Alternative Approach for the Determination of Mean Free Paths of Electron Scattering in Liquid Water Based on Experimental Data

Abstract

In a recent comment, 1 Ruth Signorell raises a number of issues that she considers to question the validity of our approach to determine mean free paths for electron scattering in liquid water 2 and our comparison with the results on amorphous ice by Michaud, Wen, and Sanche. 3 Here, we show that these critiques are unjustified, being either unfounded or based on misconceptions by the author of the comment. We nevertheless welcome the opportunity to further clarify certain aspects of our work that we did not discuss in detail in our letter. 2 Our reply is structured as the comment, i.e., the four main points of the comment are discussed individually.(1) Signorell incorrectly claims that the effective attenuation length (EAL) as defined in our work is different from the definition used in the analysis of the measurements of Suzuki et al. 4 , which we take as input for our simulations.Both our work and the analysis of Suzuki et. al. are based on the same standard definition of the EAL, i.e., the electron signal S(z) detected outside the liquid decays exponentially with the distance from the point of ionization to the surface z,and the EAL r EAL is the width parameter of 0 r EAL ionization depth 0 N photoelectron signal Ne z/rEAL Figure 1: Exponential decay of the photoelectron signal with ionization depth. The area under the exponential function is equal to the area in the box given by N × r EAL , which is used by Suzuki et al. 4 to determine r EAL experimentally. 1 arXiv:2003.05820v1 [physics.chem-ph]

Attosecond spectroscopy of liquid water

“…The nuclear configurations for the water clusters were chosen to be those obtained from ab-initio calculations (56) with lowest energy. The differential scattering cross sections (DCS) for the monomer compare well with experimental measurements and the DCS also converge rapidly with cluster size, as explained in (38). Hence, we use the calculations for the water heptamer cluster as approximations for scattering in bulk water.…”

“…The default values assumed for the calculations presented here are EMFP = 0.40 nm, N ela = 11 for sideband q = 14, and EMFP = 0.55 nm, N ela = 9 for sideband q = 20. We note that those were preliminary values, with more accurate values determined later as EMFP = 0.56 nm, N ela = 7 for sideband q = 14, and EMFP = 0.84 nm, N ela = 6 for sideband q = 20 (38). However, we did not repeat the expensive calculations because the dependencies of the non-local delay on EMFP and N ela presented here illustrate that not much difference is to be expected: If those more accurate values were used, the already negligible estimated contribution of ca.…”

“…However, our Monte-Carlo calculations show that τ nl is very small in our case, such that the contribution of τ nl is not significant for the results presented in this article. The values for the elastic and inelastic mean free path, EMFP and IMFP, are determined as described in (38). For the analysis of the calculations, the mean number of elastic scatterings…”

“…Details of this procedure are given in Ref. (38). The relevant EMFPs (IMFPs) amount to 0.56 nm (3.8 nm) + Figure 4: Contributions of photoionization and scattering to the measured delays.…”

“…Our model is based on semi-classical Monte-Carlo trajectory calculations, but includes the phases and amplitudes derived from a quantum-mechanical treatment of photoionization, electron scattering, LAPE, LAES and transport in three dimensions, which were derived from our earlier one-dimensional model (36). The Monte-Carlo trajectory calculations rely on accurate complex-valued scattering factors obtained from ab-initio scattering calculations of electrons with water clusters, for which convergence of the DCS has been observed with increasing cluster size and they use the associated values of the EMFP and IMFP (38). More than 10 8 classical trajectories were launched from at least 10 3 randomly selected initial positions with a momentum of either k q−1 or k q+1 (where q = 14 or 20 are realized in different sets of calculations).…”