Analytic formulas for above-threshold ionization or detachment plateau spectra

Closed-form analytic formulas are derived in the tunneling limit for both above-threshold detachment (ATD) of negative ions and above-threshold ionization (ATI) of neutral atoms. These formulas are shown to give precise agreement with essentially exact single-active-electron numerical results for detached or ionized electron energies corresponding to the high-energy end of the ATD and ATI plateaus (with only a small constant shift of electron energies being required in the case of ATI). These formulas for ATI and ATD rates thus provide an analytic explanation for the well-known oscillatory patterns of ATI and ATD rates as functions of electron energy and of the parameters of the laser field. They also provide an analytic explanation for the dependence of these rates on the initial orbital angular momentum of the active electron. Most significantly, these formulas provide a fully quantum justification of the well-known classical three-step scenario for strong-field ionization and detachment spectra in the high-energy region of the ATI or ATD plateau.