  The microscopic calculation of the decay width of giant monopole resonance
(GMR) anticipates the mixing of one-phonon states with configurations of
increasing complexity. To this aim we develop the effective approach for
description of monopole excited states that are obtained in the quasiparticle
random phase approximation (QRPA), with regard of the coupling between one- and
two-phonon states. Based on the QRPA one-phonon states, we generate the
coupling and two-phonon states by means of the Gaussian orthogonal ensemble
(GOE) distribution. Within our approach the spreading width of the GMRs in
$^{204,206,208}$Pb are described by means of a random matrix approach on two
energy scales. It is demonstrated that the main contribution into the decay of
the GMR is determined by a small number of two-phonon states strongly coupled
to low-energy surface vibrations. While a vast majority of the coupling matrix
elements (that are small in value and following the GOE distribution) are
responsible for the fine structure of the GMR spreading width. A remarkable
agreement between the results of the full microscopic calculations (based on
QRPA phonons coupled by means of the microscopic coupling matrix elements with
calculated two-phonon states) with those of the developed approach confirms the
vitality of the proposed ideas.
