Time-Dependent Density-Functional Theory for Determining the Electron-Capture Cross Section for Protons Impacting on Atoms and Molecules

Abstract

The use of the Time-Dependent Density-Functional Theory (TDDFT) has increased in the atomic collision field. Calculating the electron-capture cross section (ECCS) for protons is an important question in hadrontherapy and plasma physics, among other areas. In previous studies, it was shown that the approach based on the Local Density Approximation (LDA) fails in the 1−50 keV region, requiring the use of the Optimized Effective Potential (OEP) method. In this work, the ECCS values for 1−50 keV protons impacting on isolated hydrogen, carbon, nitrogen, oxygen, and nitrogenous atoms were determined using the TDDFT. It is shown that adding the Self Interaction Correction to the LDA (LDA-Sic) allows obtaining results close to those provided by the OEP and experiments, with the advantage that the LDA-Sic consumes less computational time. In addition, it was demonstrated that it is imperative to include the spin correction for the specific helium and oxygen cases, in order to get good results for the ECCS using the TDDFT. Theoretical results obtained in this work show excellent agreement with experimental values.

Time-Dependent Density Functional Theory for Atomic Collisions: A Progress Report

“…Calculations at the ALDA level appear to overestimate the capture cross-section at low collision energies [41,42]. A spin-dependent ALDA calculation with self-interaction corrections included, on the other hand, showed better agreement with the experimental data in the low-energy range [23]. State-resolved TDDFT capture results were reported in [43].…”

“…A popular example of the former option is the (adiabatic) local density approximation (ALDA), which is based on the density dependence of the homogeneous electron gas. While this is a seemingly inadequate model for an inhomogeneous atomic density, as the existing body of work indicates, it works quite well in certain circumstances, in particular when combined with a self-interaction correction scheme [23].…”