  We show that the matrix elements of integrable models computed by the
Algebraic Bethe Ansatz can be put in direct correspondence with the Form
Factors of integrable relativistic field theories. This happens when the
S-matrix of a Bethe Ansatz model can be regarded as a suitable non-relativistic
limit of the S-matrix of a field theory, and when there is a well-defined
mapping between the Hilbert spaces and operators of the two theories. This
correspondence provides an efficient method to compute matrix elements of Bethe
Ansatz integrable models, overpassing the technical difficulties of their
direct determination. We analyze this correspondence for the simplest example
in which it occurs, i.e. the Quantum Non-Linear Schrodinger and the Sinh-Gordon
models.
