The critical screening parameters for one-electron systems screened by Hulthén, Debye–Hückel, and exponential cosine screened Coulomb potentials are calculated with an accuracy close to the precision of numerical arithmetic. The results for a H atom with an infinitely heavy nucleus are reported from the ground to high-lying excited states, and those for arbitrary two-body charged systems are derived from the Zm -scaling law. A thorough comparison of the critical screening parameters for the ground and the first p -wave excited states with previous predictions is made to demonstrate the accuracy of our calculations. The critical behaviors of system-bound and pseudo-continuum eigenenergies for s - and non- s -wave states are shown to follow the quadratic and linear laws, respectively. The variation of the corresponding wave functions is analyzed in detail. For systems with non-zero orbital angular momenta, the bound states convert into shape-type resonances when the screening parameter exceeds the critical value. The resonance energy shares the same linear law as the pseudo-continuum state, while the resonance width varies by an l -dependent power law. It is further shown that the different asymptotic behaviors of the resonance energy and width are consistent with the complex analog of the Hellmann–Feynman theorem.

The electric multipole polarizabilities of one-electron atoms embedded in weakly coupled Debye plasmas are calculated in the non-relativistic framework. The static dipole, quadrupole, octopole, and hexadecapole polarizabilities for hydrogen atoms in both ground and excited states at a variety of Debye screening parameters are calculated in high precision based on the sum-over-states method, where the system bound and continuum states are produced by employing the generalized pseudospectral method. It is shown that the contribution of bound states to the polarizability decreases with increasing the plasma screening strength, whereas the contribution of continuum states is enhanced. At very small screening parameters where the plasma environment starts to take effect, it is found that the $2^l-$ pole polarizability for $s-$ wave states with principle quantum number $n\ge l+1$ has an abrupt change from its non-screening value to infinity. We attribute such a phenomenon to the sudden non-degeneracy of different angular momentum states in the n shell. With continuously increasing the screening strength, the polarizabilities for $n\ge l+1$ states decrease to certain values and, eventually, they approach to infinity at the critical screening parameter. For states with $n\le l$ , the $2^l-$ pole polarizabilities show regular enhancement from the non-screening value to infinity. The present results are compared with other theoretical calculations available in the literature and it is shown that our work has established by now the most accurate predictions of multipole oscillator strengths and polarizabilities for one-electron atoms in Debye plasmas.

Recent development of information theory provides researchers an alternative and useful tool to quantitatively investigate the variation of the electronic structure when atoms interact with the external environment. In this work, we make systematic studies on the information-theoretic measures for hydrogen-like ions immersed in weakly coupled plasmas modeled by Debye-Hückel potential. Shannon entropy, Fisher information, and Fisher-Shannon complexity in both position and momentum spaces are quantified in high accuracy for the hydrogen atom in a large number of stationary states. The plasma screening effect on embedded atoms can significantly affect the electronic density distributions, in both conjugate spaces, and it is quantified by the variation of information quantities. It is shown that the composite quantities (the Shannon entropy sum and the Fisher information product in combined spaces and Fisher-Shannon complexity in individual space) give a more comprehensive description of the atomic structure information than single ones. The nodes of wave functions play a significant role in the changes of composite information quantities caused by plasmas. With the continuously increasing screening strength, all composite quantities in circular states increase monotonously, while in higher-lying excited states where nodal structures exist, they first decrease to a minimum and then increase rapidly before the bound state approaches the continuum limit. The minimum represents the most reduction of uncertainty properties of the atom in plasmas. The lower bounds for the uncertainty product of the system based on composite information quantities are discussed. Our research presents a comprehensive survey in the investigation of information-theoretic measures for simple atoms embedded in Debye model plasmas.

Binding energies, oscillator strengths, and polarizabilities of hydrogen-like atoms embedded in dense quantum plasmas are calculated in high precision by employing the generalized pseudospectral method. Benchmark predictions of these quantities are obtained for both the ground and excited states including high-order transitions. The critical behaviour of system eigenenergies, radial mean values, oscillator strengths, and multipole polarizabilities for bound states when they approach to the corresponding continuum limit as increasing the plasma screening strength are investigated in detail. It is shown that near the critical screening parameters the quantities in s -wave states show distinct behaviour from those in non- s states and such phenomenon is attributed to the divergent asymptotic form of wave functions caused by the centrifugal potential of orbital angular momentum. Based on the power laws of energies and radial mean values extracted from numerical calculations and the approximate formulae for dipole polarizabilities, the critical behaviour of the 2 ^k -pole polarizability of s -wave states is explicitly derived and numerically validated to follow a power law with the exponent −2( k + 1).