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The multipole polarizabilities for hydrogen-like atoms with Hulthén potential are calculated with the sum-over-states formalism where the system bound and pseudocontinuum states are produced by employing the generalized pseudospectral method. Energies for nonzero angular momentum states, transition oscillator strengths, and dipole polarizabilities for the ground state of H atom with HP are calculated with high accuracy and compared with previous calculations. Quadrupole, octupole, and hexadecapole polarizabilities for both the ground and excited states are reported for the first time. The combined effect of Hulthén potential and impenetrable sphere on the polarizabilities is investigated, and the relation of such system with the confined H atom and particle in a box is discussed. Further comparison among Hulthén, screened Coulomb, and exponential cosine screened Coulomb potentials reveals that although the ground state energies follow the comparison theorem very well, their first-order energy corrections show complicated variations. [ABSTRACT FROM AUTHOR]

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 2k-pole polarizability of s-wave states is explicitly derived and numerically validated to follow a power law with the exponent −2(k + 1). [ABSTRACT FROM AUTHOR]

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 ≥ 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 ≥ l + 1 states decrease to certain values and, eventually, they approach to infinity at the critical screening parameter. For states with n ≤ 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. [ABSTRACT FROM AUTHOR]

The explicitly‐correlated basis sets are much easier to be linearly dependent than the product type bases constructed by one‐electron orbitals due to the explicit inclusion of interelectronic coordinates in system wave functions. In this work, we apply Löwdin's canonical orthogonalization method to study the linearly dependent problems arising from the variational calculations based on Hylleraas configuration‐interaction (Hy‐CI) basis functions. Both the ground and excited states of He atom are calculated with increasingly large basis sets. Our results show that the linear dependence in Hy‐CI basis sets can be successfully overcome by employing Löwdin's canonical orthogonalization method, yet without using extended higher‐precision arithmetic in numerical implementations. Therefore, the computational effort can be reduced considerably. It is expected that the present method can be applied to other types of explicitly correlated basis functions. [ABSTRACT FROM AUTHOR]

The angular quantities 〈 θ 12 〉 and 〈 cos θ 12 〉 for helium atom in both ground and singly-excited states are calculated in the framework of full configuration interaction. The two-electron system wave functions are expanded in terms of the product of Slater-type orbitals. The convergence and accuracy of reported results are examined in detail. From the comparison with previous work, it is shown that the present work establishes the most accurate prediction of the quantity 〈 θ 12 〉 for helium atom up to the present. Radial quantities of 〈 r < 〉 , 〈 r > 〉 , 〈 r 〉 , and 〈 r 12 〉 are also reported and compared with previous calculations. [ABSTRACT FROM AUTHOR]

We apply Löwdin's canonical orthogonalization method to investigate the linearly dependent problem arising from the variational calculation of atomic systems using Slater-type orbital configuration-interaction (STO-CI) basis functions. With a specific arithmetic precision used in numerical computations, the nonorthogonal STO-CI basis is easily linearly dependent when the number of basis functions is sufficiently large. We show that Löwdin's canonical orthogonalization method can successfully overcome such problem and simultaneously reduce the dimension of basis set. This is illustrated first through an S-wave model He atom, and then the real two-electron atoms in both the ground and excited states. In all of these calculations, the variational bound state energies of the two-electron systems are obtained in reasonably high accuracy using over-redundant STO-CI bases, however, without using extended high-precision technique. © 2015 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

The screening effect of dense quantum plasmas on the ground and singly excited states of two-electron atoms are investigated by employing the explicitly correlated Hylleraas configuration-interaction wave functions in the framework of Ritz variational principle. Exponential cosine screened Coulomb potential is used to model the electron–nucleus​ and interelectronic interactions in the atomic systems. Energy levels for the ground and 1 s n l 1 , 3 L (n ≤ 5 and l ≤ 4) singly excited states of H − , He, Li + , Be 2 + , and B 3 + are reported for screening parameters varying from zero to the value nearing corresponding critical screening parameter. Convergence of our calculations are estimated by systematically increasing the number of basis functions. A thorough comparison with available theoretical predictions on the ground state energies at various screening parameters is made, while for the excited states a comparison with the well-established energies of unscreened atoms is performed. The variation of ionization energy and the validity of Hund's rule for two-electron systems in dense quantum plasmas are analyzed. [ABSTRACT FROM AUTHOR]