The B-spline K-matrix Method in Atomic Physics

In the course of this thesis the B-spline K-matrix method, a theoretical technique capable of reproducing the single ionization continuum of atoms, was developed. Two systems were addressed in particular: helium and boron, as representatives of two- and three-active-electron atoms. Some of the findings presented here resulted in original cont ributions to the scientific literature. Total and partial photoionization cros s sections and asymmetry parameters of the fundamental helium state were examined up to the sixth ionization threshold, yielding the first ab initio reproduction of the first intruder state effects below N=4 threshold, the first reproduction of dipole asymmetry parameters below N=6 threshold and of nondipole anisotropy param eter γ below N=2 threshold. Most of the material presented here relies on the multiple ba sis implementation of the B-spline K-matrix method which allows the reprod uction of almost arbitrarily excited metastable satellites below a prescri bed threshold. The new technique, when used to investigate helium triplet states, yielded the most accurate and extensive existing characterization of triplet me tastable states up to the fifth ionization threshold. Within more than 1700 natural and unnatural S, P and D doubly excited states, eleven intruder states were discov ered, entirely unknown before. At least two experimental groups, at ELETTRA in Trieste and at BESSY II in Berlin, are recently tackling the problem of measuring the m etastable 2^3S helium photoionization cross section. We therefore undertook a parallel theoretical investigation of the photoionization process of both the fundame ntal and the excited ^3S helium states. The latter prelude to the future investigati on of the radiative decay of doubly excited states and already revealed interesting p eculiar features. To this purpose, we devised an extension of the K-matrix method to treat the atom-radiation interaction non perturbatively. A general three electron package has been developed and appl ied to study boron resonances. Specific formulas were derived to obtain arbitrary tensorial one-particle and scalar two-particle matrix elements between three electron states on non-orthogonal basis as required for an efficient exploitation of B-splines. A detailed study of the B-spline effective completeness led to a general result which assure that B-spline based methods are well conditioned for a large class of knot grids.