ON SIZE AND SHAPE OF THE AVERAGE MESON FIELDS IN THE SEMIBOSONIZED NAMBU AND JONA-LASINIO MODEL

We consider the bosonized form of a two-flavor Nambu & Jona-Lasinio mo del involving scalar-isoscalar and pseudoscalar-isovector quark-quark interaction. Solitonic meson fields are obtained by minimizing the eff ective Euclidean action. In dependence on the constituent quark mass, which is the only free parameter in the model, we evaluate a series of meson profiles and compare them with a properly parameterized referen ce profile. We show that the self-consistent fields do in fact practic ally not depend on the constituent quark mass. Their shape can be very well approximated by this reference profile which interpolates betwee n the correct asymptotic behavior for small and large radii. To demons trate the accuracy of the approximation we evaluate several static pro perties like energy, mean square radius, axial-vector constant and del ta-nucleon mass splitting using both self-consistent and reference pro files. The agreement is found to be very well in the physically releva nt mass region.