Slowing-down times and stopping powers for ∼2-MeVμ+ in low-pressure gases
Abstract
The times taken by positive muons (μ+) to slow down from initial energies in the range ∼3 to 1MeV , to the energy of the last muonium formation, ≈10eV , at the end of cyclic charge exchange, have been measured in the pure gases H2 , N2 , Ar , and in the gas mixtures Ar-He , Ar-Ne , Ar-CF4 , H2-He , and H2-SF6 , by the muon spin rotation (μSR) technique. At 1atm pressure, these slowing-down times, τSD , in Ar and N2 , vary from ∼14ns at the highest initial energies of 2.8MeV to 6.5ns at 1.6MeV , with much longer times, ∼34ns , seen at this energy in H2 . 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 τSD could also be used to determine the stopping powers, dE/dx , of the positive muon in N2 , Ar , and H2 , at kinetic energies near 2MeV . The results demonstrate that the μ+ 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 ≲100ns .
- Publication:
-
Physical Review A
- Pub Date:
- October 2006
- DOI:
- 10.1103/PhysRevA.74.042708
- Bibcode:
- 2006PhRvA..74d2708S
- Keywords:
-
- 34.50.Bw;
- 36.10.Dr;
- 32.10.Fn;
- Energy loss and stopping power;
- Positronium muonium muonic atoms and molecules;
- Fine and hyperfine structure