RPA Description of the Electric Polarizability of the Nucleon

Excited states of the nucleon are described as RPA configurations on a mean--field ground state taken from the MIT bag model. A residual interaction of a structure as in the Nambu--Jona--Lasinio model is used. The particle-hole states are coupled to good total angular momentum and isospin. Valence excitations of particle-hole type and quark--antiquark ($q\overline{q}$) states from the Dirac--sea are included. The dependence of the baryon spectrum and multipole response functions on the coupling constant $G$ is studied. At critical values of $G$ the 3q--ground state becomes degenerate with strongly collective $q\overline{q}$ modes. The model is used to calculate the electric polarizability of the neutron $\alpha_N$. Without residual interaction $\alpha_N=7\cdot 10^{-4}fm^3$ is found. With residual interaction the value increases to $\alpha_N=(7-11)\cdot 10^{-4}fm^3$. The measured value of $\alpha_N$ is reproduced within experimental error bars.