Two-photon double ionization of helium in the region of photon energies $42–50\mathrm{eV}$

We report the total integrated cross section (TICS) of two-photon double ionization of helium in the photon energy range from $42\text{to}50\mathrm{eV}$. Our computational procedure relies on a numerical solution of the time-dependent Schrödinger equation on a square-integrable basis and subsequent projection of this solution on a set of final field-free states describing correlation in the two-electron continuum. Our results suggest that the TICS grows monotonically as a function of photon energy in the region of $42–50\mathrm{eV}$, possibly reaching a maximum in the vicinity of $50\mathrm{eV}$. We also present fully resolved triple-differential cross sections for selected photon energies.

Figure 1

Squared overlaps $\mid ⟨{\Psi }_{\mathrm{CCC}}\mid {\Psi }_k⟩{\mid }^2$ between various $D$-symmetry eiegenfunctions of the eigenvalue problem for the field-free helium Hamiltonian on the basis (7) and a CCC wave function at the excess energy of $20\mathrm{eV}$ above the double-ionization threshold.

Figure 2

(Color online) Total integrated cross section of TPDI on He as a function of the photon energy. Present results obtained by combination of the TDSE and CCC methods and corresponding to a field intensity of $3.5\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$ are shown by red solid circles. The CCC calculation in the closure approximation [30] is shown by black crosses. Other calculations are as follows: TDCC with a ${\sin }^2$ envelope, $5\times {10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$ [15], open circles; TDCC with a ramped pulse, ${10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$ [6], open triangle; time-dependent (TD) basis, ${10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$ [8], green asterisks; $R$ matrix, ${10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$ [5], blue open squares; $J$ matrix with noncorrelated (NC) and correlated (FC) final states, ${10}^{13}\mathrm{W}∕{\mathrm{cm}}^2$ [13], light blue open and solid diamonds, respectively; LOPT [3], yellow solid circles.

Figure 3

(Color online) TDCS of He TPDI for the coplanar geometry at $\omega =42\mathrm{eV}$, $E_1=E_2=2.5\mathrm{eV}$, and various fixed electron angles. The present TDSE calculation (divided by 2.2) is shown by the red solid line. The earlier CCC calculation in the closure approximation (divided by 1.6) is shown by the blue dashed line. The black dots represent the TDCC results of Ref. 15.