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##### Chiral model of the nucleon and Delta isobar: The coherent-pair approximation

**Authors**: K. Goeke, M. Harvey, F. GrÃ¼mmer and J.N. Urbano

**Ref.**: Physical Review D **37**, 754-767 (1988)

**Abstract**: The linear chiral sigma model with quark fields and elementary pion and sigma fields is used to describe static properties of the nucleon and the Delta resonance. To this end baryon Fock states with good spin and isospin are constructed from summations of components in which three quarks in s states with the SU(2)x SU(2) quantum numbers of the nucleon and Delta are coupled to multipion states and a scalar-isoscalar coherent state of the sigma fields. The multipion states are constructed to have coherent properties as well as definite spin-isospin quantum numbers. Ignoring the effects of vacuum polarization the baryon energy is made stationary, resulting in a set of four coupled nonlinear eigenvalue equations and a diagonalization procedure between frozen fields. The corresponding solitonic solutions are used to evaluate the relevant nucleon properties. A comparison is made with the results from the cloudy-bag model, the projected mean-field chiral-soliton model, and the Skyrme approach.