Gauge discrepancies in calculations of on helium

Abstract

We have studied the dependency and sensitivity of the triple differential cross section (TDCS) for (γ, 2e) on He with respect to the gauge formulation that one employs to represent the TDCS. This analysis has been performed using a variety of analytic initial-and final-state wavefunctions. It was found that the TDCS is very sensitive to the representation of the finalstate wavefunction in all geometries and all formulations of the TDCS. When the detected electrons are of unequal energy the TDCS is also sensitive to the initial-state wavefunction. The predictions using all combinations of initial-and final-channel wavefunctions are gauge dependent and vary enormously in absolute size.

Hyperspherical partial wave calculation for double photoionization of the helium atom at 20 eV excess energy

“…The results we have obtained, go to show that the hyperspherical three-particle scattering state wave function, used in the present calculation, must be reasonably accurate from small distances to the asymptotic region, since the results in all the three gauges are practically identical. In contrast, the 3C or other similar wave functions, which are not accurate at finite distances, show strong gauge dependence [30]. We also mention that the present calculation is free from any genuine difficulty and does not show any weakness worth mentioning.…”

Perturbative analysis of the triply differential cross section and circular dichroism in photo-double-ionization of He

“…It is only in the past decade or so that attention has shifted primarily to the triply differential cross section (TDCS), which describes the angular distribution of the two ionized electrons and which is a much more sensitive test of theoretical approximations and models. These more recent theoretical treatments of the differential and total cross sections have reverted to using correlated or uncorrelated ground-state wave functions and different kinds of improved analytical final-state wave functions, including the so-called 3C (three Coulomb) functions [13] (which satisfy the proper asymptotic boundary conditions for double ionization [14][15][16][17][18][19][20][21]), independent-particle final-state wave functions calculated in the field of momentum-dependent effective Coulomb charges [22,23], and modified 3C functions that involve momentum-dependent effective charges [21,24]. In general, even though the TDCS angular patterns are reproduced qualitatively, in those works where comparison with absolute experimental data is made (see, e.g., Refs.…”

Kinetic Energies in the Direct Double Photoionization of Helium and the Electron-Electron Correlation

“…If one finds an electron pair with the kinetic energy of CM motion around some ER, it means that its relative motion kinetic energy is around Er = Ε - ER. The agreement between our model and the experiment is quite good (except for Ε = 1 eV, where our plane-wave approximation for the CM motion should not work well). It may be well to add that there exist much more complicated [9] theories, which better describe the regularities observed in the weak-field experiments. However, it is the advantage of the SFA that enables us to study nonsequential double ioniZation also for superintense laser fields.…”

“…Theoreticians put a considerable effort into the detailed calculations for the (γ, 2e) on helium [9] (it is impossible to give all references and here we quote some recent articles only), because this is probably the simplest many-electron process. The purpose of this paper is not to improve such theories, but to show that some features of one-photon two-electron weak-field ionization may be described in a very simple way, which can be applied also to description of the strong-field ionization.…”