Preliminary Study on Uncertainty of Central Force and Effect of Cross-Shell Excitation in Shell Model
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摘要: 原子核壳模型不确定度虽然很重要，但目前为止还研究较少。本工作对壳模型中的核力不确定度和模型空间效应的展开了初步研究。核力中最重要的部分是中心力，中心力也被认为包含了最多的重整化效应。如果考虑半满壳核以及只考虑中心力的强度变化，对能谱的理论描述的变化只与中心力的C10（T，S=1，0）和C11（T，S=1，1）部分相关。中心力变化时，自旋轨道耦合力和张量力都保持裸核力的强度不变。由此得到的简单核力的一套强度参数可以对Sn和Pb同位素及N=82和126同中素的188个态的能谱描述达到0.2 MeV均方根差。但是如果对这些同位素和同中素分别考虑，均方根差可以进一步减小，并且有不同的极小值。质子质子相互作用的强度比中子中子相互作用的强度要大15%，这表明中重核中存在"镜像能差"。增大模型空间对部分核的描述很重要，比如考虑跨壳激发对质子或中子数为幻数的核很重要。还通过三个哈密顿量研究了丰中子F同位素，尽管三个哈密顿量的结果不同，双中子分离能和能谱都对跨壳激发非常敏感，并且被跨壳激发影响的趋势类似。
The uncertainty of the nuclear shell model is important but rarely investigated. The present work provides preliminary investigations on the uncertainty of the nuclear force and the effect model space in shell-model calculations. The most important part of the nuclear force is the central force, which is also considered to include the largest contribution from the renormalization effect. If semi-magic nuclei are considered and only the strength of the central force varies, C10 (T,S=1,0) and C11 (T,S=1,1) channels of the central force contribute to the theoretical variances of the description of the levels, while the spin-orbit force and the tensor force are kept unchanged as the bare ones. One set of the strengths of a simple nuclear force gives an 0.2 MeV root mean square (RMS) between observed and theoretical levels from 188 states in Pb and Sn isotopes and N=82 and 126 isotones. However, if levels in these isotopes and isotones are separately considered, RMS are further reduced and found to have two minimums with 15% stronger pp interaction than nn interaction, which indicates a "mirror difference" in medium and heavy nuclei. The enlarge of the model space are of great significance for the description of certain nuclei, such as the inclusion of cross-shell excitations for the nuclei with magic neutron and/or proton numbers. The neutron-rich F isotopes are investigated through three Hamiltonians. Despite the different results among Hamiltonians, the two neutron separation energies and levels are sensitive to and similarly contributed by the cross-shell excitations.Abstract: The uncertainty of the nuclear shell model is important but rarely investigated. The present work provides preliminary investigations on the uncertainty of the nuclear force and the effect model space in shell-model calculations. The most important part of the nuclear force is the central force, which is also considered to include the largest contribution from the renormalization effect. If semi-magic nuclei are considered and only the strength of the central force varies, C10 (T,S=1,0) and C11 (T,S=1,1) channels of the central force contribute to the theoretical variances of the description of the levels, while the spin-orbit force and the tensor force are kept unchanged as the bare ones. One set of the strengths of a simple nuclear force gives an 0.2 MeV root mean square (RMS) between observed and theoretical levels from 188 states in Pb and Sn isotopes and N=82 and 126 isotones. However, if levels in these isotopes and isotones are separately considered, RMS are further reduced and found to have two minimums with 15% stronger pp interaction than nn interaction, which indicates a "mirror difference" in medium and heavy nuclei. The enlarge of the model space are of great significance for the description of certain nuclei, such as the inclusion of cross-shell excitations for the nuclei with magic neutron and/or proton numbers. The neutron-rich F isotopes are investigated through three Hamiltonians. Despite the different results among Hamiltonians, the two neutron separation energies and levels are sensitive to and similarly contributed by the cross-shell excitations.-
Key words:
- shell model /
- uncertainty /
- central force /
- cross-shell excitation
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