Abstract

The time-independent Schrödinger equation (TISE) is solved to evaluate energy eigenvalues and eigenfunctions of H-atom confined by one of the radial potentials, which is modified by a ring-shaped potential and further encaged in a spherical boundary. We have considered the following four radial potentials i.e., Debye, Exponential Cosine Screened Coulomb (ECSC), Hulthén(\(\alpha \)), and Hulthén(2\(\alpha \)). Static \(2^{l}\)-pole polarizability of H-atom in different modified ring confinement potential is evaluated for a range of screening parameter (\(\alpha \)). Repulsive ring-shaped potential affects multipole polarizabilities and reduces the critical screening parameter in different modified ring confinement potentials. The confinement parameters \(\alpha \) and \(\beta \) considerably affect the amplitude of multipole polarizabilities. Size of the spherical boundary (\(r_{0}\)) crucially affects multipole polarizabilities and overweighs the effect of \(\alpha \) and \(\beta \). The results prove that as the screening parameter increases the polarizabilities corresponding to various radial potentials become almost equal, i.e., the response due to the different radial potentials becomes indistinguishable after a particular value of the screening parameter.

Graphic abstract

中文翻译：

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修饰的环形势中H原子的静态多极极化子

摘要

求解与时间无关的Schrödinger方程（TISE），以评估由一个径向电势限制的H原子的能量本征值和本征函数，该径向电势由环形电势修改并进一步限制在球形边界中。我们已经考虑了以下四个径向势，即Debye，指数余弦屏蔽库仑（ECSC），Hulthén（\（\ alpha \））和Hulthén（2 \（\ alpha \））。针对筛选参数的范围（\（\ alpha \），评估不同修饰环约束势中H原子的静态\（2 ^ {l} \）-极化率）。排斥性的环形电势会影响多极极化率，并降低不同修饰的环约束电势中的临界筛选参数。限制参数\（\ alpha \）和\（\ beta \）极大地影响了多极极化率的幅度。球面边界（\（r_ {0} \））的大小会严重影响多极极化率，并超过\（\ alpha \）和\（\ beta \）的影响。结果证明，随着屏蔽参数的增加，对应于各种径向电位的极化率几乎相等，即，在特定的屏蔽参数值之后，由于不同的径向电位而引起的响应变得难以区分。

图形摘要