer Series in Chemical
Physics, Berlin 1982, 2nd edition)
[3] R. Juršėnas, G. Merkelis, Lithuanian J. Phys. 47, 255 (2007)
102