66
O. Yu. Khetselius et al.
discovery, measurement of CP violations in the K
− , B
− mesons, evidence of accelerated expansion of the universe, determination of the fraction of dark energy and dark
matter in the universe, etc. From the other side, there are a number of the serious factors which clearly points to some new physics beyond the Standard model despite the
desperate lack of direct experimental evidence. One could remind that the density of
matter included into the Standard model is approximately 5% of the energy density
of the universe; besides, neutrinos in the Standard model are massless, and there are
no neutrino oscillations (not to mention gravity). As it is known, the Standard model
can be divided into three sectors: the calibration sector, the fragrance sector, and
the symmetry-breaking sector. While the first two sectors are being actively studied in accelerator experiments (LEP, SLD, BELLE, etc.), the sector of spontaneous
symmetry breaking is now attracting close attention, as it may give clear hints of
existence in New Physics experiments beyond the Standard model. The observation
of a static electric dipole moment of a many-electron atom which violates parity, P,
and time reversal, T, symmetry, represents a great fundamental interest in a search
of these hints. The detailed review of these topics can be found in Refs. [1–89].
Atomic optical and Stark pumping PNC measurements have been fulfilled in a
whole number of heavy atoms, namely, in caesium (0.35% accuracy [1]), thallium
(1.7%), bismuth (2%), Pb (1.2%) etc. The atomic optical tests of the Standard model
provide important constraints on possible extensions of the SM. A recent analysis [2]
of parity-violating electron-nucleus scattering measurements combined with atomic
PNC measurements placed tight constraints on the weak neutral-current lepton-quark
interactions at low energy, improving the lower bound on the scale of relevant new
physics to ~TeV. The precise measurement of the PNC amplitudes in Cs [1] led to an
experimental value of the small contribution from the nuclear-spin dependent PNC
accurate to 14%. So, form the one side there is very actual necessity of the further
development and increasing of the theoretical approaches accuracy and carrying out
new atomic optical and Stark pumping PNC experiments.
The different methods have been used in calculation of the hyperfine structure
parameters, PNC effect. The most popular multiconfiguration Dirac-Fock (MCDF)
method for calculating parity and time reversal symmetry violations in many-electron
atoms is often, however it application requires some additional generalizations [3,
17, 26]. Among other well-known calculation methods, a relativistic many-body
perturbation theory (RMBPT), namely, the PT with relativistic Hartree-Fock (RHF)
and Dirac-Fock (DF) zeroth approximations, the relativistic all-order method, QED
perturbation theory (PT) etc. should be mentioned (e.g. [9–69]).
In present paper we present the results of application of the consistent theoretical approach, namely, the nuclear-relativistic many-body perturbation theory (NRMBPT), to study the hyperfine and electroweak interaction parameters in the heavy
finite Fermi systems and PNC effect. The N-RMBPT formalism is based on the
combining ab initio perturbation theory formalism for electron subsystem, nuclear
relativistic middle-field model for nuclear subsystem and an energy approach for
computing radiation transition amplitude. It allows to fulfil computing the PNC
amplitudes in the finite Fermi systems (atomic systems) [3, 10, 40, 41, 48–53, 90–
99]. The important feature is the correct accounting for the inter electron correlations,
O. Yu. Khetselius et al.
discovery, measurement of CP violations in the K
− , B
− mesons, evidence of accelerated expansion of the universe, determination of the fraction of dark energy and dark
matter in the universe, etc. From the other side, there are a number of the serious factors which clearly points to some new physics beyond the Standard model despite the
desperate lack of direct experimental evidence. One could remind that the density of
matter included into the Standard model is approximately 5% of the energy density
of the universe; besides, neutrinos in the Standard model are massless, and there are
no neutrino oscillations (not to mention gravity). As it is known, the Standard model
can be divided into three sectors: the calibration sector, the fragrance sector, and
the symmetry-breaking sector. While the first two sectors are being actively studied in accelerator experiments (LEP, SLD, BELLE, etc.), the sector of spontaneous
symmetry breaking is now attracting close attention, as it may give clear hints of
existence in New Physics experiments beyond the Standard model. The observation
of a static electric dipole moment of a many-electron atom which violates parity, P,
and time reversal, T, symmetry, represents a great fundamental interest in a search
of these hints. The detailed review of these topics can be found in Refs. [1–89].
Atomic optical and Stark pumping PNC measurements have been fulfilled in a
whole number of heavy atoms, namely, in caesium (0.35% accuracy [1]), thallium
(1.7%), bismuth (2%), Pb (1.2%) etc. The atomic optical tests of the Standard model
provide important constraints on possible extensions of the SM. A recent analysis [2]
of parity-violating electron-nucleus scattering measurements combined with atomic
PNC measurements placed tight constraints on the weak neutral-current lepton-quark
interactions at low energy, improving the lower bound on the scale of relevant new
physics to ~TeV. The precise measurement of the PNC amplitudes in Cs [1] led to an
experimental value of the small contribution from the nuclear-spin dependent PNC
accurate to 14%. So, form the one side there is very actual necessity of the further
development and increasing of the theoretical approaches accuracy and carrying out
new atomic optical and Stark pumping PNC experiments.
The different methods have been used in calculation of the hyperfine structure
parameters, PNC effect. The most popular multiconfiguration Dirac-Fock (MCDF)
method for calculating parity and time reversal symmetry violations in many-electron
atoms is often, however it application requires some additional generalizations [3,
17, 26]. Among other well-known calculation methods, a relativistic many-body
perturbation theory (RMBPT), namely, the PT with relativistic Hartree-Fock (RHF)
and Dirac-Fock (DF) zeroth approximations, the relativistic all-order method, QED
perturbation theory (PT) etc. should be mentioned (e.g. [9–69]).
In present paper we present the results of application of the consistent theoretical approach, namely, the nuclear-relativistic many-body perturbation theory (NRMBPT), to study the hyperfine and electroweak interaction parameters in the heavy
finite Fermi systems and PNC effect. The N-RMBPT formalism is based on the
combining ab initio perturbation theory formalism for electron subsystem, nuclear
relativistic middle-field model for nuclear subsystem and an energy approach for
computing radiation transition amplitude. It allows to fulfil computing the PNC
amplitudes in the finite Fermi systems (atomic systems) [3, 10, 40, 41, 48–53, 90–
99]. The important feature is the correct accounting for the inter electron correlations,