  The Bethe roots describing the ground state energy of the integrable 1D model
of interacting bosons with weakly repulsive two-body delta interactions are
seen to satisfy the set of Richardson equations appearing in the strong
coupling limit of an integrable BCS pairing model. The BCS model describes
boson-boson interactions with zero centre of mass momentum of pairs. It follows
that the Bethe roots of the weakly interacting boson model are given by the
zeros of Laguerre polynomials. The ground state energy and the lowest
excitation are obtained explicitly via the Bethe roots. A direct link has thus
been established, in the context of integrable 1D models, between bosons
interacting via weakly repulsive two-body delta-interactions and strongly
interacting Cooper pairs of bosons.
