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Transition of an electron from a free to a bound state is critical indetermining the qualitative shape of the spectrum in high-order harmonicgeneration (HHG), and in tomographic imaging of orbitals. We calculate andcompare the recombination amplitude, from a continuum state described by aplane wave and an outgoing scattering eigenstate, to the bound state for thenoble gases that are commonly used in HHG. These calculations are based on thesingle active electron model and the Hartree-Fock-Slater method, using both thelength form and the acceleration form of the dipole matrix element. We confirmthat the recombination amplitude versus emitted photon energy strongly dependsupon the wavefunction used to describe the free electron. Depending on thechoice of the wavefunction and the dipole form, the square of the absolutevalue of the recombination amplitude can differ by almost two orders ofmagnitude near the experimentally measured Cooper minima. Moreover, only theoutgoing scattering eigenstates with the length form roughly predict theexperimentally observed Cooper minimum for Ar (~50 eV) and Kr (~85 eV). Weprovide a detailed derivation of the photorecombination cross sections (PRCSs)from photo ionization cross sections (PICSs) calculated by the relativisticrandom phase approximation (RRPA)., For Ar, Kr and Xe, compare the total PICSscalculated using our recombination amplitudes with that obtained from RRPA. Wefind that PICS calculated using the outgoing scattering eigenstates with thelength form is in better agreement with the RRPA calculations than theacceleration form.

Recombination Amplitude Calculations of Noble Gases, in Length and Acceleration Forms, beyond Strong Field Approximation