  In this note we adress the problem of performing the semiclassical expansion
of the scalar product of Bethe states in the case of the XXZ spin chain. Our
approach closely follows the one developped in [1]: after expressing the scalar
products in terms of a central quantity - the B functional, we reinterpret it
as a grand partition function of a gas of particles with pairwise interaction
potential. This work has been done as part of the author's master thesis under
the supervision of Ivan Kostov and Didina Serban at Institut de Physique
Th\'eorique (CEA Saclay) in September 2015 - February 2016, and present a
consice summary of the results obtained at that time.
