Low- and high-energy spectroscopy of O17 and F17 within a microscopic multiphonon approach

Abstract

The extension of an equation of motion phonon method to odd nuclei is described step by step. Equations of motion are first constructed and solved to generate an orthonormal basis of correlated $n$-phonon states $(n=0,1,2,\ensuremath{\cdots})$, built of constituent Tamm--Dancoff phonons, describing the excitations of a doubly magic core. Analogous equations are then derived within a subspace spanned by a valence particle coupled to the $n$-phonon core states and solved iteratively to yield a basis of correlated orthonormal multiphonon particle-core states. The basis so constructed is used to solve the full eigenvalue problem for the odd system. The formalism does not rely on approximations but lends itself naturally to simplifying assumptions, as illustrated by its application to $^{17}\mathrm{O}$ and $^{17}\mathrm{F}$. Self-consistent calculations using a chiral Hamiltonian in a space encompassing up to three-phonon basis states generate spectra having a high level density, comparable to that observed experimentally. The spectroscopic properties are investigated at low energy through the calculation of moments, electromagnetic and $\ensuremath{\beta}$-decay transition strengths, and at intermediate and high energy through the computation of the electric-dipole spectra and pygmy and giant dipole resonance cross sections. The analysis of the particle-phonon composition of the eigenfunctions contributes to clarify the mechanism of excitation of levels and resonances and gives unique insights into their nature.