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Motivated by the precise measurement of the $1S$ level shift of kaonichydrogen, we perform accurate three-body calculations for the spectrum ofkaonic deuterium using a realistic antikaon-nucleon ($KN$) interaction. Inorder to describe both short- and long-range behavior of the kaonic atomicstates, we solve the three-body Schr\"odinger equation with a superposition ofa large number of correlated Gaussian basis functions covering distances up toseveral hundreds of fm. Transition energies between $1S$, $2P$ and $2S$ statesare determined with high precision. The complex energy shift of the $1S$ levelof kaonic deuterium is found to be $670-i508$ eV. The sensitivity of this levelshift with respect to the isospin $I=1$ component of the $KN$ interaction isexamined. It is pointed out that an experimental determination of the kaonicdeuterium level shift within an uncertainty of 25\% will provide a constraintfor the $I=1$ component of the $KN$ interaction significantly stronger thanthat from kaonic hydrogen.

Constraining the $\bar{K}N$ interaction from the $1S$ level shift of kaonic deuterium