Charge exchange collisions in the presence of competing processes: an integral equation approach

Abstract

The neutral fraction and spin depolarisation of positively charged particles during charge exchange have been investigated theoretically without simulations. In the charge exchange regime, both positive and neutral charge states contribute to the energy loss of the particle and the final product after thermalisation is determined by the competition between the charge exchange process and other energy-loss mechanisms. Integral equations for the neutral fraction and spin polarisation are expressed directly in terms of the cross sections of the atomic processes contributing to the slowing down of the particles. The integral equations for the positive muon in Ne have been solved self-consistently, where the cross section for the charge exchange, elastic and ionisation processes for positive as well as neutral species (muon and muonium, respectively) are obtained from the corresponding proton and hydrogen data by simple scaling schemes. The solutions of the integral equations are compared with experimental data obtained by the muon spin rotation ( ~s R ) technique and with the calculation based on Monte Carlo simulations reported before. It has been shown that the existing proton,/hydrogen data lead to an appreciable muonium fraction (20%) after thermalisation where experimentally no muonium has been observed (less than 3%). The discrepancy is attributed to uncertainties in the available electron loss cross sections of H in Ne at low energies. Scaling schemes of cross sections between muons and protons are also discussed.

Testing antimatter gravity with muonium

“…6). Low energy µ + elastic collision physics and Mu formation in helium gas, which were scaled from available data for protons, 27,28 were implemented into GEANT4, and simulations were done to compare with the data. In Fig.…”

Frictional Cooling Scheme for Use in a Muon Collider

“…The important physics processes for the simulation are lowenergy ionization, low-energy scattering, and charge exchange interactions [8]. The latter is a physics process written for CoolSim and is not a standard part of Geant4; it is discussed in detail below.…”

“…One of the main energy loss mechanisms at low energies for both protons and positive muons is the exchange of charge with the retarding medium through electron capture and loss [8]. The charged particle spends a significant portion of its trajectory as a neutral particle.…”

Low-energy μ+ via frictional cooling

“…Although the average density is low, the density in the foils is large, so the lower-energy particles have a significant probability to stop and decay. At low kinetic energies, a positively-charged particle picks up and loses electrons as it passes through the material [8]. With each passage of the beam through a foil, a fraction of the beam exits in the neutral charge state (muonium).…”