A universal Gaussian basis set concept for the calculation of Rydberg and continuum states by pure L2 methods is presented. It is based on the generation of optimised sequences of Gaussian exponents by maximising the overlap with a series of Slater-type functions characterised by a constant exponent and a variable principal quantum number. In this way linear combinations of Gaussian basis functions can be found which are ideally suited to imitate Laguerre-Slater functions. It is thus possible to obtain optimum representations of Rydberg orbitals or of complete orthonormal systems of Laguerre functions playing an important role in the Lz expansion of continuum functions. The basis sets are tested with the hydrogen atom. The effectiveness of the basis is illustrated by the calculation of quantum defects associated with the s, p and d Rydberg series of the alkali metal atoms Li and Na. The phaseshifts determined in the ionisation continua of these systems nicely fit the series below the ionisation limit as is finally demonstrated by an Edlen plot.

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A comparison is made of experimental far-wing profiles for the system Li(2P → 3D)He with quantum calculations of thermally averaged free-free continua. Using input adiabatic potentials and transition moment functions from both ab initio and semi-empirical approaches, the comparison shows: (i) new ab initio potentials for Li * (2P, 3P, 3D)He reproduce the spectral positions of the observed rainbow satellites well; the height of the 3D barrier predicted agrees with experiment to within ±15 cm −1 , whereas its position is too large by 0.3 a 0 ; (ii) potentials obtained with various semi-empirical methods reproduce the satellite structure qualitatively, but are generally too repulsive in the 3D state at intermediate and large internuclear separations; (iii) transition moment functions for the asymptotically forbidden 2P → 3P transitions reproduce, with different degrees of accuracy, the intensity of the red-wing satellite related to the 3P potential extremum around 12 a 0 . The vibrational energies in the 2P and 3D states calculated with the ab initio potentials reproduce to within a few cm −1 those obtained from rotationally resolved band spectra reported in the literature.

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