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The excitation of H ($1s-2s$) by electron impact in the presence and in theabsence of the laser field is studied in the framework of the first Bornapproximation. The angular variation of the laser-assisted differential crosssection (DCS) for atomic hydrogen by electronic impact is presented at variouskinetic energies for the incident electron. The use of Darwin wave function asa semirelativistic state to represent the atomic hydrogen gives interestingresults when the condition $z/c\ll1$ is fulfilled. A comparison with the nonrelativistic theory and experimental data gives good agreement. It was observedthat beyond (2700 $eV$) which represents the limit between the two approaches,the non relativistic theory does not yield close agreement with our theory andthat, over certain ranges of energy, it can be in error by several orders ofmagnitude. The sum rule given by Bunkin and Fedorov and by Kroll and Watson\cite{22} has been verified in both nonrelativistic and relativistic regimes.

Laser-Assisted Semi Relativistic Excitation of Atomic Hydrogen by Electronic Impact