Accurate evaluation of pressure effects on the electronic stopping cross section and mean excitation energy of atomic hydrogen beyond the Bethe approximation

Atomic hydrogen is used as a fundamental reference target system to explore pressure effects on the electronic stopping cross section, Se, of swift bare ions such as protons and α-particles. This is achieved by considering the hydrogen atom under pressure as a padded spherically-confined quantum system. Within this scheme, Se is calculated rigorously in the first Born approximation taking into account the full target excitation spectrum and momentum transfer distribution for different confinement conditions (pressures) and fixed projectile charge states. Pressure effects on the target mean excitation energy, I, are also formally calculated and compared with corresponding accurate calculations based on the Local Plasma Approximation (LPA). Even though atomic hydrogen is the simplest target system, its accurate treatment to account for the role of pressure in the stopping dynamics is found to provide useful means to understand the behavior of more complex systems under similar conditions. It is found that: (i) the region of projectile velocities for which the Bethe approximation remains valid is shifted towards higher values as pressure increases; (ii) shell corrections are enhanced relative to the free-atom case as pressure increases, and (iii) the LPA seems to underestimate I as pressure is increased. The results of this work for atomic hydrogen may serve as accurate benchmark reference values for studies of pressure effects on Se and I using different methodologies.