Determination of the time scale of photoemission from the measurement of spin polarization

adds important information to the previously published experimental data [39] (up to page 11 and App. A)

1 - contains too many unnecessary considerations which overshadow central result and its application to actual experimental data
2 - after the derivation of the time delays I would have expected suggestions how to measure or estimate the unknowns (in part done in [39])

I have a split opinion on the manuscript "Determination of the time scale of photoemission from the measurement of spin polarization" by Fanciulli and Dil. On the one hand, I am thankful for more elaborate follow-up papers of PRLs and other letter-style papers, on the other hand, there is not enough additional information in the manuscript (apart from an exceedingly long and in part confusing text) to warrant publication.

It starts with the concept of "interference". Since the electrons are distinguishable (spin) there is no two-path interference in this particular setup. Instead, as explained in Refs. [69,76,80], different initial and final states which may also include the direction of the outgoing electron will lead to different matrix elements and the observed polarization as shown in [72] for photoionization from Xe p-states. For this particular case the relative delay of the two contributing partial waves (s- and d-waves) can be evaluated and even classically estimated individually [6]. At this point (bottom of page 6: "The effects seen in photoionization are found also in photoemission from crystals"), a discussion on the matrix elements as in [69,76,80] and their influence on the result of Eq. (7) would have helped which is done implicitly in Sec. 2.1 by geometrical considerations influencing the polarization. Now, Eq. (14) could be inserted in Eq. 7 (side remark: the function $c(r,t)$ has two maxima/minima with $c=\pm 1$) and evaluated for the data at hand (appendix A and top of page 19). If the authors had stopped here this would have been a nice paper with a very general result applied to a specific experimental situation, add a short discussion about error estimates and that's it.

Instead, the second half of the manuscript contains a very general, lengthy discussion on possible time delays under various assumptions without clear indication why the reader should bother. And why should one vary the binding energy instead of the photon energy to change the kinetic energy of the outgoing electron? The argument of the Brillouin zone is not valid as the crystal structure should enter both the initial and final states of the electron (that is one of the reasons for the observed angular dependence of polarization) and why should a procedure become simpler by changing both initial and final states instead of the final state alone? Why should this have a smaller effect on the matrix elements than the "conventional" change of photon energy? This is not clear to me and adds unnecessary confusion in the manuscript as, of course, the photon energy has been changed in experiment (at least that is how I interpret Fig. 2a of [39]).

Finally, EWS(s) and EWS time delays are evaluated which we have learned are complicated functions of various parameters. Fig. 4 shows the delays as functions of r (are these results of the evaluation of Eqs. (26) and (27) from appendix A? Or is it silently assumed that $\dot r=0$? This is not indicated in the text. Where does the energy dependence of the polarization come from? Why the choice of other parameters? We find a reference to the experiment [39] only for the parameter choice in Fig. 5.). We see in Figs. 4 and 5 that any value from 0 to infinity appears to be possible (we have long dropped any signs) with uncertainties ("spurious effects") in all directions. It would probably have helped to analyze matrix elements as in [69,76,80] to assess the influences of different effects.

All in all, half of the paper would have been nice to read, maybe including an extended discussion on the derivation of the equations from [69,76,80]. Application to the data from [39], estimate for the error bars and then stop. All the rest of the paper is questionable, confusing, (in my view) unnecessary.

I recommend to revise the paper by making it more concise and strongly reducing its second half. Instead, a discussion of ways to experimentally determine the unknowns (e.g., discuss the experimental setup of [39]) and estimate remaining uncertainties would be interesting.