Convergence of the method of the hypersphericalRmatrix with semiclassical outgoing waves

Abstract

A systematic study is reported on the convergence of computed triply differential cross sections for photodouble ionization of helium at 20 and 25 eV above threshold, obtained using the hyperspherical R matrix with semiclassical outgoing waves method. Such a study has become feasible due to an essential improvement in the description of the radial correlation coordinate ␣ = arctan͑r 2 / r 1 ͒ at short range, and to the implementation of the code on a more powerful computer. It shows that the size requirements of the inner region R ഛ R 0 , with R = ͱ r 1 2 + r 2 2 , vary considerably depending on the dynamic situation considered. Typically, while R 0 Ӎ 20 a.u. proves sufficient in most circumstances, one has to increase the inner region up to R 0 Ӎ 60 a.u. in order to reach convergence in the triply differential cross sections obtained for very asymmetric energy sharings or in the particular case when one electron is ejected along the electric field for linearly polarized photons. The converged calculations are generally in very good agreement with new experimental data of high statistical quality recorded in the latter case, at 25 eV above threshold, for various energy sharings. The dynamic situations identified here call for further experimental and theoretical studies.

Universal few-body physics and cluster formation

“…Going beyond the double escape threshold law proved to be highly challenging, with some of the first credible absolute cross sections from a theoretical calculation, for the fundamental e + H → e + e + p process, emerging first in the numerical "convergent close-coupling" studies by (Bartlett et al, 2003;Bray and Stelbovics, 1993;Kadyrov et al, 2009), performed in ordinary independent electron coordinates. One of the first studies that obtained competitively accurate results within a hyperspherical coordinate framework was that of Watanabe, 1995, 1997), and it was followed by a subse-quent detailed study by (Kazansky et al, 2003;Malegat, 2003Malegat, , 2004Selles et al, 2004). Highly quantitative results are also now obtained for this two-electron escape process by direct solution of the time-independent (Mc-Curdy et al, 2004) or time-dependent (Pindzola and Robicheaux, 1998;Pindzola et al, 2007) Schrödinger equation.…”

Photodouble ionization and the dynamics of electron pairs in the continuum

“…One of main achievements in all cases is the agreement with the measured energy distributions, which are flat in the threshold region and become U shaped at higher energy, as already mentioned. As for the TDCSs a comparison of HRM-SOW with recent measurements at E = 25 eV, θ 1 = 0 and R = 0.087, 0.25, 0.39 is shown in figure 8 (from Selles et al (2004a)). Apart from small asymmetries of the data, all the shapes are well reproduced by the theory, but the latter converges very slowly.…”

Analysing a two-electron wavepacket by semiclassically propagating its Fourier components in space

“…Having satisfied this condition, we may define the local Fourier transform on this hypersphere -for any energy in the spectral bandwidth of the pulse. To finish, we express this Fourier transform in the adiabatic partial wave representation provided by a previous diagonalization of H at (R 0 ; Ω 5 ) within the 5D angular representation used in HRM-SOW calculations [7,29]. To monitor the accuracy of the various changes of basis involved in this operation, we define a norm on the hypersurface and control its conservation.…”

“…They become negligible in magnitude as soon as all significant SI channels are accounted for by the fully quantum inner-region treatment. This point was considered earlier [29], at least indirectly, in a convergence study of triply differential cross sections (TDCS) with the size of the inner region. It will be discussed in more detail in a forthcoming publication.…”