Solution of two nucleon systems using vector variables in momentum space - an innovative approach

Abstract

An alternate formalism that uses vector variables to treat the two-body Lippmann-Schwinger equation for realistic nucleon-nucleon potentials in momentum space is discussed in this thesis. The formalism uses the symmetry properties of the nucleon-nucleon potential and expands the nucleon-nucleon potential in terms of six linearly independent spin operators. The alternate formalism discussed in this thesis brings to light the role of time-odd spin operators. The vector variable formalism's treatment of spin degrees of freedom heavily depends on the analytical computation of hundreds of algebraic expression. A mathematical framework and computer algorithms for an automated symbolic reduction of algebraic expressions into scalar functions of vector variables are explained in this thesis. The vector variable formalism requires nucleon-nucleon potentials that are in operator form as input. The configuration space nucleon-nucleon potential Argonne V18 is one such potential that can be used for relativistic energies if it can be computed efficiently in momentum space. This thesis develops an efficient numerical technique using Chebyshev approximation to compute the Argonne V18 potential in momentum-space. The tools discussed in this thesis, the algebraic system and the efficient computation of the Argonne V18 potential in momentum space are tested by computing the binding energy and bound state wavefunctions of the deuteron using the vector variable approach. The results were successful and the first step towards a higher goal of using vector formalism of the three-body Faddeev equations for intermediate and high energies has been made.