Rotational bands in the baryon spectrum. II

A nonrelativistic constituent quark model is developed for baryons where the quarks are moving in a deformable mean field. The deformation parameters in each state are determined by minimization of the energy, subject to the constraint of volume conservation in the state. It is found that while the ground state is spherical, the excited-state configurations are deformed. The deformation increases with excitation energy. This is responsible for the observed low-lying states $N\left(1440\right)\mathrm{}{\frac{1}{2}}^{+}$ and $\Delta \mathrm{}\left(1900\right)\mathrm{}{\frac{1}{2}}^{-}$. The experimental states are grouped in rotational bands, and the deduced moment-of-inertia parameter is shown to be consistent with the quantum-mechanical calculation. A detailed comparison with experimental data is made.