Hamiltonian group actions on exact symplectic manifolds with proper   momentum maps are standard
  We give a complete characterization of Hamiltonian actions of compact Lie groups on exact symplectic manifolds with proper momentum maps. We deduce that every Hamiltonian action of a compact Lie group on a contractible symplectic manifold with a proper momentum map is globally linearizable. 
Yael Karshon and Fabian Ziltener
math.SG