Shannon entropy and Fisher information for endohedral confined one- and two-electron atoms

•New results for the Shannon entropy and Fisher information of endohedral atoms.•For the 2s state of the H@C60 system, the Shannon entropy is increased ∼2.5%.•For the H@C60 system, the Fisher information is sensitive for excited-states.•The 1s ground-state of the He, Li+, Be2+@C60 systems are slight modified. In this work, we study the Shannon entropy and Fisher information of the H, He, Li+, and Be2+ atoms confined by a C60 cavity. The fullerene cavity is described by three model potentials: the square well (SW), Woods-Saxon (WS), and the Gaussian model (GM). We solved the time-independent Schrödinger and Hartree-Fock equations by means of a numerical method. We find that the C60 endohedral cavity modifies the ground- and excited-states of the hydrogen atom where the largest effect is given for the 2s state leading to an increase of ∼2.5% of the Shannon entropy. The Fisher information results for the excited-states are highly sensitive to the presence of the C60 cavity where the largest increase is reported for the 5s state with 50%. For the two-electron atoms, we find slight changes on the ground-state properties where the larger increase is for the Shannon entropy and Fisher information of the He atom in the ground-state. Our findings show that the GM potential leads to the largest change in electronic properties due to the overlap with the wave-functions. In the absence of the C60 cavity, our findings are in excellent agreement with other theoretical results.