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We consider the isotropic spin$-\frac{1}{2}$ Heisenberg chain with the mostgeneral integrable boundaries. The scalar product between the on-shell Bethevector and its off-shell dual, obtained by means of the modified algebraicBethe ansatz, is given by a modified Slavnov formula. The correspondingGaudin-Korepin formula, \textit{i.e.}, the square of the norm, is alsoobtained.

Slavnov and Gaudin-Korepin formulas for models without $U(1)$ symmetry: the XXX chain on the segment