Angular dependence of Wigner time delay: Relativistic Effects

Laser assisted photoionization time delay mainly consists of two parts: Wigner time delay, and time delay in continuum-continuum transition [1]. Wigner time delay results from the energy derivative of the phase of the photoionization amplitude (matrix element). In general, the photoionization time delay is not the same in all directions relative to the incident photon polarization [2], although when a single transition dominates the amplitude, the resultant time delay is essentially isotropic. The relativistic-random-phase approximation [3] is employed to determine the Wigner time delay in photoionization from the outer np subshells of the noble gas atoms, Ne through Xe. The time delay is found to significantly depend on angle, as well as energy. The angular dependence of the time delay is found to be quite sensitive to atomic dynamics and relativistic effects, and exhibit strong energy and angular variation in the neighborhood of Cooper minima [4]. Work supported by DOE, Office of Chemical Sciences and DST (India). [1] R. Pazourek, S. Nagele and J. Burgd\"{o}rfer, Rev. Mod. Phys. \textbf{87}, 765 (2015) and references therein; [2] J. W\"{a}tzel, A. S. Moskalenko, Y. Pavlyukh and J. Berakdar, J. Phys. B \textbf{48}, 025602 (2015); [3] W. R.Johnson and C. D. Lin., Phys. Rev. A\textbf{ 20}, 964 (1979); [4] J. W. Cooper, Phys. Rev., \textbf{128}, 681 (1962).