Time Delay in Electron Collision with a Spherical Target as a Function of the Scattering Angle

Abstract

We have studied the angular time delay in slow-electron elastic scattering by spherical targets as well as the average time delay of electrons in this process. It is demonstrated how the angular time delay is connected to the Eisenbud–Wigner–Smith (EWS) time delay. The specific features of both angular and energy dependencies of these time delays are discussed in detail. The potentialities of the derived general formulas are illustrated by the numerical calculations of the time delays of slow electrons in the potential fields of both absolutely hard-sphere and delta-shell potential well of the same radius. The conducted studies shed more light on the specific features of these time delays.

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

“…In Equation ( 8), the P (cos θ) denotes the Legendre polynomials, and e i2δ represents the scattering matrix element. The expression for angular phase shift is obtained as the argument of scattering amplitude f (k, θ), which is obtained by taking the inverse tangent of the ratio of its imaginary part to the real part as [50]:…”

“…Hence, the angular time delay for a wave packet scattered in the direction θ with momentum vector → k is given by [50]:…”

“…Note that the scattering phase shift concerned a particular partial wave and hence was denoted as δ , which is independent of the scattering angle. However, one can express the effective scattering phase shift that results due to the interference of different partial waves, which can be obtained as the complex phase shift of the total scattering amplitude [49,50]. Needless to say, the resulting scattering phase shift due to the interference of different partial waves is angle-dependent, which is permitted by the symmetry of each partial wave through the Legendre polynomial.…”

“…Although there have been theoretical and experimental studies on angular time delay from photoionisation, the same from an electron scattering perspective are rather rare in literature. A very recent work by Amusia et al [50] discussed angular time delay in slow-electron elastic scattering by spherical targets, which is the first time this method has been used, to the best of the authors' knowledge. In that work, the C 60 molecule was modelled using the Dirac bubble potential [60].…”

“…To fill the gap in understanding the temporal delay in elastic scattering, the present work investigated the angular time delay in the resonant e-C 60 scattering using the much-used annular square well (ASW) representation of the confinement. In the work of Amusia et al [50], the interference of only two partial waves was considered to elucidate the angle dependence of the time delay. The present work examined the role of all prominent partial waves and extended the study to the impact of interference of all partial waves on the angular time delay.…”