第一性原理无核芯壳模型计算原子核谱因子

原子核谱因子表征原子核单粒子轨道的性质以及占据数等信息，是联系核结构、核反应与核天体物理的重要物理量。 对于原子核谱因子的计算强烈依赖于理论模型得到的原子核多体波函数，在实际计算中通常选用普通壳模型。随着计算机性能的提高以及核多体方法的发展，第一性原理方法被应用于研究原子核性质，并取得巨大成功。 本工作基于现实两体相互作用，利用第一性原理无核芯壳模型计算较轻原子核谱因子。首先，计算了$A =6$和$7$原子核的低激发态能量，考察第一性原理无核芯壳模型对能量计算的收敛性，并比较普通壳模型与第一性原理无核芯壳模型对于$A =6$和$7$能谱的描述。结果表明，无核芯壳模型计算结果与实验符合较好，可以很好地描述结合能和激发谱性质。 然后，利用无核芯壳模型系统计算了$^{7}{\rm{Li}}$与 $^7{\rm{Be}}$镜像核叠积函数与谱因子，并分析谱因子计算的收敛性。结果显示，谱因子随着模型空间的增大收敛较慢，对于$^{7}{\rm{Li}} $，无核芯壳模型计算的谱因子同最新实验值符合得很好。最后，采用无核芯壳模型系统计算$A =6,\, 7$和$8$原子核低激发谱能量与谱因子，为核反应与核天体研究提供必要的输入量。

Ab initio no-core Shell Model for Nuclear Spectroscopic Factor

The nuclear spectroscopic factor characterizes the properties and occupancy of single-particle orbits of nuclei and other information, which is also an essential physical quantity connecting nuclear structure, nuclear reactions, and astrophysics. The spectroscopic factor is sensitive to the many-body wave function obtained from the theoretical models, and the standard shell model is usually chosen. With the development of supercomputers and nuclear many-body methods, nuclear ab initio methods have been successfully employed to study the properties of atomic nuclei with great success. In the present paper, we study the nuclear spectroscopic factor of light nuclei with ab initio no-core shell model based on the realistic nucleon-nucleon interaction. Firstly, the energies of low-lying states in $A=6$ and 7 nuclei are calculated and compared with standard shell model calculations, and the convergence of the no-core shell model is also investigated. The results show that the no-core shell model calculations are in good agreement with the experimental data and well describe the properties of binding energy and excitation spectra. Afterward, we perform systematic calculations of overlap functions and spectroscopic factors in $^{7}{\rm{Li}} $ and $^7{\rm{Be}}$ and check the the convergence of spectroscopic factor with ab initio no-core shell model. The results indicated that the convergence of spectroscopic factor of the no-core shell model calculation is slow with the increase of model space. The calculated spectroscopic factors of $^7{\rm{Li}} $ with the no-core shell model agree with available experimental data. Finally, systematic calculations of energies and spectroscopic factors of low-lying states in $A=6,\,7$, and 8 nuclei are performed, and the input quantities for nuclear reaction and astronomy studies are provided.