  We theoretically investigate kaonic atom states based on the latest high
precision data of the $2p$ states of the kaonic atoms in $^3$He and $^4$He
(J-PARC E62). We consider the phenomenological form for the optical potential
proportional to the nuclear density distributions and determine the potential
parameters by 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. Using the potential, we investigate the structure of the kaonic
atoms and kaonic nuclei for various nuclei up to Sn. We also report the optical
potential parameters suited for the global description of the atomic data, 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. In addition, we find that the study of the $1s$ states of the
kaonic helium atom is very interesting as a next step, and the determination of
the orbital angular momenta of the kaonic nuclear states is helpful for the
unified understandings of the atomic and nuclear bound states of kaon because
of the mutual influence between the atomic and the nuclear states of kaon with
the same orbital angular momentum.
