Continuous spectrum effect on monopole excitations of the 12C nucleus considered as a system of α-particles

Monopole excitations of the 12C nucleus are studied in the α-cluster model. The continuous spectrum is taken into account by means of the scattering theory in discrete basis in the true three-body scattering approximation. The account of continuum is shown to produce three prominent regions of strong E0 excitations: 6-7, 9-10 and 20-22 MeV, which have been observed experimentally. These states exhaust 72% of the energy-weighted sum rule. When all other states with excitation energies up to 35 MeV, which have small separate contribution to the E0 excitation are included, 92% of the energy-weighted sum rule is exhausted