  Richardson equations can be mapped on the classical electrostatic problem in
two dimensions. We have recently suggested a new analytical approach to these
equations in the thermodynamical limit, which is based on the `probability' of
the system of charges to be in a given configuration at the effective
temperature equal to the interaction constant. In the present paper, we apply
this approach to excited states of the Richardson pairing model. We focus on
the equally-spaced situation and address arbitrary fillings of the energy
layer, where interaction acts. The `partition function' for the classical
problem on the plane, which is given by Selberg-type integral, is evaluated
exactly. Three regimes for the energy gap are identified, which can be treated
as the dilute regime of pairs, BCS regime, and dilute regime of holes.
