Angular dependent time delay near correlation induced Cooper minima

We analyze an angular dependence of the Wigner time delay near the Cooper minimum (CM) of the sub-valent ns shell in argon, krypton and xenon. Such an angular dependence is a result of interplay between the relativistic and correlation effects. The correlation with the outermost np valence shell induces a CM in the sub-valent ns shell which is otherwise CM free. A phase difference between the two spin-orbit split ionization continua Ep _1/2 and Ep _3/2 makes the Wigner time delay angular dependent. Both these effects are accounted for within relativistic formulations of the random phase approximation and the time-dependent density functional theory. Comparison between these two approaches illustrates a very strong sensitivity of the observed effect to the computation detail, especially the account of the ground state correlation.