  In the Skyrme model atomic nuclei are modelled as quantized soliton solutions
in a nonlinear field theory of pions. The mass number is given by the conserved
topological charge $B$ of the solitons. Conventionally, Skyrmions are
semiclassically quantized within the rigid body approach. In this approach
Skyrmions are effectively treated as rigid rotors in space and isospace that is
it is assumed that Skyrmions do not deform at all when they spin and isospin.
This approximation resulted in qualitative and encouraging quantitative
agreement with experimental nuclear physics data. In this talk, we point out
that the theoretical agreement could be further improved by allowing classical
Skyrmion solutions to deform as they spin and isospin. As a first step towards
a better understanding of how nuclei can be approximated by classically
spinning and isospinning soliton solutions, we study how classical Skyrmion
solutions of topological charges $B=1-4,8$ deform when classical isospin is
added.
