Confined variational calculation of positronium-hydrogen scattering below the positronium excitation threshold

The confined variational method is used to study $S$-, $P$-, and $D$-wave positronium-hydrogen scattering with the scattering energy between 0.068 and 3.333 eV. Accurate phase shifts and $S$-wave scattering lengths are calculated and compared with other theoretical methods. Existing discrepancies for the $D$-wave phase shifts are resolved. According to collision momentum, total orbital angular momentum, and spin configuration, the distortion effects of positronium are quantitatively studied. Finally, the finite nuclear mass effects are investigated.

Figure 1

Probability density distributions $f_e\left(R\right)$ and $f_{e^{+}}\left(R\right)$ for $S$-, $P$-, and $D$-wave singlet Ps-H scattering at $k=0.1a_0^{-1}$, where $a_0$ is the Bohr radius.

Figure 2

Probability density distributions $f_{{\mathrm{ee}}^{+}}\left(R\right)$ and $f_{{\text{e}}^{+}}\left(R\right), {\text{ee}}^{+}$ denoting the center-of-mass of the electron-positron pair, for $S$-wave singlet and triplet Ps-H scattering at $k=0.05a_0^{-1}$, where $a_0$ is the Bohr radius.