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Using the framework of the algebraic Bethe Ansatz, we study the scalarproduct of the inhomogeneous XXZ spin-1/2 chain. Inspired by theIzergin-Korepin procedure for evaluating the domain wall partition function, weobtain a set of conditions which uniquely determine the scalar product.Assuming the Bethe equations for one set of variables within the scalarproduct, these conditions may be solved to produce a determinant expressionoriginally found by Slavnov. We also consider the inhomogeneous XX spin-1/2chain in an external magnetic field. Repeating our earlier procedure, we find aset of conditions on the scalar product of this model and solve them in thepresence of the Bethe equations. The expression obtained is in factorized form.

An Izergin-Korepin procedure for calculating scalar products in six-vertex models