Applicability of modified effective-range theory to positron-atom and positron-molecule scattering

We analyze low-energy scattering of positrons on Ar atoms and ${\mathrm{N}}_2$ molecules using the modified effective-range theory (MERT) developed by O’Malley, et al. [J. Math. Phys. 2, 491 (1961)]. We use the formulation of MERT based on exact solutions of the Schrödinger equation with polarization potential rather than low-energy expansions of phase shifts into momentum series. We show that MERT describes the experimental data well, provided that effective-range expansion is performed both for $s$- and $p$-wave scattering, which dominate in the considered regime of positron energies $(0.4–2\mathrm{eV})$. We estimate the values of the $s$-wave scattering length and the effective range for $e^{+}\text{−}\mathrm{Ar}$ and $e^{+}\text{−}{\mathrm{N}}_2$ collisions.

Figure 1

(Color online) Total cross section for the scattering of positrons on argon versus the energy. Depicted are: Experimental data (squares), the theoretical fit based on effective-range expansion (solid line), its low-energy part given by Eqs. (5, 6, 7), and the theoretical results of McEachran et al. [17] (dashed line). The inset shows in addition the $s$- and $p$-wave cross-sections. Data are scaled by the characteristic distance $R^{*}$ and the characteristic energy $E^{*}$ of the polarization potential.

Figure 2

(Color online) The same as Fig. 1, but for the scattering of positrons on ${\mathrm{N}}_2$.