  We consider the finite volume mean values of current operators in integrable
spin chains with local interactions, and provide an alternative derivation of
the exact result found recently by the author and two collaborators. We use a
certain type of long range deformation of the local spin chains, which was
discovered and explored earlier in the context of the AdS/CFT correspondence.
This method is immediately applicable also to higher rank models: as a concrete
example we derive the current mean values in the SU(3)-symmetric fundamental
model, solvable by the nested Bethe Ansatz. The exact results take the same
form as in the Heisenberg spin chains: they involve the one-particle
eigenvalues of the conserved charges and the inverse of the Gaudin matrix.
