## Asymmetry (4) for θ = 45° as a function of the photon energy for different final multiplet states of Ar^{++}(3p^{4})

**Figure 5.** Asymmetry (4) for θ = 45° as a function of the photon energy for different final multiplet states of Ar^{++}(3p^{4}). The results are summed over the intermediate ionic fine-structure states Ar^{+}(3p^{5} ^{2}P_{1/2, 3/2}). Curves as in figure 1. Insets show angular distribution of electrons at the photon energies of 46.2 eV and 1 keV for the final ionic state Ar^{++}(3p^{4} ^{3}P) in the units [σ_{2}/4π] (see equation (3)). Dashed lines in the insets correspond to the dipole approximation.

**Abstract**

As an extension to recent developments in the theory of non-dipole effects in nonlinear photoprocesses in the XUV/x-ray wavelength regime, the sequential two-photon double ionization of the 3p shell in atomic argon is studied theoretically and compared to similar processes in the 2p shell of neon. The calculations predict distinct non-dipole effects in the region of the Cooper minimum in argon at photon energies around 50 eV, where they are of similar importance as at photon energies of more than 500 eV. The non-dipole effects should therefore be clearly observable in experiments performed at the present x-ray free electron lasers.