Optimal gauge and gauge invariance in non-perturbative time-dependent calculation of above-threshold ionization

We discuss the problem of the choice of the gauge in which to represent the electromagnetic field in the non-perturbative time-dependent study of the interaction of atoms with intense laser fields. Even though quantum mechanics is gauge invariant, the velocity gauge is more adopted then the length gauge for dynamical reasons. This property is even more severe when the problem is solved by expanding the wavefunction in spherical harmonics. The point is illustrated through the calculation of the above-threshold ionization photoelectron energy spectrum produced by atomic hydrogen under an intense laser pulse.