  It is known that solutions of Richardson equations can be represented as
stationary points of the "energy" of classical free charges on the plane. We
suggest to consider "probabilities" of the system of charges to occupy certain
states in the configurational space at the effective temperature given by the
interaction constant, which goes to zero in the thermodynamical limit. It is
quite remarkable that the expression of "probability" has similarities with the
square of Laughlin wave function. Next, we introduce the "partition function",
from which the ground state energy of the initial quantum-mechanical system can
be determined. The "partition function" is given by a multidimensional
integral, which is similar to Selberg integrals appearing in conformal field
theory and random-matrix models. As a first application of this approach, we
consider a system with the constant density of energy states at arbitrary
filling of the energy interval, where potential acts. In this case, the
"partition function" is rather easily evaluated using properties of the
Vandermonde matrix. Our approach thus yields quite simple and short way to find
the ground state energy, which is shown to be described by a single expression
all over from the dilute to the dense regime of pairs. It also provides
additional insights into the physics of Cooper-paired states.
