$K$-series X-ray yield measurement of kaonic hydrogen atoms in a gaseous target

We measured the $K$-series X-rays of the $K^{-}p$ exotic atom in the SIDDHARTA experiment with a gaseous hydrogen target of 1.3 g/l, which is about 15 times the $\rho_{\rm STP}$ of hydrogen gas. At this density, the absolute yields of kaonic X-rays, when a negatively charged kaon stopped inside the target, were determined to be 0.012$^{+0.004}_{-0.003}$ for $K_{\alpha}$ and 0.043$^{+0.012}_{-0.011}$ for all the $K$-series transitions $K_{tot}$. These results, together with the KEK E228 experiment results, confirm for the first time a target density dependence of the yield predicted by the cascade models, and provide valuable information to refine the parameters used in the cascade models for the kaonic atoms.