Hadrons as Skyrmions in the presence of isospin chemical potential

The stability of the Skyrmion solution in the presence of finite isospin chemical potential $\mu $ is considered, showing the existence of a critical value $\mu_{c} = 222.8$ MeV where the Skyrmion mass vanishes. Using the Hamiltonian formulation, in terms of collective variables, we discuss the behavior of different skyrmionic parameters as function of the isospin chemical potential ($\mu$), such as the energy density, the isoscalar radius and the isoscalar magnetic radius. We found that the radii start to grow very fast for $\mu \geq 140$ MeV, suggesting the occurrence of a phase transition.