1 Introduction
It is well known that studying the energy, spectral, radiation parameters, including
the spectral lines hyperfine structure, for heavy exotic (hadronic, kaonic, pionic)
atomic systems is of a great interest for the further development as atomic and
nuclear theories and quantum chemistry of strongly interacted fermionic systems
(see, for example, Refs. [1–31]). Really, the exotic atoms enable to probe aspects of
atomic and nuclear structure that are quantitatively different from what can be
studied in the electronic (“usual”) atoms. Besides, the corresponding data on the
energy and spectral properties of the hadronic atomic systems can be used as a
powerful tool for the study of particles and fundamental properties.
At present time one of the most sensitive tests for the chiral symmetry breaking
scenario in the modern hadron’s physics is provided by studying the exotic
hadron-atomic systems. Nowadays the transition energies in pionic (kaonic, muonic
etc.) atoms are measured with an unprecedented precision and from studying
spectra of the hadronic atoms it is possible to investigate the strong interaction at
low energies measuring the energy and natural width of the ground level with a
precision of few meV [20–46].
The strong interaction is the reason for a shift in the energies of the low-lying
levels from the purely electromagnetic values and the finite lifetime of the state
corresponds to an increase in the observed level width. For a long time the similar
experimental investigations have been carried out in the laboratories of Berkley,
Virginia (USA), CERN (Switzerland).
The most known theoretical models to treating the hadronic (pionic, kaonic,
muonic, antiprotonic etc.) atomic systems are presented in Refs. [1–46]. The most
difficult aspects of the theoretical modelling are reduced to the correct description of
pion-nuclear strong interaction [10–18] as the electromagnetic part of the problem
can be in principle reasonably accounted for [47–60].
In the present chapter we briefly present the fundamentals of a consistent relativistic theory of spectra of the exotic pionic atomic systems (with simultaneous
accounting for the electromagnetic and strong pion-nuclear interactions by means of
using the generalized radiation and strong pion-nuclear optical potentials) on the
basis of the Klein-Gordon-Fock. The nuclear and radiative corrections are effectively taken into account. The modified Uehling-Serber approximation is used to
take into account for the Lamb shift polarization part. In order to take into account
the contribution of the Lamb shift self-energy part we have used the generalized
non-perturbative procedure, which generalizes the Mohr procedure and radiation
model potential method by Flambaum-Ginges. There are presented data of calculation of the energy and spectral parameters for pionic atoms of the
93 Nb,
173 Yb,
181 Ta,
197 Au, with accounting for the radiation (vacuum polarization), nuclear
(finite size of a nucleus) and the strong pion-nuclear interaction corrections. The
measured values of the Berkley, CERN and Virginia laboratories and alternative
data based on other versions of the Klein-Gordon-Fock theories with taking into
72
O. Yu. Khetselius et al.
It is well known that studying the energy, spectral, radiation parameters, including
the spectral lines hyperfine structure, for heavy exotic (hadronic, kaonic, pionic)
atomic systems is of a great interest for the further development as atomic and
nuclear theories and quantum chemistry of strongly interacted fermionic systems
(see, for example, Refs. [1–31]). Really, the exotic atoms enable to probe aspects of
atomic and nuclear structure that are quantitatively different from what can be
studied in the electronic (“usual”) atoms. Besides, the corresponding data on the
energy and spectral properties of the hadronic atomic systems can be used as a
powerful tool for the study of particles and fundamental properties.
At present time one of the most sensitive tests for the chiral symmetry breaking
scenario in the modern hadron’s physics is provided by studying the exotic
hadron-atomic systems. Nowadays the transition energies in pionic (kaonic, muonic
etc.) atoms are measured with an unprecedented precision and from studying
spectra of the hadronic atoms it is possible to investigate the strong interaction at
low energies measuring the energy and natural width of the ground level with a
precision of few meV [20–46].
The strong interaction is the reason for a shift in the energies of the low-lying
levels from the purely electromagnetic values and the finite lifetime of the state
corresponds to an increase in the observed level width. For a long time the similar
experimental investigations have been carried out in the laboratories of Berkley,
Virginia (USA), CERN (Switzerland).
The most known theoretical models to treating the hadronic (pionic, kaonic,
muonic, antiprotonic etc.) atomic systems are presented in Refs. [1–46]. The most
difficult aspects of the theoretical modelling are reduced to the correct description of
pion-nuclear strong interaction [10–18] as the electromagnetic part of the problem
can be in principle reasonably accounted for [47–60].
In the present chapter we briefly present the fundamentals of a consistent relativistic theory of spectra of the exotic pionic atomic systems (with simultaneous
accounting for the electromagnetic and strong pion-nuclear interactions by means of
using the generalized radiation and strong pion-nuclear optical potentials) on the
basis of the Klein-Gordon-Fock. The nuclear and radiative corrections are effectively taken into account. The modified Uehling-Serber approximation is used to
take into account for the Lamb shift polarization part. In order to take into account
the contribution of the Lamb shift self-energy part we have used the generalized
non-perturbative procedure, which generalizes the Mohr procedure and radiation
model potential method by Flambaum-Ginges. There are presented data of calculation of the energy and spectral parameters for pionic atoms of the
93 Nb,
173 Yb,
181 Ta,
197 Au, with accounting for the radiation (vacuum polarization), nuclear
(finite size of a nucleus) and the strong pion-nuclear interaction corrections. The
measured values of the Berkley, CERN and Virginia laboratories and alternative
data based on other versions of the Klein-Gordon-Fock theories with taking into
72
O. Yu. Khetselius et al.