Scattering of near-zero-energy electrons and positrons by $H_2$

The parameters for $S$-wave elastic scattering of near-zero-energy electrons and positrons by $H_2$ molecules are calculated using the stabilization method with explicitly correlated Gaussians. The confined variational method is applied to optimize the Gaussians to describe the short-range interaction of incident $e^{\pm }$ with $H_2$ in the fixed-nuclei approximation. For $e^{+}$-$H_2$ scattering the scattering length of previous work [Phys. Rev. Lett. 103, 223202 (2009)] is substantially improved. More importantly, for $e^{-}$-$H_2$ scattering, from first principles, the scattering length is computed as a function of the internuclear distance. In the case that the two nuclei are at the equilibrium distance the results are in a good agreement with values derived from fitting experimental total and diffusion cross sections to the modified effective range theory.

Figure 1

Scattering length $A_{\mathrm{scat}}$ as a function of the angle ${\theta }_3$ for $e^{+}$-$H_2$ scattering.

Figure 2

Annihilation parameter $Z_{\mathrm{eff}}$ as a function of the angle ${\theta }_3$ for $e^{+}$-$H_2$ scattering.

Figure 3

Scattering length $A_{\mathrm{scat}}$ as a function of the internuclear distance $R$ for $e^{+}$-$H_2$ scattering.

Figure 4

Annihilation parameter $Z_{\mathrm{eff}}$ as a function of the internuclear distance $R$ for $e^{+}$-$H_2$ scattering. The experimental values are those from Table 1.

Figure 5

Scattering length $A_{\mathrm{scat}}$ as a function of the angle ${\theta }_3$ for $e^{-}$-$H_2$ scattering.

Figure 6

Scattering length $A_{\mathrm{scat}}$ as a function of the internuclear distance $R$ for $e^{-}$-$H_2$ scattering. Empty and filled circles: $A_{\mathrm{scat},\parallel }$ without and with polarization correction, respectively. Empty and filled squares: $A_{\mathrm{scat},\perp }$ without and with polarization correction, respectively. The triangle and diamond symbols refer to the references from Table 2.