S
-wave elastic scattering of 
o
-Ps from 
H2
 at low energy
The confined variational method is applied to investigate the low-energy elastic scattering of ortho-positronium from $\text{H}_2$ by first-principles quantum mechanics. Describing the correlation effect with explicitly correlated Gaussians, we obtain accurate $S$-wave phase shifts and pick-off 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, $A_s=2.06a_0$, and the zero-energy value of the pick-off annihilation parameter, $^1\!\text{Z}_\text{eff}=0.1858$. The obtained $^1\!\text{Z}_\text{eff}$ agrees well with the precise experimental value of $0.186(1)$ (J.\ Phys.\ B \textbf{16}, 4065 (1983)) and the obtained $A_s$ agrees well with the value of $2.1(2)a_0$ estimated from the average experimental momentum-transfer cross section for Ps energy below 0.3 eV (J.\ Phys.\ B \textbf{36}, 4191 (2003)).
Many-Body Theory for Positronium-Atom Interactions.
A many-body-theory approach has been developed to study positronium-atom interactions. As first applications, we calculate the elastic scattering and momentum-transfer cross sections and the pickoff annihilation rate ^{1}Z_{eff} for Ps collisions with He and Ne. For He the cross section is in agreement with previous coupled-state calculations, while comparison with experiment for both atoms highlights discrepancies between various sets of measured data. In contrast, the calculated ^{1}Z_{eff} (0.13 and 0.26 for He and Ne, respectively) are in excellent agreement with the measured values.
Theoretical Aspects of Positron Collisions in Gases
Publisher Summary This chapter discusses recent progress in the scattering and annihilation of low-energy positrons by simple atoms—in particular, hydrogen and helium. Superficially, positron–atom scattering might seem to be very similar to electron–atom scattering, the only difference being the sign of the charge of the incident particle. However, this change of sign of the charge has several very important consequences. The positron is distinguishable from the electrons in the target atom and therefore exchange effects with the incident particle are absent. In their place, however, are electronpositron correlations that take the form of states of positronium, the bound system of an electron and a positron. The potential energy of the positron in the static approximation is positive, whereas the polarization potential is negative, so that two major components in the positron–atom interaction tend to cancel each other. As a result, the low-energy scattering cross sections are much smaller than the corresponding electron–atom cross sections, and the actual values are quite strongly dependent on the accuracy of the polarization potential. A further feature of positron–atom collisions that has no counterpart at all in electron–atom collisions is electron–positron annihilation into two or three γ rays.