Photoionization from H@C60 and Ar@C60 is studied by employing two different model potentials to simulate the endohedral environment. The contrast between the diffusive Gaussian annular square well (GASW) and the compact annular square well (ASW) model potential on the photoionization dynamics is explored by studying the cross-section, phase shift, and Wigner time delay. A realistic description of the fullerene environment requires the right amount of diffuseness and compactness, and the proposed GASW model has both of these attributes. The dynamical properties of an encapsulated atom are studied systematically as a function of the well depth, and it is found that the GASW model induces mild and realistic confinement oscillations on the photoionization parameters in comparison with the ASW case. In addition, the present work brings out a few other interesting features. For a confining well depth of 1.03 a.u., the phase of the dipole matrix elements takes sharp jumps akin to the behavior of dipole phases at the Cooper minimum. In the case of free Ar, the correlation effects contribute less to the time delay in comparison with screening effects near the Cooper minimum. In search of a realistic potential to mimic confinement, the GASW model potential is recommended.
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