  We consider a lattice model in which phonons scatter with pairs of electrons.
All eigenvalues and eigenvectors can be obtained analytically. For a suitable
choice of parameters the ground state consists of a Fermi sea of
non-interacting electrons, with on top a layer of paired electrons. The binding
energy of the electron pairs is partly cancelled by an increased kinetic
energy. This results in a gap in the kinetic energy spectrum of the electrons.
