Confined variational calculation of $o$-Ps–He scattering properties

High-precision quantum-mechanical calculations have been developed to investigate positronium (Ps) scattering. Positronium scattering experiments are a powerful tool to study positronium-matter interactions, but the theoretical description of these experiments needs better accuracy. We have developed an ab initio confined variational approach that can reach higher collision energy, includes higher orbital momenta and uses small confining radii. Calculation of the Ps–He momentum-transfer cross section shows that the experimental Doppler broadening spectroscopy results are questionable. The energy dependence of the pickoff annihilation rate is also calculated, demonstrating an important role of the so far neglected $P$-wave contribution.

Figure 1

Probability density distributions of the electron (${\mathcal{C}}_1$) and positron (${\mathcal{C}}_4$) wave functions for $S$-wave $o$-Ps–He scattering with $k=0.1a_0^{-1}$. For $R>5a_0$ we have ${\mathcal{C}}_4/{\mathcal{C}}_1\approx 3$, i.e., the distortion of Ps can be neglected.

Figure 2

Comparison of theoretical and experimental results of ${\sigma }_m$ for $o$-Ps–He scattering. Theory: CVM with $R_0=15a_0$, open black circles; MBT, solid red line [26]; ${\mathrm{FTM}}_{2.5}^{\mathrm{vdW}}$, solid blue line [27]; ${\mathrm{FTM}}_{3.0}^{\mathrm{vdW}}$, solid green line [27]; ${\mathrm{FEG}}_{2.5}^{\mathrm{vdW}}$, solid yellow line [28]. Experiment: Canter et al., filled black square [19]; Rytsola et al., filled black circle [20]; Coleman et al., dash black line [21]; Nagashima et al., filled red triangle [22]; Skalsey et al., filled red circle [23]; Engbrecht et al., solid black line [24].

Figure 3

Momentum dependence of the pickoff annihilation rate for $o$-Ps–He scattering.