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##### The generalized hedgehog and the projected chiral soliton model

**Authors**: M. Fiolhais, K. Goeke, F. Grümmer and J.N. Urbano

**Ref.**: Nuclear Physics A **481**, 727-764 (1988)

**Abstract**: The linear chiral soliton model with quark fields and elementary pion and sigma fields is solved in order to describe static properties of the nucleon and the delta resonance. To this end a Fock state of the system is constructed with consists of three valence quarks in a 1s orbit with a generalized hedgehog spin-flavour configuration cos eta |mu downarrow > - sin \eta |d uparrow >. Coherent states are used to provide a quantum description for the mesonic parts of the total wave function. The corresponding classical pion field also exhibits a generalized hedgehog structure. In a pure mean field approximation the variation of the total energy results in the ordinary hedgehog form (eta = 45º). In a quantized approach, however, the generalized hedgehog baryon is projected onto states with good spin and isospin and then noticeable deviations from the simple hedgehog form occur (eta approx 20º), if the relevant degrees of freedom of the wave functions are varied after the projection. Various nucleon properties are calculated. These include proton and neutron charge radii, and the magnetic moment of the proton for which good agreement with experiment is obtained. The absolute value of the neutron magnetic moment comes out too large, similarly as the axial vector coupling constant and the pion-nucleon-nucleon coupling constant. However, due to the generalization of the hedgehog, the Goldberger-Treiman relation and a corresponding virial theorem are fulfilled. Variation of the quark-meson coupling parameter g and the sigma mass m sigma shows that the g A is always about 40% too large compared to experiment. The concepts and results of the projections are compared with the semiclassical collective quantization method. It is demonstrated that noticeable deviations occur for the delta-nucleon splitting, the isovector squared charge radius and the axial vector coupling constant.