EGAS41 - Swansea University

41 st EGAS CP 70 Gdańsk 2009
Relativistic ab initio calculations of isotopes shifts
C. Nazé 1,∗ , M. Godefroid 1 , J.P. Santos 2,3
1 SCQP, Université Libre de Bruxelles, 1050 Brussels, Belgium
2 Departamento de Física, Universidade Nova de Lisboa, Portugal
3 Centro de Física Atómica da Universidade de Lisboa, Portugal
∗ Corresponding author: cnaze@ulb.ac.be,
When the effects of the finite mass of the nucleus and the spatial charge distribution are
taken into account in an Hamiltonian describing an atomic system, the isotopes of an
element will have different electronic energy levels. The first effect is called the Mass
Shift (MS), the second the Field Shift (FS), both forming the Isotope Shift (IS). For systems
with more than one electron, the Specific Mass Shift (SMS), that does not exist for
hydrogenic systems, appears in the MS. Due to its low ponderation, the SMS parameter
can be treated as a perturbation of the Hamiltonian and its estimation requires the calculation
of Vinti integrals [1]. The computation of the SMS parameter in the full relativistic
Dirac-Fock scheme, is possible in grasp2K [2]. In the same relativistic framework, the
Multi Configuration Dirac Fock and General Matrix Element (mcdf-gme) code [3], is
often used by the atomic physics community but the current version of this code does
not allow the calculation of SMS. grasp2K and mcdf-gme use the Fano-Racah tensor
algebra and the Slater determinant algebra, for performing the angular integration of the
operators, respectively, with its own advantages and disadvantages. Recently, wishes of
sharing expertise on both sides have been expressed and even materialized through some
interesting common work (see for example [4]). In this line, we built the computer code
interface dedicated to the estimation of the SMS from multiconfiguration mcdf-gme wave
functions.
We report on our very first results in lithium-like atoms to illustrate and quantify
the importance of relativistic effects when increasing the nuclear charge, by comparing
systematically the non-relativistic Vinti integrals calculated with atsp2K [5] and the
relativistic ones estimated with our computational tool. This comparison is interesting
enough at the non-relativistic one-configuration level of approximation. However, Hartree-
Fock theory is not the end of the story for highly correlated systems and we will illustrate
how the generalization of the interface with the mcdf-gme for correlated wave functions
will be performed, taking advantage of the parallelism between the SMS and the Coulomb
interaction operators.
References
[1] J.P. Vinti, Phys. Rev. 56, 1120-1132 (1939)
[2] P. Jönsson, X. He, C. Froese Fischer, I.P. Grant, Computer Physics Communications
177, 597-622 (2007)
[3] J.P. Desclaux, Methods and Techniques in Computational Chemistry 94, 253-274
(1993); P. Indelicato, J.-P. Desclaux, MCDFGME, a MultiConfiguration Dirac-Fock and
General Matrix Elements program, URL http://dirac.spectro.jussieu.fr/mcdf
[4] J. Bieroń, C. Froese Fischer, P. Indelicato, P. Jönsson, P. Pyykkö, arXiv:0902.4307v2
[physics.atom-ph]
[5] C. Froese Fisher, G. Tachiev, G. Gaigalas, M. Godefroid, Comput. Phys. Commun.
176 559–579 (2007)
130