Many-Body Forces with Quark Meson Coupling

Abstract

The quark-meson coupling (QMC) model is a phenomenological model which seeks to describe nuclear systems in terms of quark degrees of freedom. This is done by coupling the meson fields, which describe the nuclear force, to the valence quarks inside of the baryons. Considered in this work is a many-body expansion of the QMC model, extended to include strange baryons (hyperons). From here this expansion is applied to solve for the binding energy of a number of different situations. The first of these applications is to fit the coupling constants in the model to the binding energies of Lambda hyperons. The binding energies for Lambda hyperons are known for several different nuclei, which makes it ideal for fitting the constants. This is completed by using previously established values for the coupling constants, and allowing for slight variations in the coupling constants, due to the many-body expansion being an approximation to the QMC model. Following this, the coupling constants found will be used to predict the binding energies for a number of different cascade hyperons, which have 2-strange quarks instead. An isospin-dependent term is introduced here, which includes a new coupling constant, and so these are tested for a few different values of the coupling constant. Next, a prediction for the effect of the nuclear potential on the binding of a negative cascade, bound by the Coulomb force into an iron atom, is made. This is done by calculating the energy levels of the 5g and 6h states to a high precision, and then finding the transition between them. This transition is compared to the case where there is no Coulomb potential, in order to investigate the effect the strong force has on the binding. Finally, the mean contribution of the scalar meson field is calculated, for the binding of a Sigma hyperon in a helium nucleus. This value can then be used to make a prediction for the change in the magnetic moment between the Sigma hyperon in and out of the nuclear medium.