Photoionization from H@C ₆₀ and Ar@C ₆₀ 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.

Relativistic and correlation effects in endohedrally confined atoms ($A@{\mathrm{C}}_{60}$) have been investigated using many-body techniques. The endohedral environment is approximated as an atom trapped in a spherically symmetric Gaussian annular square well model potential. The objective of the work is to present Shannon entropy as an indicator of (i) correlation effects and (ii) relativistic effects in confined atoms. The correlation energy in $\mathrm{Be}@{\mathrm{C}}_{60}$ is studied as a function of the depth of the confining potential to give some idea as to how Shannon's correlation entropy is sensitive to the minimum location of correlation energy. To see the prominent relativistic effects in the confined atom, Shannon's relativistic entropy of the valence subshell of $\mathrm{Ba}@{\mathrm{C}}_{60}$ is scrutinized for different confinement parameters. The influence of relativistic and correlation effects on the Shannon entropy of confined atoms is illustrated.

Using ${\mathrm{Cl}}^{-}$ as a test case, Wigner time delay in the photodetachment process has been investigated theoretically, along with the photoionization of the isoelectronic Ar atom, for the outer $3p$ shell using the relativistic-random-phase approximation (RRPA). Time delay was probed in these systems from threshold to 80 eV, to investigate threshold effects, the centrifugal barrier shape resonance, and the Cooper minimum region. This study focuses on ${\mathrm{Cl}}^{-}$ because, for negative ions, the phase of the photoemission process is not dominated by the Coulomb phase as it is in photoionization. The results show significant differences, both qualitative and quantitative, between the time delays for ${\mathrm{Cl}}^{-}$ and Ar photoemission at low photoelectron energy, but they are rather similar in the Cooper minimum region, where the Coulomb phase is small. In particular, the Wigner time delay in ${\mathrm{Cl}}^{-}$ exhibits a dramatic energy dependence just above threshold, and a rapidly increasing time delay in the vicinity of the shape resonance. A strong angular dependence of time delay has also been found near the threshold region for the ${\mathrm{Cl}}^{-}$ case, and is absent in the case of the photoionization of Ar. The origin of these phenomenologies is explained and a prospectus for future work is presented.