The Quark Model, Deuteron Formfactors and Nuclear Magnetic Moments

Abstract

Deuteron properties and nuclear magnetic moments are studied in the non-relativistic quark cluster model. The charge monopole, quadrupole and magnetic-dipole form factors and the tensor polarization of the deuteron in this microscopic meson-quark cluster model are calculated. The deuteron wave function is derived from a microscopic 6-quark Hamiltonian which, in addition to a quadratic confinement potential, includes the one-pion and the one-gluon exchange potentials between quarks. The electromagnetic current operators are constructed on the quark level, i.e., the photon is coupled directly to the quarks. Aside from the one-body impulse current, pionic and gluonic exchange current corrections are included. Due to the Pauli principle on the quark level, new quark interchange terms arise in the one-body and two-body current matrix elements, that are not present on the nucleon level. While these additional quark exchange currents are small for low momentum transfers, we find that they appreciably influence the electromagnetic structure of the deuteron beyond a momentum transfer of q = 5fm ⁻¹. We construct the quark exchange current operators on the quark level and then eliminate the quark degrees of freedom. The photon is directly coupled to the quarks. This effective current contains new non-local and isospin dependent terms which are generated by the Pauli principle on the quark level (quark exchange between nucleons). When we evaluate these quark exchange currents in nuclei, we use harmonic oscillator wave functions as nuclear wave functions including short-range Brueckner correlations. We solve the Bethe-Goldstone equation to include this short-range correlations in our effective N N potential, which is derived from a microscopic quark Hamiltonian. We investigate also the role of these additional quark exchange currents in the magnetic moments and the elastic magnetic form factors of several closed shell±1 nuclei, such as ¹⁵ N, ¹⁷ O and ³⁹ K. We specificly discuss the results for M ₁ electron scattering ¹⁵ N and the isovector magnetic moment for the A=39 system. Quark degrees change the Schmidt value of this isovector moment by −20%.