A Gaudin-like determinant for overlaps of Neel and XXZ Bethe states

We derive a determinant expression for overlaps of Bethe states of the XXZ spin chain with the Neel state, the ground state of the system in the antiferromagnetic Ising limit. Our formula, of determinant form, is valid for generic system size. Interestingly, it is remarkably similar to the well-known Gaudin formula for the norm of Be the states, and to another recently-derived overlap formula appearing in the Lieb-Liniger model.