2016

A Bogoliubov quasiparticle formulation of an equation-of-motion phonon method, suited for open-shell nuclei, is derived. Like its particle-hole version, it consists of deriving a set of equations of motions whose iterative solution generates an orthonormal basis of n-phonon states (n = 0,1,2,...), built of quasiparticle Tamm-Dancoff phonons, which simplifies the solution of the eigenvalue problem.

The method is applied to the open-shell neutron-rich O-20 for illustrative purposes. A Hartree-Fock-Bogoliubov canonical basis, derived from an intrinsic two-body optimized chiral Hamiltonian, is used to derive and solve the eigenvalue equations in a space encompassing a truncated two-phonon basis.

The spurious admixtures induced by the violation of the particle number and the center-of-mass motion are eliminated to a large extent by a Gram-Schmidt orthogonalization procedure. The calculation takes into account the Pauli principle, is self-consistent, and is parameter free except for the energy cutoff used to truncate the two-phonon basis, which induces an increasing depression of the ground state through its strong coupling to the quasiparticle vacuum.

Such a cutoff is fixed so as to reproduce the first 1(-) level. The two-phonon states are shown to enhance the level density of the low-energy spectrum, consistently with the data, and to induce a fragmentation of the E1 strength which, while accounting for the very low E1 transitions, is not sufficient to reproduce the experimental cross section in the intermediate energy region.

This and other discrepancies suggest the need of including the three-phonon states. These are also expected to offset the action of the two phonons on the quasiparticle vacuum and, therefore, free the calculation from any parameter.