Abstract
We present a derivation of Multichannel Quantum Defect Theory (MQDT) which is based on the configuration-interaction in the continuum (CIC) and reaction matrix (K-matrix) formalisms, generalized so that closed channels are included. The whole development focuses on obtaining and utilizing eigenfunctions composed of smooth parts only. Whereas the theories of Seaton and Fano depend on the use of irregular or unbound functions, ours does not. No separation of configuration space into inner and outer space is necessary. Furthermore, the present theory allows in a practical way the transfer of information from one part of the spectrum to another byinterpolation — as opposed to the standard ab initio MQDT which is limited toextrapolation from the continuous to the discrete spectrum. The formalism is developed for the physically important Coulomb potential. However, its structure is such that it allows the easy determination of those parts which must be altered to accomodate extension to other potentials. Furthermore, it permits the execution of reliable calculations which employ a basis of numerical fixed-core Hartree-Fock (HF) functions for the singly excited configurations, of multiconfigurational HF (MCHF) for the spectroscopic valence states and of analytic virtual orbitals for the correlation vectors.
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Komninos, Y., Nicolaides, C.A. Multi-channel reaction matrix theory and configuration-interaction in the discrete and in the continuous spectrum. Inclusion of closed channels and derivation of quantum defect theory. Z Phys D - Atoms, Molecules and Clusters 4, 301–312 (1987). https://doi.org/10.1007/BF01384882
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DOI: https://doi.org/10.1007/BF01384882