Regge oscillations in electron-atom elastic cross sections

Abstract

We consider a system trapped in a resonance state, whose decay at zero scattering angle can be related, through the optical theorem, to the total cross section ͑TCS͒. We show that for the resonance to contribute to the TCS a peak structure the resonance conditions must be satisfied: ͑i͒ Several rotations of the complex ͑the Regge trajectory-viz., imaginary part versus the real part of the complex angular momentum-stays close to the real axis͒ and ͑ii͒ coherent addition of forward-scattering subamplitudes ͑the real part of the Regge pole is close to an integer͒. We exploit the recent complex angular momentum approach of Macek et al. ͓Phys. Rev. Lett. 93, 183203 ͑2004͔͒, used to analyze low-energy oscillations observed in the elastic TCS for proton-H scattering, for a detailed analysis of Regge trajectories and their contributions to the TCS in electron-atom scattering for the case of Z = 75 using the model Thomas-Fermi potential. We conclude by demonstrating through comparison with existing theory and measurements that the Thomas-Fermi potential when used with the appropriate parameters captures the essential physics ͑Ramsauer-Townsend minima and the Wigner threshold law͒ in the near-threshold e-Ar and e-Kr elastic scattering.

The complex angular momentum (CAM) route to reactive scattering resonances: from a simple model to the F+H2→HF+H reaction

“…The reason the Mulholland formula (13) does not account for this remaining structure is simple. By construction [11], the Mulholland term contains contributions from the processes in which the resonance complex (the creeping wave) completes at least one full rotation. The slow oscillations, on the other hand come from the first round (ϕ 2π) whose contribution is hidden in two other terms in equation (13).…”

Low-energy electron elastic scattering from Mn, Cu, Zn, Ni, Ag, and Cd atoms

“…(1) is that a resonance is likely to affect the elastic TCS when its Regge pole position is close to a real integer [10].…”

“…In the CAM description of scattering we use the Mulholland formula [11] in the form [9,10] (atomic units are used throughout):…”

“…The Regge-pole methodology requires no a priori knowledge of the experimental or other theoretical data as inputs. Thus, in the near-threshold electron impact energy region the electron elastic scattering cross sections for the ground and excited states of the 5d transition metal atoms La, Hf, Pt and Au have already been studied carefully [12,13] using the Regge-pole methodology [9,10]. From the characteristic resonances in the elastic TCSs the EAs and the BEs of the excited anions were extracted and compared with available measurements.…”

“…Their wavefunctions are more diffuse than those for ground states of negative ions, which translate into the need for an even larger configuration interaction representation (expansion). It is in this context that the recent complex angular momentum (CAM) or Regge-pole methodology [9,10] has been developed; it calculates the elastic TCSs using the Mulholland formula [11]. The Regge-pole methodology requires no a priori knowledge of the experimental or other theoretical data as inputs.…”