Wigner Time Delay in Photoionization: A Simple 1D Model Study

In scattering theory, the Wigner time delay, calculated through phase shifts derivative, has been demonstrated to measure the amount of delay or advance experienced by an incoming particle during its interaction with the scattering potential [1]. Fetic, Becker, and Milosevic claim that this concept cannot be extended to include photoionization viewed as a half-scattering experiment [2]. Their argument is based on the lack of information about scattering phase shifts in the part of the wave function (satisfying the incoming-wave boundary condition) going to the detector. This work aims to test this claim by examining a photoionization process in a simple 1D model with a short-range symmetrical potential. Using time-dependent perturbation theory with a dipole interaction, the relevant wave packet of the outgoing particle is analyzed and compared to the free wave packet as a reference. Our findings reveal a time delay in the analytic form of the liberated particle wave packet determined directly through the scattering phase shifts. We further support this result by carrying out a numerical simulation for both the non-free wave packet and the free one. The amount of the observed time delay is found to be half of that appearing in a typical collision experiment.



[1] F. T. Smith, Lifetime Matrix in Collision Theory, Phys. Rev. 118, 349 (1960).

[2] B. Fetic, W. Becker, and D. B. Miloševic, Can we measure the Wigner time delay in a photoionization experiment?, arXiv:2210.05219, (2022).