these studies provide insight into the nature of interatomic forces and, hence, they
provide an excellent test of theory.
An accurate analysis of the spectral line profiles is a powerful technique for
studying atomic and molecular interactions and is often necessary for probing
matter in extreme conditions, such as in stellar atmospheres, ultracold traps and
Bose–Einstein condensates [5–7, 13, 14]. Besides, calculation of the hyperfine
structure line shift and broadening allows to check a quality of the wave functions
(orbitals) and study a contribution of the relativistic and correlation effects to the
energetic and spectral characteristics of the two-center (multi-center) atomic systems.
From the applied point of view, the mentioned physical effects form a basis for
creating an atomic quantum measure of frequency [22–29]. The corresponding
phenomenon for the thallium atom has attracted a special attention because of the
possibility to create the thallium quantum frequency measure. Alexandrov et al. [26]
have realized the optical pumping thallium atoms on the line of 21 GHz, which
corresponds to transition between the components of hyperfine structure for the Tl
ground state. These authors have measured the collisional shift of this hyperfine line
in the atmosphere of the He buffer gas.
The detailed non-relativistic theory of collisional shift and broadening the
hyperfine structure lines for simple elements (such as light alkali elements etc.) was
developed by many authors (see, for example, Refs. [1–35]). However, until now an
accuracy of the corresponding available data has not been fully adequate to predict
or identify transitions within accuracy as required for many applications. It is
obvious that correct taking into account the relativistic and correlation effects is
absolutely necessary in order to obtain sufficiently adequate description of spectroscopy of the heavy atoms in an atmosphere of the buffer gases. This stimulated
our current investigation whose goals were to propose a new relativistic perturbation theory approach to calculating the interatomic potentials and hyperfine structure line collision shifts and broadening for the alkali and lanthanide atoms in an
atmosphere of the inert gases. The basic expressions for the collision shift and
broadening hyperfine structure spectral lines are taken from the kinetic theory of
spectral lines [13, 14, 16, 17, 25–27, 30–32].
The exchange perturbation theory (the modified version EL-HAV) has been used
to calculate the corresponding potentials (see details in [1–12]). Let us note that
sufficiently detailed reviews of the different versions of exchange perturbation
theory are presented, for example, in Refs. [1–21]. It is worth to remind about the
known difficulties of the exchange perturbation theory, associated with complex
structure series, which contain the overlap integrals and exchange integrals [1, 2].
Due to the ambiguity of the expansion in the antisymmetric functions it had been
built a number of different formalisms of an exchange perturbation theory. Usually
one could distinguish two groups in dependence on the zero-order approximation of
the Hamiltonian. In the symmetry adapted theories the zeroth-approximation
Hamiltonian is an asymmetric, but the zeroth-approximation functions have
the correct symmetry. In symmetric formalisms there is constructed a symmetric
zeroth-approximation Hamiltonian such as the antisymmetric function is its eigen
function. Further formally standard Rayleigh–Schrodinger perturbation theory is
56
O.Yu. Khetselius
provide an excellent test of theory.
An accurate analysis of the spectral line profiles is a powerful technique for
studying atomic and molecular interactions and is often necessary for probing
matter in extreme conditions, such as in stellar atmospheres, ultracold traps and
Bose–Einstein condensates [5–7, 13, 14]. Besides, calculation of the hyperfine
structure line shift and broadening allows to check a quality of the wave functions
(orbitals) and study a contribution of the relativistic and correlation effects to the
energetic and spectral characteristics of the two-center (multi-center) atomic systems.
From the applied point of view, the mentioned physical effects form a basis for
creating an atomic quantum measure of frequency [22–29]. The corresponding
phenomenon for the thallium atom has attracted a special attention because of the
possibility to create the thallium quantum frequency measure. Alexandrov et al. [26]
have realized the optical pumping thallium atoms on the line of 21 GHz, which
corresponds to transition between the components of hyperfine structure for the Tl
ground state. These authors have measured the collisional shift of this hyperfine line
in the atmosphere of the He buffer gas.
The detailed non-relativistic theory of collisional shift and broadening the
hyperfine structure lines for simple elements (such as light alkali elements etc.) was
developed by many authors (see, for example, Refs. [1–35]). However, until now an
accuracy of the corresponding available data has not been fully adequate to predict
or identify transitions within accuracy as required for many applications. It is
obvious that correct taking into account the relativistic and correlation effects is
absolutely necessary in order to obtain sufficiently adequate description of spectroscopy of the heavy atoms in an atmosphere of the buffer gases. This stimulated
our current investigation whose goals were to propose a new relativistic perturbation theory approach to calculating the interatomic potentials and hyperfine structure line collision shifts and broadening for the alkali and lanthanide atoms in an
atmosphere of the inert gases. The basic expressions for the collision shift and
broadening hyperfine structure spectral lines are taken from the kinetic theory of
spectral lines [13, 14, 16, 17, 25–27, 30–32].
The exchange perturbation theory (the modified version EL-HAV) has been used
to calculate the corresponding potentials (see details in [1–12]). Let us note that
sufficiently detailed reviews of the different versions of exchange perturbation
theory are presented, for example, in Refs. [1–21]. It is worth to remind about the
known difficulties of the exchange perturbation theory, associated with complex
structure series, which contain the overlap integrals and exchange integrals [1, 2].
Due to the ambiguity of the expansion in the antisymmetric functions it had been
built a number of different formalisms of an exchange perturbation theory. Usually
one could distinguish two groups in dependence on the zero-order approximation of
the Hamiltonian. In the symmetry adapted theories the zeroth-approximation
Hamiltonian is an asymmetric, but the zeroth-approximation functions have
the correct symmetry. In symmetric formalisms there is constructed a symmetric
zeroth-approximation Hamiltonian such as the antisymmetric function is its eigen
function. Further formally standard Rayleigh–Schrodinger perturbation theory is
56
O.Yu. Khetselius