The method of unitary clothing transformations in the theory of nucleon-nucleon scattering

TL;DR

This paper applies the clothing transformation method from quantum field theory to nucleon-nucleon scattering, deriving energy-independent operators and a T-matrix equation to better understand nuclear forces.

Contribution

It introduces a novel application of unitary clothing transformations to nucleon-nucleon interactions, providing explicit analytic expressions and a numerical framework for scattering analysis.

Findings

Derived Hermitian, energy-independent operators for clothed nucleons.

Compared analytic expressions with meson exchange potentials.

Developed a numerical code for solving the T-matrix in momentum space.

Abstract

The clothing procedure, put forward in quantum field theory by Greenberg and Schweber, is applied for the description of nucleon-nucleon (N-N) scattering. We consider pseudoscalar, vector and scalar meson fields interacting with 1/2 spin fermion ones via the Yukawa-type couplings to introduce trial interactions between "bare" particles. The subsequent unitary clothing transformations are found to express the total Hamiltonian through new interaction operators that refer to particles with physical (observable) properties, the so-called clothed particles. In this work, we are focused upon the Hermitian and energy-independent operators for the clothed nucleons, being built up in the second order in the coupling constants. The corresponding analytic expressions in momentum space are compared with the separate meson contributions to the one-boson-exchange potentials in the meson theory of nuclear forces. In order to evaluate the T-matrix of the N-N scattering we have used an equivalence theorem that enables us to operate in the clothed particle representation (CPR) instead of the bare particle representation with its huge amount of virtual processes. We have derived the Lippmann-Schwinger-type equation for the CPR elements of the T-matrix for a given collision energy in the two-nucleon sector of the Hilbert space of hadronic states and elaborated a code for its numerical solution in momentum space.