Strong-field approximation for intense-laser–atom processes: The choice of gauge

The strong-field approximation (SFA) can be and has been applied in both length gauge and velocity gauge with quantitatively conflicting answers. For ionization of negative ions with a ground state of odd parity, the predictions of the two gauges differ qualitatively: in the envelope of the angular-resolved energy spectrum, dips in one gauge correspond to humps in the other. We show that the length-gauge SFA matches the exact numerical solution of the time-dependent Schrödinger equation.

Figure 1

(Color online) SFA electron-energy spectrum for emission in the (positive) direction of the laser field (four-cycle ${\sin }^2$ pulse with $\varphi =0$, $\omega =0.056\mathrm{a.u.}$, $E_0=0.0834\mathrm{a.u.}$) in L gauge, starting from an initial $1s$ (solid line) or $2p$ (dashed line) state. The corresponding V-gauge result is shown in the inset.

Figure 2

(Color online) Same as Fig. 1, but computed from the numerical solution of the TDSE.

Figure 3

(Color online) Direct comparison of TDSE and SFA (L-gauge) photoelectron spectra. The initial states are (a) $1s$ and (b) $2p$, the other parameters as in Fig. 1. For convenience, the TDSE spectra are rescaled (but unshifted in energy).