Nuclear clustering using a modern shell model approach

Abstract

Nuclear clustering, alpha decays, and multi-particle correlations are important components of nuclear dynamics. In this work we put forward the Cluster-Nucleon Configuration Interaction Model. We use the modern configuration-interaction approach with advanced realistic shell-model Hamiltonians in order to study clustering phenomena; the study is facilitated by the algebraic properties of many-nucleon configurations in the harmonic oscillator basis.Using translationally invariant formalism we built cluster channels that satisfy Pauli exclusion principle as well as orthogonality and normalization conditions. We formally justify the formalism and demonstrate that, within the new method, clustering strengths satisfy sum rules that are consistent with the statistical properties of nuclear reactions with composite particles. Using properly renormalized cluster form factors our approach appears to resolve long-standing problems related to absolute normalization of the alpha clustering spectroscopic factors and their behavior in sd-shell nuclei.Our methods are demonstrated in studies of α spectroscopic factors in sd-shell nuclei and in 16 O treated in p-sd shells. Comparison with experimental data supports validity of the approach.

Structure of Ne20 states in resonance O16+α elastic scattering

“…We compared our findings with those obtained theoretically using clusternucleon configuration interaction approach developed in several previous works, including Ref. [2] and references therein. There is good overall agreement between theoretically predicted and observed spectra.…”

“…The CNCIM [2] is among the latest developments of the classical shell model approaches towards clustering. This model targets a combination of configuration interaction techniques with algebraic methods that emerge in the description of clustering.…”

“…In order to fully explore the problem, we considered several different model spaces and corresponding Hamiltonians: the sd model space with USDB interaction [5]; unrestricted p-sd shell model Hamiltonian [23], the same Hamiltonian has been used in Ref. [2]; WBP Hamiltonian [24] allowing 0 ω, 1 ω, and 2 ω excitations in p-sd-pf valence space; and the sd-pf Hamiltonian [25]. This sequence of Hamiltonians represents and expands the valence space from sd to p-sd, to p-sd-pf.…”

“…It is remarkable that almost all of the observed states below 10 MeV can be classified into several overlapping rotational-like bands. The ground state band (based on 0 + 1 ) has a transient character from the shell to the cluster structure; this stems from algebraic symmetry properties [2]. Three other bands based on 0 + levels, on 0 16 O + α core structure as can be seen from their reduced α particle widths; probably the 0 + 3 band has a predominant 12 C+ 8 Be structure which manifests itself through the selectivity of the 8 Be transfer reactions [7].…”

“…For a long time, the surprising alpha cluster structure has been a stimulus for the development of classical shell model approaches (see [2] for new results). Additionally, recent work by the authors of Ref.…”