  For the sl_2 Gaudin model (degenerated quantum integrable XXX spin chain) an
exponential generating function of correlators is calculated explicitely. The
calculation relies on the Gauss decomposition for the SL_2 loop group. From the
generating function a new explicit expression for the correlators is derived
from which the determinant formulas for the norms of Bethe eigenfunctions due
to Richardson and Gaudin are obtained.
