  Even tin isotopes of mass number $A = 108 \sim 124$ are calculated with
realistic interactions in the generalized-seniority approximation of the
nuclear shell model. For each nucleus, we compute the lowest ten thousand
states ($5000$ of each parity) up to around $8$ MeV in excitation energy, by
allowing as many as four broken pairs. The lowest fifty eigen energies of each
parity are compared with the exact results of the large-scale shell-model
calculation. The wavefunctions of the mid-shell nuclei show a clear pattern of
the stepwise breakup of condensed coherent pairs with increasing excitation
energy. We also compute in the canonical ensemble the thermal properties --
level density, entropy, and specific heat -- in relation to the thermal pairing
phase transition.
