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)).
Resonance scattering of positronium atoms by nitrogen molecules
We study theoretically the resonance scattering of positronium (Ps) atoms by nitrogen molecules and compare it with resonance e–N2 scattering in the Πg symmetry. The velocity positions of the Ps–N2 resonances in Σu, Πu, and Δg symmetries are very close to the velocity position of the e–N2 resonance which leads to the total Ps–N2 cross section being very similar to the e–N2 cross section when both are plotted as functions of the projectile velocity. However, in the Ps–N2 case the resonances are much wider and their positions vary much slower with increasing internuclear separation than in the e–N2 case. This makes the Ps-impact vibrational excitation cross section much smaller than the electron-impact vibrational excitation cross section, and no boomerang oscillations are observed in Ps–N2 scattering. We analyze the role of the static potential in the e–N2 case and compare exchange potentials for e–N2 and Ps–N2 interactions. This analysis allows us to explain the difference in the vibrational dynamics in these two cases.
ELECTRON SCATTERING FROM HYDROGEN
Kohn's variational principle was used to calculate Swave elastic scattering of electrons from atomic hydrogen, using up to 50 trial functions of the type introduced by Hylleraas to describe the bound states of two-electron atoms. The phase shifts calculated at several energies up to l0 ev apparentiy converged well, leaving residual uncertainties mostly less than one thousandth of a radian. Including the effect of the long-range force at zero energy, accurate values for the scattering lengths were obtained. (auth)