Skyrmions in the presence of isospin chemical potential

We analyze the existence of localized finite energy topological excitations on top of the perturbative pion vacuum within the Skyrme model at finite isospin chemical potential and finite pion mass. We show that there is a critical isospin chemical potential ${\mu }_I^c$ above which such solutions cease to exist. We find that ${\mu }_I^c$ is closely related to the value of the pion mass. In particular for vanishing pion mass we obtain ${\mu }_I^c=0$ in contradiction with some results recently reported in the literature. We also find that below ${\text{mui}}^c$ the skyrmion mass and baryon radius show, at least for the case of the hedgehog ansatz, only a mild dependence on the isospin chemical potential.