Quantum scattering using a novel implementation based on the variational R matrix formalism and the finite element method: a comparative study

We developed a finite element implementation of the variational R matrix formalism to study quantum scattering problems. That methodology utilizes a novel algorithm to invert matrices using a generalization of the partition method based on the Löwdin–Feshbach algebra. In this Letter, we study three representative problems and develop a detailed study of the procedure efficiency. The matrix elements calculation and the CPU time used for the linear algebra computation scale linearly with the number of elements used in the radial basis. The results for the phase shift and its tangent are in agreement with accurate results obtained using S matrix Hulthén–Kohn variational principles.