Abstract
We present model calculations of the quasiparticle random phase approximation (QRPA) with a new form of the phonon operator. This modification of the QRPA is applied to the proton-neutron Lipkin model and we shall review it briefly. The present calculations show that the inclusion of nonlinear terms in the phonon operator leads to a much better agreement with the exact results obtained by the diagonalization of the nuclear Hamiltonian. It is further found that if all relevant nonlinear terms of the phonon operator are taken into account, all odd excited states are also exactly reproduced.
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