Determination of Quantum Defects and Phase Shifts from a Smooth K Matrix

Quantum defects and phase shifts are determined using a smooth K matrix which is free of poles throughout the energy spectrum. Enforcement of the bound-state boundary condition on the wavefunction introduces poles in the usual negative-energy Green's function and causes the K matrix in this region to be highly dependent on energy. Alternative boundary conditions remove this energy dependence and yield a smooth K matrix from which a smooth quantum-defect curve can be determined. Application of the bound-state boundary condition to this curve identifies the bound states for an entire Rydberg series. In a multichannel formalism, the boundary conditions are applied in the closed channels via reduction of the K matrix prior to calculation of the quantum-defect curve. A projection operator is used to enforce orthogonality between the basis functions and the target states, and iteration is used to systematically improve the basis set. Results are presented for a single -channel calculation of the quantum defects of Be II and B III and for a multichannel calculation of the He I quantum defects and e-H elastic phase shifts.