Semirelativistic Schrödinger Equation for Relativistic Laser-Matter Interactions

A semirelativistic formulation of light-matter interaction is derived using the so called propagation gauge and the relativistic mass shift. We show that relativistic effects induced by a superintense laser field can, to a surprisingly large extent, be accounted for by the Schrödinger equation, provided that we replace the rest mass in the propagation gauge Hamiltonian by the corresponding time-dependent field-dressed mass. The validity of the semirelativistic approach is tested numerically on a hydrogen atom exposed to an intense extreme ultraviolet laser pulse strong enough to accelerate the electron towards relativistic velocities. It is found that while the results obtained from the ordinary (nonrelativistic) Schrödinger equation generally differ from those of the Dirac equation, demonstrating that relativistic effects are significant, the semirelativistic formulation provides results in quantitative agreement with a fully relativistic treatment.