$S$-wave elastic scattering of $o$-Ps from ${\mathrm{H}}_2$ at low energy

The confined variational method is applied to investigate the low-energy elastic scattering of orthopositronium from ${\text{H}}_2$ by first-principles quantum mechanics. Describing the correlations with explicitly correlated Gaussians, we obtain accurate $s$-wave phase shifts and pickoff annihilation parameters for different incident momenta. By a least-squares fit of the data to the effective-range theory, we determine the $s$-wave scattering length $A_S=2.02a_0$ and the zero-energy value of the pickoff annihilation parameter, ${}^1{Z}_{\text{eff}}=0.1839$. The obtained ${}^1{Z}_{\text{eff}}$ agrees well with the precise experimental value of 0.186(1) [G. L. Wright et al., J. Phys. B 16, 4065 (1983)] and the obtained $A_S$ agrees well with the value of $2.1\left(2\right)a_0$ estimated from the average experimental momentum-transfer cross section for positronium energy below 0.3 eV [F. Saito et al., J. Phys. B 36, 4191 (2003)].

Figure 1

Plot of the $s$-wave phase shift ${\delta }_0$ for ${\mathrm{\Sigma }}_g$ $o\text{–}\mathrm{Ps}\text{–}{\mathrm{H}}_2$ scattering as a function of $k$. The line represents an effective range fit using Eq. (21).

Figure 2

Plot of the $s$-wave pickoff annihilation parameter ${}^1{Z}_{\text{eff}}$ for ${\mathrm{\Sigma }}_{g}o\text{–}\mathrm{Ps}\text{–}{\mathrm{H}}_2$ scattering as a function of $k$. The line represents an effective range fit using Eq. (22).