Different Methods for the Two-Nucleon T-Matrix in the Operator Form

TL;DR

This paper compares three computational methods for calculating the nucleon-nucleon t-matrix within a three-dimensional framework, demonstrating their agreement and effectiveness in modeling neutron-proton and proton-proton scattering with realistic potentials.

Contribution

It introduces and evaluates three distinct approaches to compute the nucleon-nucleon t-matrix, including direct solution, iterative methods, and a two-step process, within a three-dimensional operator formalism.

Findings

Excellent agreement among the three methods for neutron-proton scattering observables.

Converged results for proton-proton scattering with Coulomb force using different screening functions.

Validation of the three-dimensional approach against other established methods.

Abstract

We compare three methods to calculate the nucleon-nucleon t-matrix based on the three-dimensional formulation of J. Golak et al., Phys. Rev. C 81, 034006, (2010). In the first place we solve a system of complex linear inhomogeneous equations directly for the t-matrix. Our second method is based on iterations and a variant of the Lanczos algorithm. In the third case we obtain the t-matrix in two steps, solving a system of real linear equations for the k-matrix expansion coefficients and then solving an on-shell equation, which connects the scalar coefficients of the k- and t-matrices. A very good agreement among the three methods is demonstrated for selected nucleon-nucleon scattering observables using a chiral next-to-next-to-leading-order neutron-proton potential. We also apply our three-dimensional framework to the demanding problem of proton-proton scattering, using a corresponding version of the nucleon-nucleon potential and supplementing it with the (screened) Coulomb force, taken also in the three-dimensional form. We show converged results for two different screening functions and find a very good agreement with other methods dealing with proton-proton scattering.