Abstract
We present precise three-body calculations for the spectrum of kaonic deuterium with a realistic antikaon-nucleon interaction. Thanks to the precise measurement of kaonic hydrogen, it is now possible to construct realistic $\bar KN$ interactions which reproduce the whole set of experimental data in the threshold region. Employing such realistic interactions, the energy of the three-body system of kaonic deuterium is determined with the accuracy of eV, by expanding its wave function with a large number of correlated Gaussian basis functions. The level shift and width of the 1S state are found to be 670 eV and 1016 eV, respectively. The improved Deser formulas work reasonably well to estimate the shift and width of kaonic hydrogen, but their application to kaonic deuterium does not give an accurate estimation. It is shown that the result is sensitive to the I = 1 component of the $\bar KN$ interaction, which will be further constrained in future experiments.
Highlights
The antikaon-nucleon (K N) interaction is one of the intensively studied subjects in the strangeness nuclear physics [1]
Introducing a large number of correlated Gaussian basis functions [22,23,24,25] to express the spatial part of the wave function, the energy convergence is achieved at eV level in the calculation of kaonic deuterium
These results indicate that the measurement of kaonic deuterium with a 25% accuracy will improve the determination of the I = 1 component of the K N interaction, in a more stringent manner than the existing kaonic hydrogen data
Summary
The antikaon-nucleon (K N) interaction is one of the intensively studied subjects in the strangeness nuclear physics [1] This two-body interaction is closely related with the properties of the Λ(1405) resonance which exists near the K N threshold [2,3,4,5,6]. In contrast to previous works, we have combined (i) the rigorous three-body treatment, and (ii) the realistic K N interaction constrained by the SIDDHARTA data. These are the essential requirements for reliable predictions of kaonic deuterium We briefly introduce the construction of such realistic K N potentials, and apply them to calculate kaonic atoms
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