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

We consider the isotropic spin $-\frac{1}{2}$ Heisenberg chain with the most general integrable boundaries. The scalar product between the on-shell Bethe vector and its off-shell dual, obtained by means of the modified algebraic Bethe ansatz, is given by a modified Slavnov formula. The corresponding Gaudin–Korepin formula, i.e., the square of the norm, is also obtained. (letter)