Abstract :
Working in a boson formalism, we define a new class of phonon operators for RPA-like calculations. These operators remind the standard RPA ones, namely they have “upward” and “backward” amplitudes and an overall one-particle one-hole nature. However, their structure is more complex. As a basic feature, the vacuum of these phonon operators is characterized by only a limited (and variable at will) set of particle–hole excitations. In addition, multiphonon states constructed by repeated actions of these phonon operators on the vacuum state have a particle–hole structure never exceeding in complexity that of the vacuum itself. We discuss advantages and disadvantages deriving from the use of this new class of phonon operators and show an application of the formalism within the Lipkin model. Diagonalizations in multiphonon spaces built in terms of new and standard RPA phonon operators exhibit a faster convergence toward the exact results in the former case.
