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原子核由质子和中子组成,要弄清一个原子核有多大、里面核子怎样分布,就需要一幅从中心到边缘的“密度地图”。其中很关键的是点质子密度分布:它既反映质子的半径尺度,也告诉我们质子在核内的细致分布。点质子密度分布对核结构模型和约束核物质状态方程同样至关重要,是核反应模型的关键输入参数,通常是连接核结构与反应的纽带。实验上,人们常用弹性电子散射测量原子核电荷密度分布,但这与点质子密度并不等同,需要把电荷密度中子与质子自身大小的影响“还原”掉,才能得到真正的点质子密度。基于这一点,我们首先从电荷密度出发,梳理了它的成分以及与核半径的关系;随后基于电子散射测量的电荷密度,结合常用的密度分布函数,建立了一套统一的质子密度抽取方法,系统地完成了从7Li到232Th 共 130 个稳定原子核的点质子密度分布还原。在此基础上,我们对结果进行了精度评估,标注并剔除了不可靠的数据,同时总结出一组便于实际使用的经验公式,由此得到的一套覆盖广、流程一致的点质子密度数据库。该工作可以为核反应模型提供可靠的密度输入,也可直接比对核结构理论计算结果。
Atomic nuclei are composed of protons and neutrons. To understand how large a nucleus is and how its nucleons are distributed, we need a “density map” from the center to the surface. A key quantity in this map is the point-proton density distribution: it captures both the overall proton radius scale and the detailed spatial distribution of protons. It is essential for nuclear structure models and for constraining the nuclear matter equation of state, and it also serves as an indispensable input to nuclear reaction models that link structure to reactions. Experimentally, elastic electron scattering is commonly used to measure the charge density distribution of nuclei; however, this is not identical to the point-proton density. One must remove the effects associated with the finite size of the proton from the charge density to recover the true point-proton density. With this motivation, we first analyze the composition of the charge density and its relation to nuclear radii. We then develop a unified extraction procedure that, using electron-scattering charge densities together with commonly used functional forms of density distributions, systematically reconstructs point-proton densities for 130 stable nuclei from7Li to 232Th. On this basis, we assess the precision of the extracted results, flag and exclude unreliable cases, and summarize a set of practical empirical formulas for routine use. The resulting broad-coverage, method-consistent database of point-proton densities provides reliable inputs for nuclear reaction modeling and serves as a readily usable reference for nuclear structure calculations.