Confinement of atoms inside various cavities has been studied for nearly eight decades. However, the Compton profile (CP) for such systems has not yet been investigated. Here we construct the CP for a H atom radially confined inside a hard spherical enclosure, as well as in a free condition. Some exact analytical relations for the CP’s of circular or nodeless states of free atoms is presented. By means of a scaling idea, this has been further extended to the study of a H-like atom trapped inside an impenetrable cavity. The accuracy of these constructed CPs 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 ℓ, this rate diminishes with a rise in n. However, at a certain n, this rate accelerates with progress in ℓ. Similar analysis on the respective free counterpart displays an exactly opposite trend as that in a confined system. However, in both free and confined environments, the 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 atoms (and isoelectronic series) and investigated adopting an information-theoretic framework.

已经研究了近八十年来原子在各种腔体内的约束。但是，尚未研究此类系统的康普顿规范（CP）。在这里，我们为径向限制在硬球形外壳内以及自由状态下的H原子构造CP 。给出了自由原子的圆形或无节点状态CP的一些精确解析关系。借助于定标思想，这已进一步扩展到对无法穿透的腔体内捕获的类H原子的研究。通过构造各种动量矩可以确认这些构造的CP的精度。除此之外，还有几种信息理论测量方法，例如香农熵（S）和奥尼切斯库能量（E）已被用来表征这些配置文件。使用自由H状原子中的基态CP，可以得出S和E的精确封闭式表达式。一项详细的研究表明，约束的增加会抑制动能的耗散率。在固定的ℓ下，此速率随着n的增加而减小。然而，在一定的ñ，这个速度与进程加快ℓ。对各个自由对应物的类似分析显示的趋势与密闭系统中的趋势完全相反。但是，在自由和受限环境中，CP通常随着Z的增加而变宽。。对受限系统的低洼状态进行数值计算，采用两种形式的位置-空间波函数：（a）精确的（b）通过广义伪谱方法的高度精确的本征函数。从本质上讲，CP报道了受限的H原子（和等电子序列），并采用信息理论框架进行了研究。