Translational invariance and soliton models of the nucleon

Abstract

We present a relativistic model of nucleon structure which places particular emphasis on translational invariance. An analysis of the field equations of the Friedberg-Lee soliton model is presented which avoids the static approximation. The matrix element of the quark-field operator between a nucleon state and a diquark state is written in terms of a quark wave function, and an equation which determines this wave function is given. We do not solve this equation here. Instead, we introduce a simple parametrization of the quark wave functions and proceed to calculate various nucleon observables. We present a calculation of nucleon electromagnetic form factors using a vector dominance model. We also calculate the axial current form factors and discuss the Goldberger-Treiman and partially-conserved axial vector current relations in our model. In our calculations the nucleon magnetic moment is given as the sum of three terms: a recoil a and a the latter term contributing about 50 percent of the proton (or neutron) moment. We find that the recoil part of the proton moment is equal to $(\frac{3}{5}){g}_{A}$, where ${g}_{A}$ is the ratio of the axial vector coupling constants, ${g}_{A}=\frac{{G}_{A}}{{G}_{V}}$. Other models of the nucleon moment usually stress only one aspect of the calculation. For example, in the (static-cavity) MIT bag models the moment is entirely a confinement moment, the calculated moment being proportional to the radius. In nonrelativistic quark models the quarks are assigned an anomalous magnetic moment and the entire nucleon moment is explained on that basis; in our calculations the analogous contribution to the magnetic the mesonic term, contributes only about 50 percent of the total as noted above.NUCLEAR STRUCTURE: Intermediate energy; analysis of the Friedberg-Lee soliton model; matrix elements of quark currents; nucleon electromagnetic form factors, magnetic moments and axial form factors.