Clustering in structure and reactions using configuration interaction techniques

Abstract

Background: Atomic nuclei are remarkable quantum many-body systems where clustering properties develop naturally from underlying interactions between the constituent nucleons. Clustering degrees of freedom manifest themselves in multiple structure and reaction observables.Purpose: Our goal is to study nuclear clustering and its emergence in many-nucleon dynamics from nucleon-nucleon interactions. Clustering is a phenomenon that is known to emerge on the boundary between structure and reactions, therefore developing appropriate techniques that bridge the structure-reaction divide and establishing connections to observables is among our principal objectives. Showing consistency and how the new techniques can be reduced to well established other methods is an important part of this work.Methods: The configuration-interaction technique based on second quantization is used to treat the quantum many-body problem assuring that fermionic antisymmetry is fully satisfied. The use of the harmonic oscillator single-particle basis allows for the center-of-mass coordinate to be separated and prepared in a desired oscillator state for each cluster. The relative motion reaction basis channels are constructed by coupling clusters in different harmonic oscillator states with respect to their relative motion. Finally, using a resonating group method strategy we solve the generalized eigenvalue problem to obtain scattering channels. Structural clustering characteristics are discussed and the modified harmonic oscillator representation for scattering equations method is used to extract scattering observables.Results: New methods for treating clustering problems have been put forward. We demonstrate broad applicability of the developed techniques. Examples highlight connections with algebraic techniques, and the role of approximations leading to algebraic limits is assessed using realistic examples. Various types of clustering characteristics are used to study alpha clustering in light nuclei that are relevant to currently ongoing experimental efforts. We demonstrate the emergence of strongly clustered bands of states in beryllium, triple alpha channels in $^{12}\mathrm{C}$, and molecular type clustering in $^{21}\mathrm{Ne}$. Starting from nucleon-nucleon interactions without any additional assumptions scattering phase shifts for alpha-alpha scattering are determined and shown to be consistent with those observed.Conclusions: In this work we put forward a new configuration-interaction-based method that targets the physics of clustering, and further unifies nuclear structure and reactions. We provide detailed discussions and many examples highlighting features and advantages of the approach.