  The solution of the classical Fermi problem of low-energy neutron scattering
by nuclei, when the excitations of the nuclei in scattering processes are taken
into account, is found by the method of zero-range potentials with inner
structure. This model is a generalization of the Fermi zero-range potential
obtained by adding a non-trivial inner Hamiltonian and inner space with
indefinite metric. We propose a general principle of analyticity of the
Caley-transform of the S-scattering matrix, written as a function of wave
number. This permits us to evaluate all parameters of the model, including the
indefinite metric tensor of the inner space, once the spectrum of the inner
Hamiltonian, the scattering length and the effective radious are chosen.
