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

Abstract

An equation of motion phonon method, developed for even nuclei and recently extended to odd systems with a valence particle, is formulated in the hole-phonon coupling scheme and applied to A=15 and A=21 isobars with a valence hole. The method derives a set of equations which yield an orthonormal basis of states composed of a hole coupled to an orthonormal basis of correlated n-phonon states (n = 0, 1, 2, . . .), built of constituent Tamm-Dancoff phonons, describing the excitations of a doubly magic core. The basis is then adopted to solve the full eigenvalue problem. The method is formally exact but lends itself naturally to simplifying approximations. Self-consistent calculations using a chiral Hamiltonian in a space encompassing up to two-phonon and three-phonon basis states in A=21 A=15 nuclei, respectively, yield full spectra, moments, electromagnetic and β-decay transition strengths, and electric dipole cross sections. The analysis of the hole-phonon composition of the eigenfunctions contributes to clarify the mechanism of excitation of levels and resonances and to understand the reasons of the deviations of the theory from the experiments. Prescriptions for reducing these discrepancies are suggested.

Investigation of Λ-Hypernuclei within the Equation of Motion Phonon Method

“…( 5) using the multiphonon basis {|λ Λ α 1 }. The eigenvectors |β 1 so obtained plus the TD Λ phonons |β 0 were used to solve the final eigenvalue equation in the full multiphonon space which yielded the final eigenstates | Ψ ν (7).…”

“…The EMPM is quite suitable for this purpose [2][3][4][5][6][7][8][9][10]. Starting from the Hatree-Fock (HF) vacuum (n = 0) and the constituent TD (n = 1) phonons, such a method derives a set of equations of motion whose iterative solution generates a self-consistent orthonormal basis of n-phonon (n = 0, 1, 2, ...) states which is used to solve the eigenvalue problem in the full multiphonon space.…”

A center of mass free equation of motion method and its application to 4He

“…The method is not confined to doubly magic nuclei. It can be extended to open shell eveneven nuclei by resorting to the qp version of the EMPM [9] as well as to odd nuclei with a valence particle (hole) coupled to a doubly magic core [16][17][18][19] and, also, to the other odd open shell nuclei within the qp scheme. Investigations in these directions are under way.…”

Spectroscopic properties of 4He within a multiphonon approach

“…A few years ago, we developed for closed shell nuclei an equation of motion phonon method (EMPM) [25][26][27], which yields an orthonormal multiphonon basis built out of phonons generated in the particle-hole (p-h) Tamm-Dancoff approximation (TDA) and adopts such a basis to solve the full eigenvalue problem under no approximation apart from the truncation of the multiphonon space. The method was also formulated in the quasiparticle language suitable for open shell nuclei [28] and in the p(h)-phonon scheme for the study of odd-nuclei [29][30][31][32][33][34].…”