不可穿透球内类氢原子康普顿轮廓的信息论分析
Analysis of Compton profile through information theory in H-like atoms inside impenetrable sphere
摘要：
原子在各种腔中的限制已经研究了近八十年。然而，这种系统的康普顿轮廓尚未被研究。在这里，我们构建的康普顿轮廓（CP）的H原子径向限制内的\emph{hard}球形外壳，以及在\emph{free condition}。给出了自由原子圆态和无节点态的CP的精确解析关系。通过标度的思想，这已被进一步扩展到一个H类原子被困在一个不可穿透的腔的研究。这些构造的CP的准确性已被证实通过计算各种动量矩。除此之外，一些信息理论的措施，如香农熵（$S$）和Onicescu能量（$E$）已被利用来表征这些配置文件。利用自由类氢原子的基态CP，导出了$S$和$E$的精确封闭形式表达式.详细的研究表明，约束的增加抑制了动能的耗散率。在固定的$\ell$下，该速率随着$n$的升高而减小。然而，在一定的$n$下，该速率随着$\ell$的进展而加速。对自由体系的类似分析显示出与受限体系完全相反的趋势。然而，在自由和受限环境中，CP通常随着$Z$的升高而变宽。有代表性的计算是在数值上为低的封闭系统的状态，采取两种形式的位置空间波函数：（a）精确（b）高精度的本征函数通过广义伪谱方法。在本质上，CP的报道限制H原子（和等电子系列），并采用信息理论框架进行研究。
英文摘要：
Confinement of atoms inside various cavities has been studied for nearly eight decades. However, the Compton profile for such systems has not yet been investigated. Here we construct the Compton profile (CP) for a H atom radially confined inside a \emph{hard} spherical enclosure, as well as in \emph{free condition}. Some exact analytical relations for the CP's of circular or nodeless states of free atom is presented. By means of a scaling idea, this has been further extended to the study of an H-like atom trapped inside an impenetrable cavity. The accuracy of these constructed CP has been confirmed by computing various momentum moments. Apart from that, several information theoretical measures, like Shannon entropy ($S$) and Onicescu energy ($E$) have been exploited to characterize these profiles. Exact closed form expressions are derived for $S$ and $E$ using the ground state CP in free H-like atoms. A detailed study reveals that, increase in confinement inhibits the rate of dissipation of kinetic energy. At a fixed $\ell$, this rate diminishes with rise in $n$. However, at a certain $n$, this rate accelerates with progress in $\ell$. A similar analysis on the respective free counterpart displays an exactly opposite trend as that in confined system. However, in both free and confined environments, CP generally gets broadened with rise in $Z$. Representative calculations are done numerically for low-lying states of the confined systems, taking two forms of position-space wave functions: (a) exact (b) highly accurate eigenfunctions through a generalized pseudospectral method. In essence, CPs are reported for confined H atom (and isoelectronic series) and investigated adopting an information-theoretic framework.
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