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We have calculated the energy and angular distributions for double ionization of He by one photon, over the range of photon energies 89 -140 eV. Our results compare favorably with experimental data. PACS number(s): 32.80.FbThe theoretical treatment of double ionization of an atom at photon energies of a few eV or more above threshold remains a difficult challenge. The problem is all the more interesting in view of recent measurements of the energy distribution and the angular asymmetry parameter for double ionization of He by one photon. We report below the results of calculations of the energy distribution, the asymmetry parameter, the cross section for double ionization, and its ratio to the singleionization cross section, for one-photon double ionization of He over the range of photon energies 89 -140 eV. We compare our results with experimental data and other theoretical data.Taking the light to be linearly polarized, along the z axis, and the atomic states to be spin-singlet (we factor out the spin), we work in the velocity gauge, and unless specified otherwise we use atomic units. I et k~and k2 be the final momenta of the two electrons, with Ei = ki/2 and E2 = k2/2 their final energies. Let Oi and O2 be the angles which kq and k2 make with the z axis, and let Oq2 be the angle between kq and k2. The difFerential cross section for the atom to absorb one photon, of frequencỹ , and for the two electrons to emerge into solid angles dn, and dn, is dEgdOgd02 4'' kik2~f (ki, k2) i', (dC where, since the atom absorbs only one unit of angular momentum and is initially in a spherically symmetric spin-singlet state, the amplitude f(ki, k2) has the form f(ki, k2) = g(ki, k2, cos Oi2) cos Oi +g(k2) ki, cos Oi2) cos O2,where ki --~k i~a nd k2 --~k 2~, and where the function g(ki, k2, cos Oi2) is to be determined. The energy distribution do/dEi and the angular asymmetry parameter P(Ei) can be expressed in terms of the auxiliary functions [1] dc' 1 do [1+P(Ei)P2(cos Oi)], dEgdOg 4' dEg where [1] (5) d~64~'k, I, u(ki, k2, 0) + u(k2, ki, 0) dEy 34)c 1 + -v(ki, k2, 1) 2[15u(ki, k2, 0) + 3u(k2, ki, 2) + 5v(ki, k2, 1)] 15[u(ki, kg) 0) + u(k2) ki, 0) + s v(kl, k2, 1)] We see that do/dEi is symmetric about the midpoint Ey/2, where Ey = Ei + E2 is the total final energy, but P(Ei) is asymmetric. The function g(ki, k2, cos Oi2) may be calculated by evaluating f(ki, k2) at selected values of kg and k2. For computational purposes it is convenient to start from the following expression [3] for the amplitude:where yz z (ri, r2) is any trial wave function that cor- ( -) rectly describes two outgoing electrons at asymptotically large distances [4] and that is an eigenvector, with eigenvalue Ey, of soxne (possibly nonlocal) trial operator Hp (whose form may depend on ki and k2) and where~X+) satisfies the inhomogeneous equationNote that v(ki, k2, l) is symmetric in ki and k2 but that u(ki, k2, l) is not. Integrating the right-hand side of Eq.(1) over all directions of k2, using Eq.(2), gives, after some algebra, the result [2] dp lg(...

Experiments using new sources of XUV pulses now tackle the difficult problem of few-photon direct double ionization of atoms. Despite its apparent simplicity, the fundamental process of two-photon direct double ionization of helium is far from being understood. Here, we use a time-dependent approach to study the process. Our results for the electron angular and energy distributions demonstrate that the dominant mechanism for double-electron escape involves a highly correlated electron motion. Angular correlations strongly favour back-to-back electron emission along the polarization axis, while dynamical screening leads to an equipartition of the electron energy for a broad range of field frequencies. These features are reflected in the recoil-ion-momentum distributions that are presently accessible to experiments.