applied. However, this approach deals with the serious difficulties in switching to
systems with a number of electrons, larger than two. In addition, the bare Hamiltonian is not hermitian.
So the symmetry adapted theories gain more spreading. In particular, speech is
about versions as EL-HAV (Eisenschitz-London-Hirschfelder–van der Avoird),
MS-MA (Murrel-Shaw-Musher-Amos) and others (see details in Refs. [8–12]). The
detailed analysis of advantages and disadvantages of the exchange perturbation
theory different versions had been performed by Batygin et al. (see, for example,
[25–27, 30–32]) in studying the hyperfine structure line shift of the hydrogen atom
in an atmosphere of an inert buffer gas. In our work the modified version of the ELHAV exchange perturbation theory has been used to calculate the corresponding
potentials (see details in [8–10]). On fact [8–10] this is the Schrödinger type perturbation theory for intermolecular or interatomic interactions, using the wave
operator formalism. To include all exchange effects, wavefunctions are used whose
symmetry with respect to permutations of both electronic and nuclear coordinates
can be prescribed arbitrarily. The interaction energy is obtained as a series in
ascending powers of the interaction operator. Further van der Avoird [8–10] has
proved that every term in this series is real and that the terms of even order are
negative definite for perturbation of the ground state. It has been also verified that
up to and including third order the results of this theory, if they are restricted to
electron exchange only, agree exactly with those of the Eisenschitz-London theory
(see other details in Refs. [1–12]).
The next important point is choice of the most reliable version of calculation
for multielectron atomic field and generating the basis of atomic orbitals. In Refs.
[36–54] a consistent relativistic energy approach combined with the relativistic
many-body perturbation theory has been developed and applied to calculation of
the energy and spectroscopic characteristics of heavy atoms and multicharged ions.
This is the relativistic many-body perturbation theory with the optimized DiracFock (Dirac-Kohn-Sham) zeroth approximation and taking into account the nuclear,
radiation, exchange-correlation corrections. It is worth to remind that this approach
has been successfully used to calculate the β-decay parameters for a number of
allowed (super allowed) transitions and study the chemical bond effect on β-decay
parameters [53]. This approach has been used in our work to generate a basis of
relativistic orbitals for heavy atoms. Besides, the correct procedures of accounting
for the many-body exchange-correlation effects and relativistic orbital basis optimization (in order to provide a performance of the gauge-invariant principle) as
well as accounting for the highly excited and continuum states have been used.
Earlier it was shown [40–54] that an adequate description of the energy and
spectral characteristics of the multi-electron atomic systems requires using the
optimized basis of wave functions. In Refs. [55, 56] a new ab initio optimization
procedure for construction of the optimized basis had been proposed and based on
the principle of minimization of the gauge dependent multielectron contribution
ImδE ninv of the lowest QED perturbation theory corrections to the radiation widths
of atomic levels. The minimization of the functional ImδE ninv leads to the DiracKohn-Sham-like equations for the electron density that are numerically solved. This
Optimized Perturbation Theory for Calculating the Hyperfine …
57
systems with a number of electrons, larger than two. In addition, the bare Hamiltonian is not hermitian.
So the symmetry adapted theories gain more spreading. In particular, speech is
about versions as EL-HAV (Eisenschitz-London-Hirschfelder–van der Avoird),
MS-MA (Murrel-Shaw-Musher-Amos) and others (see details in Refs. [8–12]). The
detailed analysis of advantages and disadvantages of the exchange perturbation
theory different versions had been performed by Batygin et al. (see, for example,
[25–27, 30–32]) in studying the hyperfine structure line shift of the hydrogen atom
in an atmosphere of an inert buffer gas. In our work the modified version of the ELHAV exchange perturbation theory has been used to calculate the corresponding
potentials (see details in [8–10]). On fact [8–10] this is the Schrödinger type perturbation theory for intermolecular or interatomic interactions, using the wave
operator formalism. To include all exchange effects, wavefunctions are used whose
symmetry with respect to permutations of both electronic and nuclear coordinates
can be prescribed arbitrarily. The interaction energy is obtained as a series in
ascending powers of the interaction operator. Further van der Avoird [8–10] has
proved that every term in this series is real and that the terms of even order are
negative definite for perturbation of the ground state. It has been also verified that
up to and including third order the results of this theory, if they are restricted to
electron exchange only, agree exactly with those of the Eisenschitz-London theory
(see other details in Refs. [1–12]).
The next important point is choice of the most reliable version of calculation
for multielectron atomic field and generating the basis of atomic orbitals. In Refs.
[36–54] a consistent relativistic energy approach combined with the relativistic
many-body perturbation theory has been developed and applied to calculation of
the energy and spectroscopic characteristics of heavy atoms and multicharged ions.
This is the relativistic many-body perturbation theory with the optimized DiracFock (Dirac-Kohn-Sham) zeroth approximation and taking into account the nuclear,
radiation, exchange-correlation corrections. It is worth to remind that this approach
has been successfully used to calculate the β-decay parameters for a number of
allowed (super allowed) transitions and study the chemical bond effect on β-decay
parameters [53]. This approach has been used in our work to generate a basis of
relativistic orbitals for heavy atoms. Besides, the correct procedures of accounting
for the many-body exchange-correlation effects and relativistic orbital basis optimization (in order to provide a performance of the gauge-invariant principle) as
well as accounting for the highly excited and continuum states have been used.
Earlier it was shown [40–54] that an adequate description of the energy and
spectral characteristics of the multi-electron atomic systems requires using the
optimized basis of wave functions. In Refs. [55, 56] a new ab initio optimization
procedure for construction of the optimized basis had been proposed and based on
the principle of minimization of the gauge dependent multielectron contribution
ImδE ninv of the lowest QED perturbation theory corrections to the radiation widths
of atomic levels. The minimization of the functional ImδE ninv leads to the DiracKohn-Sham-like equations for the electron density that are numerically solved. This
Optimized Perturbation Theory for Calculating the Hyperfine …
57