The use of skyrmions for two-nucleon systems

Abstract

We first define our goals for studying the nucleon-nucleon force with skyrmions by discussing briefly the general issue of the formulation of nuclear physics using degrees of freedom based on quarks and gluons. A short review is then given of the use of the skyrmion description for single-hadrons in order to prepare the way for the application of this method to two-nucleon systems. In the context of the B = 1 sector, we discuss cursorily how the skyrmion arises as an approximation to quantum chromodynamics (QCD) for the artificial situation where the number of colors N is very large, and the use of the original Skyrme lagrangian, and various modifications of it, in that situation. We consider the hedgehog solution for that lagrangian, noting how integer baryon number emerges in the course of fulfilling the necessary boundary conditions. First-quantization, which allows for the treatment of spin and isospin, is introduced. A detailed discussion of the use of the London-Heitler method—which applies the B = 1 hedgehog solution, in one form or another, to the B = 2 case—is presented. This includes such issues as the use of higher-order terms in the lagrangian, the incorporation of higher-order dynamic terms, and the mutual distortion of hedgehog solutions in the B = 2 system. In order to emphasize one area of potential usefulness of skyrmions in nuclear physics, we consider their application to the calculation of exchange currents as well as the more common usage for studying the nucleon-nucleon potential. More recently, studies of skyrmions for B = 2 systems have gone well beyond the simplest form of London-Heitler form with hedgehog skyrmions. We review briefly the treatment of B = 2 systems with skyrmions using a full three-dimensional computation without recourse to these assumptions. Last, we discuss three mechanisms that yield some degree of attraction in the central potential: (i) the admixture of states involving nucleon-Δ and Δ-Δ components along with the asymptotic nucleon-nucleon ones; (ii) the use of a form of the London-Heitler method that takes into account the proper symmetries of the two-skyrmion state; and (iii) the treatment of internal excitations of the single-baryon and their effects on the nucleon-nucleon force.