P-matrix and J-matrix approaches. Coulomb asymptotics in the harmonic oscillator representation of scattering theory

The relation between the R- and P-matrix approaches and the harmonic oscillator representation of the quantum scattering theory (J-matrix method) is discussed. We construct a discrete analogue of the P-matrix that is shown to be equivalent to the usual P-matrix in the quasiclassical limit. A definition of the natural channel radius is introduced. As a result, it is shown to be possible to use well-developed technique of R- and P-matrix theory for calculation of resonant states characteristics, scattering phase shifts, etc., in the approaches based on harmonic oscillator expansions, e.g., in nuclear shell-model calculations. P-matrix is used also for formulation of the method of treating Coulomb asymptotics in the scattering theory in oscillator representation.Comment: Revtex, 57 pages including 15 figures; to be published in Annals of Physic

Spectral characteristics of anisotropic dielectric disk resonator with imperfect conducting end walls

The electrodynamic analysis of a dielectric disk resonator with imperfect conducting end walls is carried out at excitation of "whispering gallery" oscillations. The possibility of solving the inverse problem is considered: it consists in the determination of permittivity tensor components of anisotropic uniaxial crystal. The spectral characteristics of teflon disk resonator with copper end surfaces are studied in the 8 mm wave band