Classical-trajectory Monte Carlo calculation for collision processes ofe++(e−p) andμ++(μ−p)

Classical-trajectory Monte Carlo (CTMC) method is applied to the pickup process, A+(BC)→(AB)+C, of a bound light particle in a heavy particle by an incident light particle as well as the breakup process A+(BC)→A+B+C. Calculation has been made for the cross sections of the processes in the case of A=$e^{+}$,${\mu }^{+}$, B=$e^{\mathrm{-}}$,${\mu }^{\mathrm{-}}$, and C=p. The cross sections for positronium formation agree with those of recent quantum-mechanical calculations except for low impact velocities. The cross sections for (${\mu }^{+}$ ${\mu }^{\mathrm{-}}$) formation are smaller in magnitude than those of the quantum-mechanical calculations using the first-order Born approximation and the first-order distorted-wave Born approximation.