X-ray energies of circular transitions and electron screening in kaonic atoms

The QED contribution to the energies of the circular $(n,\ell =n-1)$, $2⩽n⩽13$, transitions have been calculated for several kaonic atoms throughout the periodic table, using the current world-average kaon mass. Calculations were done in the framework of the Klein-Gordon equation, with finite nuclear size, finite particle size, and all-order Uelhing vacuum polarization corrections, as well as Källén and Sabry and Wichmann and Kroll corrections. These energy level values are compared with other computed values. The circular transition energies are compared with available measured and theoretical transition energies. Electron screening is evaluated using a Dirac-Fock model for the electronic part of the wave function. The effect of electronic wave-function correlation is evaluated.

Figure 1

Feynman diagrams obtained when the Uehling term is added to the nuclear potential; A1, A2, and A3 are, respectively, contributions of order of $\alpha \left(\alpha Z\right)$, ${\left[\alpha \left(\alpha Z\right)\right]}^2$, and ${\left[\alpha \left(\alpha Z\right)\right]}^3$. The dashed lines starting with a × represent the interaction with the nucleus, the double line a bound-kaon wave function or propagator, and the wavy line a retarded photon propagator.

Figure 2

Feynman diagrams for the two-loop vacuum polarization Källén and Sabry contribution of the order of ${\alpha }^2\left(\alpha Z\right)$. The dashed lines starting with a × represent the interaction with the nucleus, the double line a bound-kaon wave function or propagator, and the wavy line a retarded photon propagator.

Figure 3

Feynman diagrams for the Wichmann-Kroll potential of the order $\alpha {\left(\alpha Z\right)}^3$. The dashed lines starting with a × represent the interaction with the nucleus, the double line a bound-kaon wave function or propagator, and the wavy line a retarded photon propagator.

Figure 4

Nuclear radius and average radius of the kaonic-atom levels for $Z=1–92$.