Ab Initio Description of Nuclear Structure and Reactions in a Unified Framework

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.

核理论长期追求的一个目标是在统一框架内对核结构和反应进行自洽描述。核结构自洽方法中，核壳模型（NCSM）已得到充分发展，其中薛定谔方程被作为哈密顿矩阵的本征值问题在谐波振荡（HO）基下求解，该基由最大振荡量子数Nmax截断。在NCSM/RGM框架中，结合共振群方法（RGM）实现了对核结构和反应的统一描述。RGM是一种微观方法，其中核子被组织成群（簇），允许描述核反应以及所考虑系统的结构。在NCSM/RGM中，多核子系统的波函数在由NCSM内计算的簇波函数的乘积和表示簇间相对运动的函数构成的态基下展开。通过将复合系统的NCSM本征态添加到基中扩展NCSM/RGM，实现了结果在模型空间大小上的更好收敛性。该框架被称为无核心壳模型连续（NCSMC）。

在先前的研究中，NCSMC被应用于7Li和7Be系统，考虑了核子在不同簇之间的分布（质量分区）在单独的计算中。我们在NCSMC框架内对7Li和7Be的性质以及单核子投射体的反应进行了计算，考虑了以下质量分区：对于7Li，6Li+n、6He+p；对于7Be，6Li+p、6Be+n。在两种情况下，我们将质量分区包含在单个耦合通道计算中，以研究质量分区耦合的影响。所呈现的结果包括束缚态能量、本征相移、共振的能量和宽度，以及单核子投射体反应的截面，包括电荷交换反应6Li(n,p)6He，其描述得益于质量分区的耦合。

由于随着Nmax和核子数的增加，谐波振荡基的大小迅速增长，导致计算需求高，NCSM（以及NCSM/RGM和NCSMC）的应用受到限制。为了尝试解决这个问题，可以采用基于对称性的方法，将模型空间分解为描述核子近似对称性的群的不可约表示（irreps），并尝试仅保留对核波函数贡献主导的irreps来截断基。为此，我们使用了基于核子近似Sp(3,R)对称性的辛无核心配置相互作用（SpNCCI）框架。我们研究了SpNCCI基截断方案在减少模型空间维度的同时，尽量减少结果精度损失的能力。

为了开发一种基于对称性的结构反应统一描述方法，我们将SpNCCI与RGM结合在SpNCCI/RGM框架中。我们仅限于两个簇的情况，其中一个簇是单个核子。SpNCCI框架用于计算较重簇的结构。我们在SpNCCI/RGM框架中对基于近似Sp(3,R)对称性的简单基截断对6Li+n系统的描述进行了初步研究。通过这种基截断，我们再现了在完整Nmax截断空间中6Li+n散射和束缚态计算的某些定性特征。