Roper Resonances and Skyrmion Vibration Modes

The Skyrme model is a model for nuclear physics that describes atomic nuclei as topological soliton solutions, called skyrmions, in an effective field theory of pions. We study radial vibrations of spherically symmetric skyrmions in the Skyrme model and its variants. Concretely, we numerically solve the linearised field equations for small fluctuations in a skyrmion background, both for linearly stable oscillations and for (unstable) resonances. This is complemented by numerical solutions of the full nonlinear system, which confirm all the results of the linear analysis. In all cases, the resulting fundamental excitation provides a rather accurate value for the Roper resonance, supporting the hypothesis that the Skyrme model already gives a reasonable approximate description of this resonance.