Nondipole Effects in Photo-Double-Ionization of He by a vuv Photon

Circular dichroism at equal energy sharing in photo-double-ionization of He

“…One may expect this rule to fail if one treats the electron-photon interaction beyond the EDA, i.e., if one introduces the dependence of the TDCS upon the wave vector of the incident light wave (or upon its spatial inhomogeneity). As has been shown recently [18] (for the case of the quadrupole-induced asymmetry of the TDCS with respect to the direction of a linearly polarized photon beam), retardation effects can modify the TDCS considerably even at relatively small excess energies. Though existing measurements of the CD effect [12][13][14][15][16] do not show any signatures of nondipole effects, this fact is expected because all of them have been performed in the orthogonal geometry (i.e., when the photon wave vector, k, is orthogonal to the detection plane spanned by the vectors p 1 and p 2 ), in which case the lowest-order retardation effects do not contribute to the TDCS [18].…”

“…(This "degenerate" asymmetry for the case of linear polarization has been discussed in Ref. [18].) The difference in (i) and (ii) for 0,…”

“…In terms of the vectors p 1 ± p 2 and the symmetrized (gerade and ungerade) amplitudes a g,u [1,8,19]; note that f ͑g,u͒ =2a g,u .] The parametrization of our symmetrized amplitudes in terms of Legendre polynomials and reduced matrix elements follows immediately from that for the functions f͑p , pЈ , cos ͒ [7] and g͑p , pЈ , cos ͒, g s ͑p , pЈ , cos ͒ [18].…”

“…The dependence of the functions g and g s on the mutual angle have been parametrized in Ref. [18] in terms of derivatives of the Legendre polynomials, P l ͑cos ͒, and reduced matrix elements of the quadrupole momentum operator between the initial 1 S 0 -state, ͉0͘, and the D-wave component of the two-electron continuum state, ͉p 1 p 2 ͘, with individual angular momenta l and lЈ = l, l ± 2. The parametrization of the dipole amplitude, A d , is well-known (see, e.g., Refs.…”

Nondipole Effects in Double Photoionization of He

“…[3], to derive a parametrization of the quadrupole amplitude Aq we use the expansion (5) and the reduction formulae [3] for the rank-2 bipolar harmonics. Thus, Aq may be presented as follows [2,5]:…”