38
O. Yu. Khetselius et al.
[86], which has been used with success in many problems of classical atomic and
molecular spectroscopy. The detailed description of the method is presented in Refs.
[38, 39, 86, 87, 91–96].
Unlike leptons such as electrons or muons, a kaon is the composite particle with
a nonzero radius of charge distribution. To describe the electrical interaction of a
nucleus of finite size (with a radius of R 1 ) with a kaon (of finite size with a radius of
R 2 ), one should consider the potential by Indelicato–Desclaux et al. [44] (e.g. Refs.
[42, 43, 49, 50] too).
The next principally important aspect of a precise theory of the kaonic atomic
systems is connected with a consistent and accurate treatment of the radiative or
QED effects. Naturally, at present, the theory of QED effects has been worked out
at a very good level (e.g., [41, 57–68]).
In this work we use the procedures, which are presented in detail in Refs. [37–39,
86–90]. These procedures allow to take effectively the main radiative effects into
account. In particular, the contributions, provided by the standard Uehling–Serber
term and the known Källen–Sabry and Wichmann–Kroll corrections, are taken into
consideration. The modification of the generalized Uehling–Serber potential allows
to account for the high-order radiation corrections in the first perturbation theory
order.
It should be noted that another important QED effect (not important for kaonic
atoms), namely, the self-energy part of the Lamb shift can be determined in our
approach within the procedures [91–93]. This method generalizes the known formalism by Mohr and radiation model potential method by Flambaum–Ginges (look
details in Refs. [41, 57, 58, 85–87]).
It is worth also mentioning other precision corrections that should be considered
when describing the energy spectra of kaonic atoms. First, for deep-lying levels in the
kaonic atomic system, the contribution will be made by the vacuum polarization due
to the formation of virtual muon pairs, which is naturally taken into account in the
modified Uehling–Serber approximation. This correction turns out to be numerically
smaller than all the others and in any case it turns out to be significantly less than
the energy shift, say 1 s level in the kaonic atom, due to the strong kaon-nucleon
interaction.
Secondly, the correction for the reduced mass (1 + m
−
K /M KA ), where m
−
K is the
kaon mass, M KA is the mass of the entire atomic system, is actually already present
in the energy calculated from the solution of the Klein–Gordon–Fock equation. The
relativistic recoil correction can be elementarily estimated as B
2 /2M KA , where B is
the energy level.
Note that similar corrections of the following orders for fermions are known and
analyzed in detail (e.g. [1–5]). For bosons, the situation with these effects is more
complicated. In any case, accounting for the relativistic corrections sought is beyond
the scope of the experiment. The other details of our approach can be found in
Refs. [51–55, 90–140]. All calculations are performed with using the numeral code
Superatom (version 98).
O. Yu. Khetselius et al.
[86], which has been used with success in many problems of classical atomic and
molecular spectroscopy. The detailed description of the method is presented in Refs.
[38, 39, 86, 87, 91–96].
Unlike leptons such as electrons or muons, a kaon is the composite particle with
a nonzero radius of charge distribution. To describe the electrical interaction of a
nucleus of finite size (with a radius of R 1 ) with a kaon (of finite size with a radius of
R 2 ), one should consider the potential by Indelicato–Desclaux et al. [44] (e.g. Refs.
[42, 43, 49, 50] too).
The next principally important aspect of a precise theory of the kaonic atomic
systems is connected with a consistent and accurate treatment of the radiative or
QED effects. Naturally, at present, the theory of QED effects has been worked out
at a very good level (e.g., [41, 57–68]).
In this work we use the procedures, which are presented in detail in Refs. [37–39,
86–90]. These procedures allow to take effectively the main radiative effects into
account. In particular, the contributions, provided by the standard Uehling–Serber
term and the known Källen–Sabry and Wichmann–Kroll corrections, are taken into
consideration. The modification of the generalized Uehling–Serber potential allows
to account for the high-order radiation corrections in the first perturbation theory
order.
It should be noted that another important QED effect (not important for kaonic
atoms), namely, the self-energy part of the Lamb shift can be determined in our
approach within the procedures [91–93]. This method generalizes the known formalism by Mohr and radiation model potential method by Flambaum–Ginges (look
details in Refs. [41, 57, 58, 85–87]).
It is worth also mentioning other precision corrections that should be considered
when describing the energy spectra of kaonic atoms. First, for deep-lying levels in the
kaonic atomic system, the contribution will be made by the vacuum polarization due
to the formation of virtual muon pairs, which is naturally taken into account in the
modified Uehling–Serber approximation. This correction turns out to be numerically
smaller than all the others and in any case it turns out to be significantly less than
the energy shift, say 1 s level in the kaonic atom, due to the strong kaon-nucleon
interaction.
Secondly, the correction for the reduced mass (1 + m
−
K /M KA ), where m
−
K is the
kaon mass, M KA is the mass of the entire atomic system, is actually already present
in the energy calculated from the solution of the Klein–Gordon–Fock equation. The
relativistic recoil correction can be elementarily estimated as B
2 /2M KA , where B is
the energy level.
Note that similar corrections of the following orders for fermions are known and
analyzed in detail (e.g. [1–5]). For bosons, the situation with these effects is more
complicated. In any case, accounting for the relativistic corrections sought is beyond
the scope of the experiment. The other details of our approach can be found in
Refs. [51–55, 90–140]. All calculations are performed with using the numeral code
Superatom (version 98).