Boson expansion methods applied to a two-level model in the study of multiple giant resonances

We apply boson expansion methods to an extended exactly solvable Lipkin-Mes hkov-Glick model including anharmonicities in analogy with previous microsc opic calculations. We study the effects of different approximations present in these calculations, among which the truncation of the Hamiltonian and o f the space, in connection with the study of the properties of two-phonon s tates. By comparing the approximate results on the spectrum with the exact ones we conclude that the approximations made in the microscopic calculatio ns on two-phonon states are well justified. We find also that a good agreem ent with the exact results for the three-phonon state is obtained by using a bosonic Hamiltonian truncated at the fourth order. This result makes us c onfident that such approximation can be used in future realistic calculatio ns, thus allowing a theoretical study of triple excitations of giant resona nces. (C) 1999 Elsevier Science B.V.