Slowing-down times and stopping powers for similar to 2-MeV mu(+) in low-pressure gases

The times taken by positive muons (mu(+)) to slow down from initial energies in the range similar to 3 to 1 MeV, to the energy of the last muonium formation, approximate to 10 eV, at the end of cyclic charge exchange, have been measured in the pure gases H-2, N-2, Ar, and in the gas mixtures Ar-He, Ar-Ne, Ar-CF4, H-2-He, and H-2-SF6, by the muon spin rotation (mu SR) technique. At 1 atm pressure, these slowing-down times, tau(SD), in Ar and N-2, vary from similar to 14 ns at the highest initial energies of 2.8 MeV to 6.5 ns at 1.6 MeV, with much longer times, similar to 34 ns, seen at this energy in H-2. Similar variations are seen in the gas mixtures, depending also on the total charge and nature of the mixture and consistent with well-established (Bragg) additivity rules. The times tau(SD) could also be used to determine the stopping powers, dE/dx, of the positive muon in N-2, Ar, and H-2, at kinetic energies near 2 MeV. The results demonstrate that the mu(+) and proton have the same stopping power at the same projectile velocity, as expected from the historic Bethe-Bloch formula, but not previously shown experimentally to our knowledge for the muon in gases at these energies. The energy of the first neutralization collision forming muonium (hydrogen), which initiates a series of charge-exchanging collisions, is also calculated for He, Ne, and Ar. The formalism necessary to describe the stopping power and moderation times, for either muon or proton, in three energy regimes-the Bethe-Bloch, cyclic charge exchange, and thermalization regimes-is developed and discussed in comparison with the experimental measurements reported here, and elsewhere. The slowing-down times through the first two regimes are controlled by the relevant ionization and charge-exchange cross sections, whereas the final thermalization regime is most sensitive to the forwardness of the elastic scattering cross sections. In this regime the slowing-down times (to kT) at nominal pressures are expected to be less than or similar to 100 ns.