PERIODIC-ORBITS OF THE SKYRMION BREATHING MODE - CLASSICAL AND QUANTAL ANALYSIS

We construct the periodic classical orbits of the Skyrmion breathing mode by a perturbation expansion in the amplitude of the vibration. We first examine the lowest-order construction associated with linear response theory. We find that the monopole response function exhibits a sharp unbound peak which we identify as the Roper resonance N(1440). A calculation of second-order terms provides an evaluation of the anharmonic corrections. In a second part, we construct a collective Bohr-type Hamiltonian using the knowledge of periodic trajectories. This provides a natural requantization scheme with which we calculate the spectrum of monopole excitations of the Skyrmion. Finally we apply our results to the calculation of color transparency effects. We find that anharmonicities decrease significantly the time taken by a nucleon of small radius to regain its normal size. This effect should diminish the importance of the color transparency phenomenon.