A finite element approach for the continuum spectrum of the Dirac radial equation

The Dirac radial functions are expanded in polynomial B-spline basis, transforming the Dirac equation in a generalized eigensystem matrix problem. Due to the locality nature of the B-spline functions the matrix representation of all the involved operators are highly sparse. Diagonalization of the matrix equations provides the bound and continuum eigenstates. Energies and oscillator strengths for Hydrogen and Rubidium are presented.