Gauge Problem in S-Matrix Theory of Above-Threshold Ionization

The gauge problem of Keldysh-Faisal-Reiss theories is discussed. It is found that the E-gauge used by Keldysh is more reasonable than the A-gauge used by Reiss. The Keldysh theory is then developed further. Its differential ionization rate gives more hot electrons than Reiss's and therefore better agrees the experimental result. The another remarkable point is that the differential ionization rate as a function of energy is rapidly oscillatory.