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The use of a pseudo-state expansion within the standard low-energy R-matrix framework to facilitate the study of electron scattering by complex atoms and ions at both low and intermediate energies is discussed. Electron scattering from atomic hydrogen is considered as an example, and results for elastic scattering phase shifts and excitation cross sections are found to be in excellent agreement with recent IERM results in these energy regions. The advantage of this procedure is that existing computer codes, which have been developed over many years, can be directly extended to study electron scattering from a general N-electron target atom or ion.

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A new R-matrix approach for calculating cross sections and rate coefficients for electron-impact excitation of complex atoms and ions is described. This approach, based on an expansion of the total wavefunction in target configurations rather than in individual target states and taking advantage of the special status of the scattered electron in the collisional wavefunction, enables the angular integrals to be performed very much more efficiently than hitherto. It also enables electron correlation effects in the target and in the electron-target collision complex to be treated consistently, eliminating pseudo-resonances which have caused serious difficulties in some earlier work. A major new program package RMATRX II has been written that implements this approach and, as an example, electron-impact excitation of Fe2+ is considered where the four target configurations 3d6, 3d54s, 3d54p and 3d54d are retained in the expansion of the total wavefunction. RMATRX II is compared with the standard R-matrix program package and is found to be much more efficient showing that accurate electron scattering calculations involving complex targets, such as the astrophysically important low ionization stages of iron-peak elements, are now possible.

A new time-dependent R-matrix theory of multiphoton processes is described which can be applied to an arbitrary many-electron atom. The theory is complementary to the R-matrix Floquet theory developed by Burke, Francken and Joachain (1991 J. Phys. B: At. Mol. Opt. Phys. 24 761) enabling processes involving higher laser field intensities and shorter laser pulses to be treated. The new theory is illustrated by analysing the multiphoton ionization of a charged particle bound initially in a one-dimensional potential well where the results are compared with an independent R-matrix Floquet calculation.In recent years there has been a considerable increase in interest in the study of the interaction of intense laser fields with many-electron atoms. Work in this area has been stimulated by increasingly powerful lasers which have led to the discovery of new phenomena such as high harmonic generation (e.g. L'Huillier et al 1992), above-threshold ionization (e.g. Muller et al 1992) and stabilization in super-intense high-frequency fields (Pont and Gavrila 1990). Nevertheless, in spite of this rapidly growing interest, most theoretical work until recently has been limited to atomic hydrogen or to single active electron models, where one electron is treated explicitly and the effect of the remaining electrons in the atom is treated in some average way (e.g. Potvliege and Shakeshaft 1988a, 1989.However, this situation has now begun to change as new theoretical approaches and computational methods are developed and as experimental interest moves increasingly to situations where electron-electron interaction effects in many-electron atoms play an important role. For example, in the case of two-electron atoms a major new programme of research has been initiated by Parker et al (1996) to solve the time-dependent twoelectron Schrödinger equation by direct numerical integration using a massively parallel supercomputer. In addition, a unified R-matrix Floquet theory has been developed by Burke, Francken and Joachain (1991), referred to hereafter as BFJ, which can be used to study both multiphoton ionization and laser-assisted electron-atom scattering for an arbitrary many-electron atom. Based on this theory, a general computer program package has been developed that has enabled multiphoton ionization and detachment rates as well as harmonic generation rates to be calculated for a number of complex atomic targets (e.g. see the recent review by Dörr 1997).The objective of the present letter is to present a new theory which will enable the timedependent Schrödinger equation for an arbitrary many-electron atom in an intense laser field to be solved directly using the R-matrix method. This work is complementary to the Rmatrix Floquet work mentioned above in that it will enable higher laser field intensities

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Effective collision strengths for electron-impact excitation of Fe II are presented for all sextet-to-quartet transitions among the 38 LS states formed from the basis configurations 3d64s, 3d7 and 3d64p. A total of 112 individual transitions are considered at electron temperatures in the range 30–100 000 K, encompassing values of importance for applications in astrophysics as well as laboratory plasmas. A limited comparison is made with earlier theoretical work and large differences are found to occur at the temperatures considered. In particular, it is found that the inclusion or omission of some (N + 1)-bound configurations in the Hamiltonian matrices describing the collision process can have a huge effect on the resulting effective collision strengths, by up to a factor of four in some cases.