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Hydrogen and helium ionization by relativistic projectiles in collisions with small momentum transfer

Hydrogen ionization in soft collisions with relativistic charged projectiles is considered for the ranges of parameters: (a) v Z<<v2, v0<<v<c; (b) Z<<v, v0<<v<c (here Z is the projectile charge, v the collision velocity, v0 the Bohr velocity in the hydrogen ground state, the Lorentz factor and c = 137 is the speed of light). Analytical expressions have been obtained for differential cross sections of hydrogen ionization accompanied by the emission of soft electrons. It is found that the electric-dipole interaction contributes most to the soft emission. An asymmetry in the angular distribution of soft electrons is found which can be interpreted as a result of two effects: (i) an absorption of virtual photon momenta by the atomic system, (ii) so-called `post-collision interaction'. These results are generalized to describe analytically soft-electron emission from helium colliding with relativistic projectiles. This generalization gives a simple fit to experimental data on both differential and total cross sections for helium single ionization in a wide range of projectile charges and velocities.