Occupation numbers of spherical orbits in self-consistent beyond-mean-field methods

Abstract

We present a method to compute the number of particles occupying spherical single-particle (SSP) levels within the energy density functional (EDF) framework. These SSP levels are defined for each nucleus by performing self-consistent mean-field calculations. The nuclear many-body states, in which the occupation numbers are evaluated, are obtained with a symmetry conserving configuration mixing (SCCM) method based on the Gogny EDF. The method allows a closer comparison between EDF and shell model with configuration mixing in large valence spaces (SM-CI) results, and can serve as a guidance to define physically sound valence spaces for SM-CI calculations. As a first application of the method, we analyze the onset of deformation in neutron-rich N = 40 isotones and the role of the SSP levels around this harmonic oscillator magic number, with particular emphasis in the structure of 64 Cr.

Status and future of nuclear matrix elements for neutrinoless double-beta decay: a review

“…MCSM calculations now can to work with configuration spaces of dimension 10 23 [242], while exact diagonalization currently requires a space of dimension 10 11 or less. The MCSM number is large enough to allow the extension of shell model configuration spaces so that they include all spin-orbit partners in ββ-decaying nuclei and all single-particle orbitals found relevant in QRPA or EDF calculations [243,244]. The Monte Carlo approach could also facilitate ab initio no-core shell model calculations [245], which are currently limited to nuclei with less than about 20 nucleons [246,247], in isotopes closer to those used in ββ-decay experiments.…”

Shape coexistence and multiparticle-multihole structures in Cd110,112

“…However, full SCCM calculations are required to obtain excitation energies and transition rates for comparisons with experimental data. Additionally, the collective behavior of the nucleus can be analyzed with the collective wave functions defined within the SCCM method [60], and the shell structure can be assessed by computing the occupation numbers of spherical orbitals for each individual nuclear state, taking into account all beyond-mean-field effects [78].…”

“…These quantities are derived from the number of protons/neutrons occupying the orbitals defined by the spherical Hartree-Fock field (see Ref. [78] for details). Particles and holes are defined by taking a core made of the 0s, 0p, 0d1s, 0f 1p and 0g 9/2 spherical orbitals as the reference.…”

Variational approximations to exact solutions in shell-model valence spaces: Calcium isotopes in the pf shell

“…This is equivalent to the diagonalization of the Hamiltonian in the subspace spanned by the set of projected states P J M K P N P Z P π |Φ(q) , ∀ qK . exc (MeV) (g) 54 Ca In practice, however, due to the linear redundancy among the projected states, the dimension of the subspace within which the Hamiltonian is effectively diagonalized is much smaller. In Table IV, we compare the dimensions of the exact diagonalization using Slater determinants coupled to J with the dimensions of the GCM diagonalization using the natural basis states for even and odd calcium isotopes (the dimensions are symmetric with respect to particles and holes).…”