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An equation of motion phonon method, developed for even nuclei and recentlyextended to odd systems with a valence particle, is formulated in thehole-phonon coupling scheme and applied to A=15 and A=21 isobars with a valencehole. The method derives a set of equations which yield an orthonormal basis ofstates composed of a hole coupled to an orthonormal basis of correlatedn-phonon states (n = 0, 1, 2, . . .), built of constituent Tamm-Dancoffphonons, describing the excitations of a doubly magic core. The basis is thenadopted to solve the full eigenvalue problem. The method is formally exact butlends itself naturally to simplifying approximations. Self-consistentcalculations using a chiral Hamiltonian in a space encompassing up totwo-phonon and three-phonon basis states in A=21 A=15 nuclei, respectively,yield full spectra, moments, electromagnetic and beta-decay transitionstrengths, and electric dipole cross sections. The analysis of the hole-phononcomposition of the eigenfunctions contributes to clarify the mechanism ofexcitation of levels and resonances and to understand the reasons of thedeviations of the theory from the experiments. Prescriptions for reducing thesediscrepancies are suggested.

Microscopic multiphonon approach to nuclei with a valence hole in the oxygen region