  We present an ab initio analytic theory to account for both the very low
energy 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 energy
structure (LES) [W. Quan et al. Phys. Rev. Lett. 103, 093001 (2009); C.I. Blaga
et al., Nat. Phys. 5, 335 2009)] of above threshold ionization. The origin of
both VLES and LES lies in a forward scattering mechanism by the Coulomb
potential. We parameterize the S matrix in terms of ?, which is the
displacement 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 Coulomb
scattering without absorption of light quanta. By devising a regularization
scheme, the resulting S matrix is non-singular when ? = 0, and the origins of
VLES and LES are revealed. We attribute VLES to multiple forward scattering of
near-threshold electrons by the Coulomb potential, with no absorption of light
quanta, signifying the role of the Coulomb threshold effect. We attribute LES
to be due to the combined role of the Coulomb threshold effect and rescattering
in the forward direction by the Coulomb potential with the absorption of light
quanta. A comparison of theory with experiment confirms these conclusions.
Further more, recently Dura et al. [Sci. Rep. 3, 2675 (2013)] reported the
detection of slow electrons at near zero momentum, at 1.3 meV, which is much
below the VLES, almost at threshold. Our theoretical formulation gives rise to
slow electrons at near zero momentum and at threshold. In addition, for
circularly polarized fields, it conserves the angular momentum in the
ionization process which necessitate the disappearance of the VLES, LES and the
slow electrons near threshold.
