Investigation of Kaonic Atom Optical Potential by the High-Precision Data of Kaonic 3He and 4He Atoms

Abstract We investigate kaonic atom optical potentials of $^3$He and $^4$He phenomenologically based on the latest high-precision data of the $2p$ states of the kaonic atoms in helium (J-PARC E62). We consider a simple phenomenological form for the optical potential proportional to the nuclear density distributions and clarify the meanings and implications of the data by determining the potential parameters using the latest data. We find two sets of potential parameters for each of $K^--^3$He and $K^--^4$He that reproduce the data. We then extract the potential parameters consistent with the data of $^3$He and $^4$He atoms simultaneously. We report the possible strong isospin dependence of the potential, and the different strength of the data of $K^--^3$He and $K^--^4$He in the restrictions on the potential parameters. We mention that the study of the $1s$ states of the kaonic helium atom is very interesting as a next step. Observing these states could provide valuable information on potential parameters and kaonic nuclear s states because of the mutual influence between the atomic and the nuclear states of kaons with the same orbital angular momentum.