Nucleon-nucleon interactions and quarks I: General considerations with numerical results in the 1S0 channel

Abstract

In this paper, we discuss a general development of a quark-model description of nucleon-nucleon (NN) interactions, assuming that quarks are Dirac particles and nucleons are specified approximately by flavor SU(6) wave functions. The down (d) quark is differentiated from the up (u) quark allowing isospin symmetry violating effects. As a simple model calculation, we include effects due to one-gluon exchange (which dictates the short-range behavior of NN forces), one-pion exchange (which gives rise to the Yukawa tail in NN forces), single sigma-exchange (which mocks up to the intermediate attraction in an economical manner), and one-photon exchange (which contributes to isospin symmetry violations). To avoid introduction of additional shape parameters, we adopt a double-sphere geometry with an adjustable isolated nucleon radius. All quark-interchange effects are explicitly evaluated and Pauli blocking is incorporated. Numerical results in the 1 S 0 p− p, n− p, and n− n channels are described and discussed. In particular, it is found that the simple one-boson exchange model (at the quark level) provides a reasonable description of the 1 S 0 phase shifts for 10 MeV ≤ T CM ≤ 150 MeV with T CM the center-of-mass [CM] kinetic energy. It is also found that, with the nonzero up-down quark mass difference as determined by an overall fit to the observed baryon mass splittings, isospin-symmetry violating effects arising from quark interchange are of marginal numerical importance for a nucleon radius R of 0.8 fm and become fairly sizable for R = 1.0 fm. It turns out that, for R = 0.8 fm, the predicted a nn with a nn the low-energy scattering lengths in the 1 S 0 n- n channel is in good agreement with a recent experimental result of Gabioud et al. and the observed large charge dependent effect as given by | a np | − | a nn | can also be understood.