Normal modes around classical hadronic excitations

Skyrme-like models of pions and vector mesons are known to admit a plethora of classical solutions. In the topological sector of the vacuum, a sequence of static spherically symmetric configurations satisfies the equations of motion and constitutes a set of extrema of the energy functional. We investigate the variations of the energy for small fluctuations around these extrema by performing a normal-mode analysis of the quadratic form in the fluctuations. The nature of the extrema is discussed in relation to the occurrence of negative modes of the associated eigenvalue problem.