Lattice Calculations of the Photoionization of Li

Calculations are presented for the double photoionization (with excitation) and triple photoionization of the Li atom. The motion of all three electrons is treated equally by solving the time-dependent Schrodinger equation in nine dimensions. A radial lattice is used to represent three of the nine dimensions, while a coupled channel expansion is used to represent the other six dimensions. Probabilities for photoionization are obtained by t !1 projection onto fully antisymmetric spatial and spin functions. Double photoionization cross sections for lithium leaving the ion in the 1s, 2s ,a nd 2p states are presented. Good agreement is found with the measurements of Huang et al. (Phys. Rev. A 59, 3397 (1999)) for the total double photoionization cross section and with the measurements of Wehlitz et al. (Phys. Rev. Lett. 81, 1813 (1998)) for the triple photoionization cross section. DOI: 10.1103/PhysRevLett.93.053201 PACS numbers: 34.50.Fa, 32.80.Fb The last decade has seen the development of several nonperturbative theoretical methods that have success- fully treated two continuum electrons moving in the field of a charged core, that is, Coulomb three-body breakup. The converged close coupling (1), the hyperspherical close coupling (2), the R matrix with pseudostates (3), the time-dependent close coupling (4), and the exterior complex scaling (5) methods have all obtained total cross sections for the electron-impact ionization of hydrogen that are in excellent agreement with the crossed-beams experiment of Shah et al. (6). To date these nonperturba- tive methods (7-9) have also successfully calculated the wide range of energy and angle differential cross sections found in the electron induced breakup of the hydrogen atom. In addition, the converged close-coupling (10), the hyperspherical close-coupling (11), and the time- dependent close-coupling (12) methods have all obtained energy and angle differential cross sections for the double photoionization of helium that are in excellent agreement with the recent synchrotron experiment of Brauning et al. (13). In this Letter we develop a nonperturbative theoretical method to study the double photoionization (with excita- tion) and triple photoionization of Li. There have been several theoretical studies of these multiple ionization processes in Li. The first such calculation by van der Hart and Greene (14) investigated the double photoionization and triple photoionization of Li in the high-energy limit. Ratios of double-to-single ionization were in good agreement with the experimental measure- ments of Wehlitz et al. (15). The contribution of doubly excited states to the double photoionization cross section was found to be significant (over 40%) demonstrating that one must go beyond a ''frozen-core'' model of double photoionization of Li to obtain accurate results. Pattard and Burgdorfer (16) used a half-collision model to study the triple ionization and related cross section ratios. Good agreement was found with the triple photoionization cross section measurements of Wehlitz et al. (15). In contrast to these previous theoretical approaches, we treat all three electrons of Li equally by propagating in time a nine-dimensional wave function according to the Schrodinger equation, with the three radial dimensions represented on a numerical lattice and the six angular dimensions represented by a coupled channels expansion. Double photoionization with excitation, and triple photo- ionization probabilities are obtained by t !1 projection onto fully antisymmetric spatial and spin functions, with care as to orthogonality of different representations. We compare our results with the measurements of Huang et al. (17) for double photoionization, and with the recent synchrotron experiments of Wehlitz et al. (15) for triple photoionization. Unless otherwise stated, we use atomic units.