Partial wave analysis for folded differential cross sections

Abstract

The value of modified effective range theory (MERT) and the connection between differential cross sections and phase shifts in low-energy electron scattering has long been recognized. Recent experimental techniques involving magnetically confined beams have introduced the concept of folded differential cross sections (FDCS) where the forward (θπ/2) and backward scattered (θπ/2) projectiles are unresolved, that is the value measured at the angle θ is the sum of the signal for particles scattered into the angles θ and π−θ. We have developed an alternative approach to MERT in order to analyse low-energy folded differential cross sections for positrons and electrons. This results in a simplified expression for the FDCS when it is expressed in terms of partial waves and thereby enables one to extract the first few phase shifts from a fit to an experimental FDCS at low energies. Thus, this method predicts forward and backward angle scattering (0 to π) using only experimental FDCS data and can be used to determine the total elastic cross section solely from experimental results at low-energy, which are limited in angular range.

Elastic scattering and electronic excitation in positron interactions with neon

“…The discrepancy at the two lower energies remains unexplained. At 1, 2 and 3 eV, phase shifts were extracted from the experimental data for the lowest angular momentum components of the scattering, using the techniques developed by Machacek and McEachran [19]. These phase shifts agree reasonably with those calculated using the ROP theory at 1 and 2 eV, although the disagreement seen in the comparison of the measured cross section and theory at 3 eV is reflected in the phase shift comparison at this energy.…”

“…Table 1. Phase shifts extracted from the experimental data, using the fitting technique developed in reference [19]. Numbers in bracket represent the error in the phase shifts extracted in the fitting process.…”

“…For the lowest energy DCS measurements presented here, we are also able to fit the DCS curves to extract scattering phase shifts, as described in the recent work of Machacek and McEachran [19]. These phase shifts can be compared to the calculated values, as well as being used to reconstruct an 'unfolded' experimental DCS.…”

“…Figure 4. Unfolded DCS for (a) 1 eV, (b) 2 eV and (c) 3 eV, using the technique of Machacek and McEachran[19]. Blue solid lines are the DCS extracted from the fitting to the experimental data, with the red lines the ROP calculations presented in this paper.…”