Recombination-amplitude calculations of noble gases, in both length and acceleration forms, beyond the strong-field approximation

Abstract

Transition of an electron from a free to a bound state is critical in determining the qualitative shape of the spectrum in high-order-harmonic generation (HHG), and in tomographic imaging of orbitals. We calculate and compare the recombination amplitude, from a continuum state described by a plane wave and an outgoing scattering eigenstate, to the bound state for the noble gases that are commonly used in HHG. These calculations are based on the single active electron model and the Hartree-Fock-Slater method, using both the length form and the acceleration form of the dipole matrix element. We confirm that the recombination amplitude versus emitted photon energy strongly depends upon the wave function used to describe the free electron. Depending on the choice of the wave function and the dipole form, the square of the absolute value of the recombination amplitude can differ by almost two orders of magnitude near the experimentally measured Cooper minima. Moreover, only the outgoing scattering eigenstates with the length form roughly predict the experimentally observed Cooper minimum for Ar (∼50 eV) and Kr (∼85 eV). We provide a detailed derivation of the photorecombination cross sections from photoionization cross sections (PICSs) calculated by the relativistic random phase approximation (RRPA). For Ar, Kr, and Xe, we compare the total PICSs calculated using our recombination amplitudes with that obtained from RRPA. We find that PICS calculated using the outgoing scattering eigenstates with the length form is in better agreement with the RRPA calculations than the acceleration form.

Compton spectra of atoms at high x-ray intensity

“…Lastly, xatom has been extended to treat atoms and ions immersed in a plasma environment to investigate ionization potential lowering in warm dense matter [62,63], which has further been employed for studying x-ray resonant magnetic scattering in materials [64]. Also note that the atomic electronic continuum states that are accurately calculated by xatom have been used for modeling high harmonic generation of rare gas atoms [65]. Inclusion of resonant photoexcitation and of relativistic effects for heavy atoms is in progress [66].…”

Complete reconstruction of ultra-broadband isolated attosecond pulses including partial averaging over the angular distribution

“…The photoionization matrix elements for the target gas were obtained from Kheifets [36] for the case of xenon (shown in Fig. 4(B)) and from Bhardwaj [37] in the case of helium. For the xenon ionization potentials the following values were used: I p,5p = 12.1 eV, I p,5s = 23.4 eV [32], and I p,4d = 67.5 eV [33].…”

“…Here, it is shown, that the ML-VTGPA method, when reduced to a single line (N s = 1, similar to the original implementation [26]), is also suitable for attosecond pulses shorter than the atomic unit in time. To show this, a streaking trace with a τ SXR = 20 as, chirp-free (flat phase) pulse at a central photon energy of W 0 = 260 eV was reconstructed using the ML-VTGPA method, where the PMEs for helium [37,39] were used. The retrieved streaking spectrogram is shown in Fig.…”

Volkov transform generalized projection algorithm for attosecond pulse characterization

“…Argon was used as a target gas in the simulation. The DTME used for simulating the spectrogram was calculated using the method described in [24]. The resulting spectrogram is shown in figure 3.…”

“…For instance, a pulse with a bandwidth of 30-40 eV can be retrieved within 15-20 min using our current implementation. This makes the VTGPA an attractive choice even for narrower bandwidths in regions where the DTME is highly dispersive, such as at low energies [24]. While preliminary, we have also begun testing methods that ignore samples in the EUV pulse that are not contributing significantly to the fit, which have shown speed enhancements up to 33%.…”