Energy Level Displacement of Excited np State of Kaonic Deuterium In Faddeev Equation Approach

Abstract

We calculate the energy level displacement of the excited $np$ state of kaonic deuterium in terms of the P-wave scattering length of $K^{-}d$ scattering. We solve the Faddeev equations for the amplitude of $K^{-}d$ scattering in the fixed centre approximation and derive the complex P-wave scattering length of $K^{-}d$ scattering in terms of the S-wave and P-wave scattering lengths of $\bar{K}N$ scattering. The estimated uncertainty of the complex P-wave scattering length is of about $15$. For the calculated width ${\Gamma }_{2p}=10.203\mathrm{meV}$ of the excited $2p$ state of kaonic deuterium we evaluate the yield $Y_{K^{-}d}=0.27$ of $X$-rays for the $K_{\alpha }$ emission line of kaonic deuterium. Using the complex S-wave and P-wave scattering lengths of $\bar{K}N$ scattering, calculated in \cite{ECL1,Weise1}, we get the width ${\Gamma }_{2p}=2.675\mathrm{meV}$ of the excited $2p$ state and the yield $Y_{K^{-}d}=1.90$ of $X$-rays for the $K_{\alpha }$ emission line of kaonic deuterium. The results, obtained in this paper, can be used for the planning of experiments on the measurements of the energy level displacement of the ground state of kaonic deuterium, caused by strong low-energy interactions.

13 pages

References in corpus (12)

• A New Measurement of Kaonic Hydrogen X rays
• K^- p scattering length from scattering experiments
• Chiral unitary approach to the K^- deuteron scattering length
• Kaon-nucleon scattering lengths from kaonic deuterium experiments
• Hadronic atoms in QCD + QED
• On the scattering length of the K^- d system
• Chiral SU(3) Dynamics and Antikaon-Nuclear quasibound States
• The role of nucleon recoil in low-energy antikaon-deuteron scattering
• On kaonic deuterium. Quantum field theoretic and relativistic covariant approach
• On Continuum-State and Bound-State Beta Decay Rates of the Neutron
• Energy level displacement of excited np states of kaonic hydrogen
• Pion Deuteron Scattering and Chiral Expansions

Cited by in corpus (3)

• Preliminary study of kaonic deuterium X-rays by the SIDDHARTA experiment at DAFNE
• Faddeev-Chiral Unitary Approach to the $K^{-}d$ scattering length
• A walk through the world of chiral dynamics