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We present an ab initio analytic theory to account for both the very lowenergy structure (VLES) [C. Y. Wu et al., Phys. Rev. Lett. 109, 043001 (2012);W. Quan et al., Phys. Rev. Lett. 103, 093001 (2009)], and the low energystructure (LES) [W. Quan et al. Phys. Rev. Lett. 103, 093001 (2009); C.I. Blagaet al., Nat. Phys. 5, 335 2009)] of above threshold ionization. The origin ofboth VLES and LES lies in a forward scattering mechanism by the Coulombpotential. We parameterize the S matrix in terms of ?, which is thedisplacement of the the classical motion of an electron in the laser field.When ? = 0, the S matrix is singular, which we attribute to be forward Coulombscattering without absorption of light quanta. By devising a regularizationscheme, the resulting S matrix is non-singular when ? = 0, and the origins ofVLES and LES are revealed. We attribute VLES to multiple forward scattering ofnear-threshold electrons by the Coulomb potential, with no absorption of lightquanta, signifying the role of the Coulomb threshold effect. We attribute LESto be due to the combined role of the Coulomb threshold effect and rescatteringin the forward direction by the Coulomb potential with the absorption of lightquanta. A comparison of theory with experiment confirms these conclusions.Further more, recently Dura et al. [Sci. Rep. 3, 2675 (2013)] reported thedetection of slow electrons at near zero momentum, at 1.3 meV, which is muchbelow the VLES, almost at threshold. Our theoretical formulation gives rise toslow electrons at near zero momentum and at threshold. In addition, forcircularly polarized fields, it conserves the angular momentum in theionization process which necessitate the disappearance of the VLES, LES and theslow electrons near threshold.

Origin of the Low Energy Structure in Above Threshold Ionization