Double photoionization of helium:: The hyperspherical R-matrix method with semiclassical outgoing waves

We present an nb initio scheme for computing the wave function of the pair of electrons projected into the double continuum of the helium atom by a one-photon dipolar excitation. The scheme uses the Floquet approach to convert the time-dependent Schrodinger equation into an infinite set of coupled time-independent equations, The latter reduces to a single stationary inhomogeneous Schrodinger equation in the weak-field limit, which is relevant here. This equation is solved using an R matrix approach to combine a quantum treatment of all variables within the hypersphere R less than or equal to R-0 with a semiclassical treatment of the R motion outside this hypersphere. We apply this approach to a model helium atom where r(1) = r(2). We thus demonstrate the feasibility of the method, and obtain insights into the dynamics of the double photoionization of helium at equal sharing of a low excess energy. [S1050-2947(99)01210-X].