Derived properties from the dipole and generalized oscillator strength distributions of an endohedral confined hydrogen atom

We report the electronic properties of a hydrogen atom confined by a fullerene molecule by obtaining the eigenvalues and eigenfunctions of the time-independent Schrodinger equation by means of a finite-differences approach. The hydrogen atom confinement by a C-60 fullerene cavity is accounted for by two model potentials: a square-well and a Woods-Saxon. The Woods-Saxon potential is implemented to study the role of a smooth cavity on the hydrogen atom generalized oscillator strength distribution. Both models characterize the cavity by an inner radius R-0, thickness Delta, and well depth V-0. We use two different values for R-0 and Delta, found in the literature, that characterize H@C-60 to analyze the role of the fullerene cage size and width. The electronic properties of the confined hydrogen atom are reported as a function of the well depth V-0, emulating different electronic configurations of the endohedral cavity. We report results for the hyper-fine splitting, nuclear magnetic screening, dipole oscillator strength, the static and dynamic polarizability, mean excitation energy, photo-ionization, and stopping cross section for the confined hydrogen atom. We find that there is a critical potential well depth value around V-0 = 0.7 a.u. for the first set of parameters and around V-0 = 0.9 a.u. for the second set of parameters, which produce a drastic change in the electronic properties of the endohedral hydrogen system. These values correspond to the first avoided crossing on the energy levels. Furthermore, a clear discrepancy is found between the square-well and Woods-Saxon model potential results on the hydrogen atom generalized oscillator strength due to the square-well discontinuity. These differences are reflected in the stopping cross section for protons colliding with H@C-60.