# Kaonic Deuterium In the Excited States

## Summary

For high energies the coupling of strong interactions is small and perturbation theory can be applied successfully. The knowledge of physical scattering processes in this energy regime is therefore very good in contrast to the low energy regime, where perturbation theory fails due to the high coupling. The physical processes are completely different in the low energy regime compared to high energy physics. In this project the low energy physics of the strong intereactions was investigated with phenomenological models, in particular the energy level displacement of kaonic deuterium was analyzed.

The examined exotic atom, kaonic deuterium, consists of a negatively charged K-meson, a proton and a neutron. Besides the Coulomb interaction, mesons also interact strongly with the nucleus. This causes, compared to the electromagnetic interaction, a complex displacement of the energy levels. Since the K-meson-deuterium system decays into neutron, hyperon and pion, the imaginary part of the complex energy level displacement is defined by a finite width of these decays. The goal of this project was to calculate the complex energy level displacement for kaonic deuterium and predict experimental data.

The theoretical basis for this analysis is chiral dynamics described by the chiral Lagrangian with the non-linear realisation of chiral SU(3) x SU(3) symmetry and derivative meson-baryon couplings, used in chiral perturbation theory and non-perturbative coupled-channels techniques. We defined the energy level displacement and its width with the solution of the Faddeev equation for the complex P-wave K-d scattering length. We proved the Faddeev equation for this case and solved it in the heavy nuclei approximation and provided general formulae for the energy level displacement. The knowledge of the complex energy level displacements of the excited np states of kaonic atoms is very important for the theoretical analysis of the yield of Kα X-rays. The former is necessary for the correct extraction of the energy level displacements of the ground states from the experimental spectra of the X-ray transitions.

Our results [arxiv:nucl-th/1012.3933] will be used for future experiments.

## Contributors

- Mario Pitschmann
- Andrej Ivanov
- Manfried Faber
- Markus Wellenzohn

## Collaborators

- Johann Marton, SMI, Wien
- Mark P. Faifman, Kurchatov Institute of Atomic Energy, Moskau
- Paul Kienle, TU München

## Publications

1) ** Molecule model for deeply bound and broad kaonic nuclear clusters.**

A.N. Ivanov, P. Kienle, J. Marton, M. Pitschmann. Feb 2011. 4pp.

e-Print: **arXiv:1102.4163** [nucl-th], Abstract, PDF

2) ** Time Modulation of K-Shell Electron Capture Decay Rates of H-Like Heavy Ions and Neutrino Masses.**

R. Höllwieser, A.N. Ivanov, P. Kienle, M. Pitschmann. Feb 2011. 3pp.

e-Print: **arXiv:1102.2519** [nucl-th], Abstract, PDF

3) ** Energy Level Displacement of Excited np State of Kaonic Deuterium In Faddeev Equation Approach.**

M. Faber, M.P. Faifman, A.N. Ivanov, J. Marton, M. Pitschmann, N.I. Troitskaya, . Dec 2010. 4pp.

e-Print: **arXiv:1012.3933** [nucl-th], Abstract, PDF

4) ** Molecule model for kaonic nuclear cluster K-bar NN.**

M. Faber, A.N. Ivanov, P. Kienle, J. Marton, M. Pitschmann. Dec 2009. 16pp.

e-Print: **arXiv:0912.2084** [nucl-th], Abstract, PDF

5) ** On the influence of the magnetic field of the GSI experimental storage ring on the time-modulation of the EC-decay rates of the H-like mother ions.**

M. Faber, A.N. Ivanov, P. Kienle, M. Pitschmann, N.I. Troitskaya. Jun 2009. 3pp.

e-Print: **arXiv:0906.3617** [nucl-th], Abstract, PDF

6) ** On Continuum-State and Bound-State Beta Decay Rates of the Neutron.**

M. Faber, A.N. Ivanov, V.A. Ivanova, J. Marton, M. Pitschmann, A.P. Serebrov, N.I. Troitskaya, M. Wellenzohn. Jun 2009. 8pp.

Published in **Phys.Rev.C80:035503,2009**.

e-Print: **arXiv:0906.0959** [hep-ph], Abstract, PDF

7) ** Rates of K-shell Electron Capture Decays of Re-180 and Pm-142 Atoms.**

A.N. Ivanov, P. Kienle, M. Pitschmann. May 2009. 6pp.

e-Print: **arXiv:0905.1904** [nucl-th, Abstract, PDF

8) ** On Bound-State beta- Decay Rate of the Free Neutron.**

M. Faber, A.N. Ivanov, V.A. Ivanova, J. Marton, M. Pitschmann, N.I. Troitskaya, M. Wellenzohn. Feb 2009. 3pp.

e-Print: **arXiv:0902.1728** [hep-ph], Abstract, PDF

9) ** On Continuum- and Bound-State l- -Decay Rates of Pionic and Kaonic Hydrogen in the Ground State.**

M. Faber, A.N. Ivanov, V.A. Ivanova, J. Marton, M. Pitschmann, N.I. Troitskaya, M. Wellenzohn. Feb 2009. 6pp.

Prepared for Developments in Mathematical Relativity, Vienna, Austria, 20-21 Aug 2008.

Published in **J.Phys.G36:075009,2009**.

e-Print: **arXiv:0902.1713** [hep-ph], Abstract, PDF

**Participation in scientific conferences **

1) Talk at 7th Workshop on Ultra Cold and Cold Neutrons, Physics and Sources, June 8 - 14, 2009, St. Petersburg, Russia

2) ECT* Hadronic Atoms and Kaonic Nuclei, October 12-16, 2009, Trento

3) ECT* Strangeness in Nuclei, October 4-8, 2010, Trento, Italy