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如何较好地描述远离稳定线的丰中子核素,是核结构理论研究的重要目标之一。对于滴线区附近的核素来说,目前还没有较为适用的有效相互作用。与WBT和WBP相互作用有所不同,YSOX相互作用重新考虑了(0~1)HW与(2~3)
$ h\omega $ 之间的跨壳相互作用,其矩阵元$ \left\langle pp|V|sdsd \right\rangle $ 与$ \left\langle psd|V|psd \right\rangle $ 有了不同的强度系数。具体来说,YSOX的两体矩阵元$ \left\langle pp|V|pp \right\rangle $ 来自于SFO,$ \left\langle sdsd|V|sdsd \right\rangle $ 来自于SDPF-M[15]。矩阵元$ \left\langle psd|V|psd \right\rangle $ 和$ \left\langle pp|V|sdsd \right\rangle $ 则基于VMU和自旋-轨道耦合,形式如下[3]:$$ \begin{split} V=&\sum _{S,T}{f}_{S,T}{P}_{S,T}\mathrm{exp}\left[-{\left(r/\mu \right)}^{2}\right]+{V}_{\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{o}\mathrm{r}}\left(\pi +\rho \right)+\\&{V}_{\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}-\mathrm{o}\mathrm{r}\mathrm{b}\mathrm{i}\mathrm{t}}\left(M3Y\right), \end{split}$$ (1) 这里求和项为中心力,其中S,T为自旋和同位旋;
$ {P}_{S,T} $ 为相应的投影算符; r为两个核子之间的距离;$ \mu $ 为高期参数。$ {V}_{\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}-\mathrm{o}\mathrm{r}\mathrm{b}\mathrm{i}\mathrm{t}} $ 是用M3Y力构建的自旋轨道耦合项,$ {V}_{\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{o}\mathrm{r}} $ 为基于$ \pi +\rho $ 介子交换势的张量力成分。模型空间以4He为冻结核心,其中p壳层对应的单粒子能量为$ {p}_{3/2}\!=\!1.05\,\mathrm{M}\mathrm{e}\mathrm{V} $ ,$ {p}_{1/2}\!=\!5.30\;\mathrm{M}\mathrm{e}\mathrm{V} $ ,sd壳层对应的单粒子能量为$ {\varepsilon }_{5/2}\!=\!8.01\,\mathrm{M}\mathrm{e}\mathrm{V} $ ,$ {\varepsilon }_{3/2}\!=\!10.11\,\mathrm{M}\mathrm{e}\mathrm{V} $ 和$ {\varepsilon }_{1/2}\!= 2.11\,\mathrm{M}\mathrm{e}\mathrm{V} $ 。
Spectral Structure Analysis of Nuclei 14C, 14,15N, and 14-18O Near Double Magic Nucleus 16O by Shell Model Calculations
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摘要: 根据YSOX,WBT以及WBP三种不同的有效相互作用对双幻核16O附近同位素14C, 14,15N, 和 14-18O的能谱结构进行了比较分析,在结合相应的实验值的基础上揭示了重新考虑跨壳相互作用对壳模型理论计算的优化效果。借助不同的相互作用以及大量理论数据与实验值的对比,发现了已有壳模型有效相互作用在该核区的不足之处,例如部分能级误差较大、能级次序反转等,这为下一步改进这些有效相互作用创造了条件。Abstract: According to three different interactions of YSOX, WBT and WBP, the spectral structure of nuclei 14C, 14,15N, and 14-18O near double magic nucleus 16O are analyzed by shell model calculations. The good effects have been found in spectral structure of these nuclei after reconsidering shell interaction. The large data analysis between these different shell model interactions and experiment also revealed the limitations of these existing interactions in this nuclei region, for example the large difference between theory and experiment, the reversed order of states and so on, which brings the further motivations of modifying shell model Hamiltonians.
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Key words:
- shell model /
- hamiltonians /
- spectral structure /
- configurations
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图 1 (在线彩图)14C的能级和主要组态成分,以及对应的实验值[14]
其中红色的水平短线为实验值,蓝色圆点(条形柱)为相互作用YSOX计算的能级值(主要组态成分),黑色方块(条形柱)为WBP相互作用计算的能级值(主要组态成分),粉色三角形(条形柱)为WBT相互作用计算的能级值(主要组态成分)。同一个能级在三种相互作用下给出的主要组态不相同时,在图中用标记斜杠(反斜杠)的空心条形柱区别。
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