DOI: 10.7274/26288734.v1
title: <em>Ab Initio</em> Description of Nuclear Structure and Reactions in a Unified Framework

description: One long-standing goal of nuclear theory is an ab initio description of nuclear structure and reactions in a unified framework. A well established ab initio method for nuclear structure is the no-core shell model (NCSM), where the Schrodinger equation is solved as an eigenvalue problem for the Hamiltonian matrix constructed in harmonic oscillator (HO) basis truncated by the maximal number Nmax of HO excitation quanta. The combination of the NCSM with the resonating-group method (RGM) in the NCSM/RGM framework achieves a unified description of nuclear structure and reactions. The RGM is a microscopic method in which the nucleons are organized into groups (clusters) allowing for description of nuclear reactions as well as structure of the system under consideration. In the NCSM/RGM the wave function of the many-nucleon system is expanded in a basis of states consisting of products of the wave functions of the clusters calculated within the NCSM and functions representing the inter-cluster relative motion. The extension of the NCSM/RGM by augmenting the basis with NCSM eigenstates for the composite system achieves better convergence properties of the results with respect to the size of the model space. The resulting framework is called the no-core shell model with continuum (NCSMC).

In a previous work the NCSMC was applied to the 7Li and 7Be systems taking into account distributions of nucleons between the clusters (mass partitions) in separate calculations. We carry out calculations of properties of 7Li and 7Be and reactions with a single-nucleon projectile within the NCSMC, taking into account the following mass partitions: 6Li+n, 6He+p for 7Li, and 6Li+p, 6Be+n for 7Be. In both cases we include the mass partitions in a single-coupled channel calculation to investigate the effect of the coupling of the mass partitions. The presented results include bound-state energies, eigenphase shifts, energies and widths of resonances, and cross sections of reactions with a single nucleon projectile, including the charge exchange reaction 6Li(n,p)6He, description of which is allowed by the coupling of the mass partitions.

The applicability of the NCSM (and thus also NCSM/RGM and NCSMC) is limited due to high computational demand caused by rapid growth of the size of the HO basis with increasing Nmax and number of nucleons. To attempt to address this issue one can use symmetry-based approaches, where the model space is decomposed into irreducible representations (irreps) of a group describing an approximate symmetry of nuclei, and try to truncate the basis by keeping only irreps dominantly contributing to nuclear wave functions. For this purpose we use the symplectic no-core configuration interaction (SpNCCI) framework based on the approximate Sp(3,R) symmetry of nuclei. We investigate the ability of SpNCCI basis truncation schemes to reduce the dimension of the model space without significant loss of precision of the results.

To develop a symmetry-based approach for unified description of structure and reactions we combine the SpNCCI with the RGM in the SpNCCI/RGM framework. We restrict ourselves to the case of two clusters one of which is a single nucleon. The SpNCCI framework is used to calculate the structure of the heavier cluster. We do a preliminary study of the effect of a simple basis truncation based on the approximate Sp(3,R) symmetry on description of the 6Li+n system in the SpNCCI/RGM framework. With this basis truncation we reproduce some qualitative features of the 6Li+n scattering and bound-state calculations in the full Nmax-truncated space.