A multishell solution in the Skyrme model

Abstract

We consider multishell configurations in the Skyrme model within the rational map ansatz. We show that equations for the Skyrme field are linearized in the limit of large number of shells, thus allowing for a simple analytic solution. Although this solution is approximate, it provides an accurate description of multishell configurations in the Skyrme model in the region where the Skyrme field is large, $F\gg1$. We use this solution to calculate the mass and the root mean square radius of multishell skyrmion configurations. In particular, for solutions with one unit of baryon charge per shell (the ``hedgehog'' solution) the mass scales as $M\propto B^2$, and its rms radius scales as $B^{1/2}$ with the baryon charge $B$. This scaling for the mass can be reduced to $M\propto B^{4/3}$ in the model with many units of baryon charge per shell. Although this solution is unstable against decays into single-shell or single-skyrmion configurations, it may be useful for modelling skyrmion stars or compact composite objects in some models of dark matter if the decay of such configurations is prevented by some mechanism.