Photoionization phase shift and Wigner time delay of endohedrally confined atoms using transient phase methods

In contrast to the conventional finite difference methods, two transient phase methods have been effectively used in the present work to directly compute the photoionization phase shift and Wigner time delay of confined atoms (A@C60) in the single-active electron (SAE) approximation. The different phase methods: (A) employing logarithmic derivatives at shell boundaries, and (B) Born approximation are verified with the help of well-established finite difference methods in SAE approximation and sophisticated many-electron techniques. In this work, confinement oscillations on the dipole phase and photoelectron group delay following ionization from 1s subshell of H@C60, 3p subshell of Ar@C60 and 5p subshell of Xe@C60 are analyzed. The comparison with many-body calculation shows that the features in the time delay of a confined system are governed mainly by the effects of screening apart from that due to the external potential. A systematic study and comparison of the results from phase methods and many-electron techniques indicate that these techniques can be effectively used in the analysis of photoionization phase shift and time delay in confined atoms.