An Investigation of the Resonant and Non-Resonant Angular Time Delay of e-C60 Elastic Scattering

Abstract

Time delay in electron scattering depends on both the scattering angle θ and scattered electron energy E. A study on the angular time delay of e-C60 elastic scattering was carried out in the present work. We employed the annular square well (ASW) potential to simulate the C60 environment. The contribution from different partial waves to the total angular time delay profile was examined in detail. The investigation was performed for both resonant and non-resonant energies, and salient characteristics in the time delay profile for each case were studied.

EWS Time Delay in Low Energy e−C60 Elastic Scattering

“…Care is taken to ensure the continuity of the wave function and its derivative at the boundary of C 60 . As in the earlier study [9], the elastic scattering phase shift (δ ℓ ) of the ℓ th partial wave is obtained by considering the asymptotic form of the wave function [53]:…”

“…The idea of time delay was initially proposed in the context of electron-scattering by Eisenbud [5], Wigner [6], and Smith [7]. Later, a few notable studies analyzed temporal dynamics in scattering [2,8,9]. The Eisenbud-Wigner-Smith (EWS) time delay is defined as the energy derivative of the scattering phase shift and it is an observable quantum mechanical parameter [1,[10][11][12].…”

“…On the theoretical side, a study by Amusia et al [2] used the Dirac bubble potential model of fullerene to analyze the time delay, taking into account six partial waves. Additionally, a study conducted by Aiswarya and Jose [9], employing only the annular square well (ASW) model potential analyzed the EWS and angular delay in e−C 60 scattering.…”

Angular time delay in quantum mechanical scattering

“…As described above, we match the energy eigenstates |E〉 for the two evolutions by identifying the 'in' part, i.e. we 'identify' the energy eigenstates (24) and (14). In other words, we identify two states for the evolution with and without potential if their decompositions (8) w.r.t.…”

“…Driven by the availability of attosecond light pulses, the topic of time delay in photoemission has attracted considerable attention in recent years, cf [8,9] for example. Also its angular dependence has been studied extensively in recent years, both theoretically and experimentally, see [10][11][12][13][14], for example. The angular time delay (2) was also suggested as a tool to identify resonances in reactive molecular collisions [15].…”