In the framework of the first Born approximation, we investigate the scenario where in addition to a laser field, a nuclear Coulomb field is also present to affect a proton. We work in the approximation in which the proton is considered to be a structureless spin 1/2 Dirac particle with a mass m p . Furthermore, in the laboratory system, the fixed nucleus is treated as a point-like Coulomb potential. In the presence of a laser field, and taking into account the Coulomb effect, the proton will be described by distorted Dirac-Volkov wave functions. The introduction of the Coulomb effect to both the incident and scattered proton will enhance the relativistic differential cross sections (RDCSs). Regarding the physical picture, it is found that for the various kinetic energies of the incident proton, the Coulomb effect can be neglected at high kinetic energies in this particular geometry. Therefore, Dirac-Volkov states are largely sufficient to describe the laser-dressed protons. The behavior of the various RDCSs versus the atomic number Z is also presented.

A theoretical treatment, using the first Born approximation, is presented to analyse the results of relativistic laser-assisted proton – hydrogen atom scattering. Specific calculations are carried out for excitation of hydrogen atoms from 1s1/2 to 2s1/2 states by proton impact. We work in an approximation in which the incoming proton may be described by Dirac–Volkov states in the presence of a laser field. Semi-relativistic Darwin wave functions are used to describe the hydrogen atom in its initial and final states, while relativistic, spin, and laser interaction effects are also accounted for. The results presented in this paper show that the differential cross section for this process depends not only upon the energy of the incident proton, but also upon its interaction with the laser field through intensity and frequency.

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Relativistic triple differential cross-sections (TDCS) for ionization of hydrogen atoms by positron impact have been calculated in the symmetric coplanar geometry. We have used Dirac wave functions to describe free electron's and positron's sates. The relativistic formalism is examined by taking the non relativistic limit. Present results are compared with those for the corresponding electron-impact case. In the first Born approximation, we found that the TDCS for positron impact ionization exceeds that for electron impact for all energies in accordance with the result obtained by several other theories.