  In this article we study the thermodynamic limit of the form factors of the
XXX Heisenberg spin chain using the algebraic Bethe ansatz approach. Our main
goal is to express the form factors for the low-lying excited states as
determinants of matrices that remain finite dimensional in the thermodynamic
limit. We show how to treat all types of the complex roots of the Bethe
equations within this framework. In particular we demonstrate that the Gaudin
determinant for the higher level Bethe equations arises naturally from the
algebraic Bethe ansatz.
