  We use far-UV absorption spectra obtained with FUSE towards three late B
stars to study the formation and excitation of H2 in the diffuse ISM. The data
interpretation relies on a model of the chemical and thermal balance in
photon-illuminated gas. The data constrain well the nR product between gas
density and H2 formation rate on dust grains: nR = 1 to 2.2 e-15 s-1. For each
line of sight the mean effective H2 density n, assumed uniform, is obtained by
the best fit of the model to the observed N(J=1)/N(J=0) ratio, since the
radiation field is known. Combining n with the nR values, we find similar H2
formation rates for the three stars of about R = 4 e-17 cm3/s.
  Because the target stars do not interact with the absorbing matter we can
show that the H2 excitation in the J>2 levels cannot be accounted for by the UV
pumping of the cold H2 but implies collisional excitation in regions where the
gas is much warmer. The existence of warm H2 is corroborated by the fact that
the star with the largest column density of CH+ has the largest amount of warm
H2.
