Positronium breakup versus hydrogen ionization in collisions with fast charged projectiles: a comparative study

TL;DR

The paper investigates the breakup of positronium (Ps) and the ionization of atomic hydrogen (H) by fast charged projectiles in the weak perturbation regime $Z_p e_0^2/bar v\ll 1$, isolating the effect of mass differences between Ps constituents. It develops a first-order semiclassical-quantum framework for a two-body target, derives a transition amplitude with coherent contributions from each constituent, and computes energy, angular, and momentum distributions, comparing Ps breakup to H ionization. The results show a strong mass-driven influence: Ps breakup is enhanced by constructive interference and its lower binding energy, yielding a total cross section about four times that of H ionization, while the heavy hydrogen nucleus acts as a passive spectator; the analysis provides simple Bethe-Born-type expressions that agree with numerical calculations and extends to fast electrons/positrons as projectiles. These findings clarify how target mass distribution shapes collision outcomes in weak perturbation regimes and offer quantitative benchmarks for Ps-beam experiments and related atomic-collision dynamics.

Abstract

We perform a comparative study of the breakup of positronium and ionization of atomic hydrogen by projectile-nuclei in the weak perturbation collision regime, $Z_p e_0^2/\hbar \ll v < c $ ($v$ is the collision velocity, $Z_p$ the projectile atomic number, $e_0$ the elementary charge and $c$ the speed of light). In this regime the only principal difference between the collisions with these atomic systems lies in the masses of their positively charged constituents. We have shown that the corresponding mass effects strongly influence the spectra of the target fragments and the total cross sections. This influence manifests itself via i) the significantly smaller binding energy in positronium resulting in smaller momentum transfers necessary to break the system, ii) a strong constructive interference between the inelastic scattering of the projectile on the electron and the positron in collisions with positronium that also increases the chances for the breakup and iii) the "passive" role of the hydrogen nucleus caused by its heavy mass that prohibits hydrogen ionization to proceed via the interaction between the projectile and the nucleus.

Figures (9)

• Figure 1: The energy spectra of the emitted electrons in the breakup of Ps(1s) and ionization of H(1s) by $3$ MeV/u projectiles (the collision velocity $\approx 11$ a.u.). Solid and dot curves: the emission in collisions with Ps(1s) calculated by including and neglecting, respectively, interference in the projectile scattering on the electron and positron. Dash curve: electron emission in collisions with H(1s).
• Figure 2: Same as in figure \ref{['figure-energy-MeV']} but for $1$ GeV/u projectiles (the collision velocity $\approx 120$ a.u., the collisional Lorentz factor $\gamma \approx 2.08$).
• Figure 3: The angular spectra of the target fragments in the breakup of Ps(1s) and ionization of H(1s) by $3$ MeV/u projectiles. Solid and dot curves: electron emission in collisions with Ps(1s) calculated by including and neglecting, respectively, interference in the projectile scattering on the electron and positron. Dash and dash-dot curves: electron and proton emission, respectively, in collisions with H(1s).
• Figure 4: Same as in figure \ref{['figure-angle-MeV']} but for an impact energy of $1$ GeV/u.
• Figure 5: The longitudinal momentum spectra of the target fragments in the breakup of Ps(1s) and ionization of H(1s) by $3$ MeV/u projectiles. Solid and dot curves: emission in collisions with Ps(1s) calculated by including and neglecting, respectively, interference in the projectile scattering on the electron and positron. Dash and dash-dot curves: electron and proton emission, respectively, in collisions with H(1s).