镜像位移能与电荷半径中常见的有限密度电荷对称性破缺响应
Charge-symmetry-breaking effects on displacement energies and charge radius differences in mirror nuclei
中文总结 AI 辅助
研究通过差分Skyrme能量密度泛函分析，用同一类III电荷对称性破缺泛函生成镜像位移能和电荷半径差，映射残差到相关项，分析多组数据，得出需量化表面梯度敏感的CSB修正才能用镜像电荷半径差探测试验，且相关一致性比绝对半径修正更稳健的结论。
中文摘要 AI 辅助
只有当超出库仑相互作用的核同位旋对称性破缺得到控制时，镜像电荷半径才能约束中子皮。我们进行了一种差分Skyrme能量密度泛函分析，其中镜像位移能（MDEs）和镜像电荷半径差由同一类III电荷对称性破缺（CSB）泛函产生。从仅含库仑作用的自洽SLy4和SkM*基线出发，我们将减去库仑作用后的MDE残差映射到体积和表面梯度CSB项上。MDEs确定了几乎简并的体积 - 表面方向，而测量的锚定半径选择该方向上用于目标预测的点，且不引入特定于半径的参数。测量的$^{34}$Ar - $^{34}$S、$^{36}$Ca - $^{36}$S、$^{38}$Ca - $^{38}$Ar和$^{54}$Ni - $^{54}$Fe对形成了紧凑的表面梯度类响应类别，SLy4的$\lambda_B = 1.32 \pm 0.04~fm^{-2}$，SkM*的为$1.20 \pm 0.05~fm^{-2}$。MDEs主要约束有效组合$t_0^{\mathrm{III}} - \lambda_{\mathrm{cl}}C_\Delta^{\mathrm{III}}$，而非两个耦合项单独约束。联合体积加表面梯度拟合在SLy4中给出的MDE和$\Delta R_{\rm ch}^{\rm mirr}$RMS残差分别为$0.0529$MeV和$0.0031$fm；SkM*恢复了响应类别，但给出的$\Delta R_{\rm ch}^{\rm mirr}$残差更大。校准后的响应在$10^{-2}$fm水平上改变了富质子镜像皮，并给出了$^{40}$Ti、$^{42}$Ti、$^{46}$Cr和$^{50}$Fe的电荷半径预测，SLy4 - SkM*的差值高达$0.021$fm。因此，在将镜像电荷半径差用作清洁的中子皮或对称能探针之前，必须对表面梯度敏感的CSB修正进行量化。SLy4和SkM*在响应类别分配上的一致性比它们的绝对半径修正更稳健，绝对半径修正仍依赖于能量密度泛函。
英文摘要
We study the effect of charge symmetry breaking (CSB) energy density function (EDF) on the mirror displacement energies (MDEs) and charge radius differences of mirror nuclei within the self-consistent Hartree-Fock-Bogolyubov (HFB) model taking Skyrme EDFs, SLy4 and SkM* as the central part of nuclear potential. We introduce the volume and the derivative terms in CSB EDF and calibrate the strength adopting four reference mirror pairs $^{34}$Ar--$^{34}$S, $^{36}$Ca--$^{36}$S, $^{38}$Ca--$^{38}$Ar, and $^{54}$Ni--$^{54}$Fe, for which experimental data of both MDEs and mirror charge-radius differences are available. We introduce a sensitivity matrix which connects two CSB terms to residuals of MDEs and mirror charge-radius differences after subtracting the effect of Coulomb interaction. By using the sensitivity matrix, we found out that the derivative term is important to reproduce both observables in a good accuracy together with the volume term, especially for the residual of mirror charge radii. The optimized CSB EDF are further applied to predict the charge radius differences of mirror pairs, $^{40}$Ti--$^{40}$Ar, $^{42}$Ti--$^{42}$Ca, $^{46}$Cr--$^{46}$Ti, and $^{50}$Fe--$^{50}$Cr. We pointed out also that the CSB effects change neutron skins of mirror proton-rich nuclei at the $10^{-2}$ fm level so that the CSB contributions must be included before charge-radius differences between mirror nuclei are used to extract neutron-skin or symmetry-energy parameters.
