Amplitude-phase methods for analyzing the radial Dirac equation: calculation of scattering phase shifts

Abstract

Approaches inspired by a recent amplitude-phase method for analyzing the radial Dirac equation are presented to calculate phase shifts. Regarding the spin- and pseudo-spin symmetries of relativistic spectra, the coupled first-order and the decoupled second-order differential forms of the radial Dirac equation are investigated by using a novel and the 'classical' amplitude-phase methods, respectively. The quasi non-relativistic limit of the amplitude-phase formulae is discussed for both positive and negative energies. In the positive (E> mc2) low-energy region, the relativistic effects of scattering phase shifts are discussed based on two scattering potential models. Results are compared with those of non-relativistic calculations. In particular, the numerical results obtained from a rational approximation of the Thomas–Fermi potential are discussed in some detail.