Recoil-ion-momentum spectrum for few-photon double ionization of helium

We provide an efficient and accurate numerical method to deduce the recoil-ion-momentum spectrum of He from the two-electron momentum distribution, which is obtained by solving the full-dimensional time-dependent Schrödinger equation. We apply this method to study the ion spectra of one-photon double ionization and two-photon sequential and nonsequential double ionization of He. The present calculations agree rather well with the absolute magnitude of the recoil-ion triply differential cross sections published recently [S. A. Abdel-Naby, M. S. Pindzola, and J. Colgan, Phys. Rev. A 86, 013424 (2012); S. A. Abdel-Naby et al., Phys. Rev. A 87, 063425 (2013)]. Nevertheless, significant differences are also found in several detailed features of the spectra and straightforward physical analysis indicates that the present results appear more reasonable, which should be confirmed by future experiments or additional independent calculations.

Figure 1

Recoil-ion singly differential cross section for the one-photon double ionization at a photon energy of 99 eV. The present numerical calculation is compared with the experimental measurement [28] and the theoretical calculations of [19, 24].

Figure 2

Recoil-ion triply differential cross section for the one-photon double ionization at photon energies of 99, 125, and 225 eV. We show the signals along the axis that is (a)–(c) perpendicular [(d)–(f) parallel] to the laser polarization, where $Q_y=Q_z=0$ ($Q_x=Q_y=0$). The present numerical calculations are compared with those by Abdel-Naby et al. [24]. The thin blue and thick black lines are explained in the text.

Figure 3

Same as Fig. 2, but for two-photon double ionization at a photon energy of 44 eV. The present numerical calculations are compared with the recent numerical calculations by Abdel-Naby et al. [23].

Figure 4

Recoil-ion-momentum distribution in the $x$-$z$ plane for (a) one-photon, (b) two-photon nonsequential, and (c) two-photon sequential double ionization. The dashed black circles in (c) are explained in the text. White circles indicate the maximum possible ion momentum in each process.