Exponential Cosine Screened Coulomb Potential Research Articles

Doubly excited resonance states of two-electron systems in exponential cosine-screened Coulomb potentials

We have made an investigation on the 2 s 2 S e 1 resonance states in two-electron systems interacting with exponential cosine-screened Coulomb potentials (ECSCP) within the framework of stabilization method. Highly correlated wave functions are used to take into account the correlations of the charge particles. Results for resonance energies and widths are reported for Z = 1 , 2 and 3. For the unscreened case, our reported results are in nice agreement with the results so far available in the literature.

Borromean bindings in muonic molecular ions with screened Coulomb potentials

We have investigated the stability of muonic molecular ions interacting with screened Coulomb potentials of various strengths. Particular emphasize has been given to study the Borromean bindings in these ions. Two types of screened potentials are considered, namely, static screened Coulomb potentials and exponential cosine-screened Coulomb potentials. Making use of extensive correlated variational wavefunctions, Borromean windows for these ions are determined accurately. The possibility of existence of Borromean binding for other three-body systems has also been explored. Moreover, the results for ground state energies, excited states energies and several expectation values associated with ppμ, ddμ and tdμ molecular ions are reported for various values of the screening parameter.

Photodetachment of the Positronium Negative Ion with Exponential Cosine-Screened Coulomb Potentials

We have made an investigation to study the photodetachment of positronium negative ion (Ps −) interacting with exponential cosine-screened Coulomb potentials (ECSCP) within the framework of dipole approximation. The dipole transition matrix elements are calculated using the asymptotic form of highly accurate initial wave function of the bound ionic state and plane wave for final electron–positronium state. Results for photodetachment cross section in ECSCP are reported for the screening parameter in the range [0.0,0.35] (in \({a_0^{-1}}\)). Our results for the unscreened case agree nicely with some of the most accurate results available in the literature. Furthermore we make a comparative study of the photodetachment of Ps − in ECSCP with the photodetachment of Ps − in screened Coulomb potential. To the best of our knowledge, such a study on the photodetachment of Ps − in ECSCP is carried out for the first time in the literature.

Photodetachment ofH−in dense quantum plasmas

We have made an investigation to study the plasma screening effect of dense quantum plasmas on the photodetachment cross section of hydrogen negative ion within the framework of dipole approximation. Plasma screening effect has been taken care of by the exponential cosine-screened Coulomb potential (ECSCP). The asymptotic forms of highly correlated wave functions for the initial bound states of H(-) and the plane wave form for the final e(-)-H states are used to evaluate the transition matrix elements. Results for photodetachment cross section in dense quantum plasmas are reported for the plasma screening parameter in the range [0.0,0.6] (in a(0)(-1)). In respect of the photodetachment process of H(-), we have also compared the plasma screening effect of a dense quantum plasma with that of a weakly coupled plasma for which plasma screening effect has been represented by the Debye model. Our results for the unscreened case agree nicely with some of the most accurate results available in the literature.

Autoionization states of the positronium negative ion in exponential cosine-screened Coulomb potentials

The $2s^2~^1{\rm S}^e$ autoionization resonance states of the positronium negative ion (Ps-) in exponential cosine-screened Coulomb potentials (ECSCP) are investigated using stabilization method. Highly correlated wave functions for Ps- are used to take into account the correlation effect of the charged particles. Results for resonance energies and widths are reported for the screening parameter in the range 0.0-0.07 (in a0 -1), to the best our knowledge, for the first time in the literature.

Resonance states of helium in exponential cosine-screened Coulomb potentials

We have made a first investigation on the 2s2 1Se autoionization resonance of helium (He) in exponential cosine-screened Coulomb potential (ECSCP). Highly correlated wave functions have been used to take into account the correlation effect of the charged particles. Resonance energies and widths for the doubly excited He in ECSCP have been determined using the stabilization method. We report results for the resonance energies and widths for screening parameter in the range 0.0 – 0.275 a.u.

Properties of the Positronium Negative Ion Interacting with Exponential Cosine-Screened Coulomb Potentials

The positronium negative ion (Ps −) in exponential cosine-screened Coulomb potentials (ECSCP) has been theoretically investigated. Using highly correlated wave functions with 525 terms we report binding energies, annihilation rates and several other parameters for various values of the screening parameter. Our reported results for the unscreened case are in nice agreement with some of the most accurate results in the literature. Further we make a comparative study of the properties of Ps − in ECSCP with the corresponding properties in screened Coulomb potential (SCP). To the best of our knowledge, such a study on Ps − in ECSCP is carried out for the first time in the literature.

Ground states and doubly excited resonance states of H− embedded in dense quantum plasmas

We have made an investigation on the ground states and the 2s21Se resonance states of H− in dense quantum plasmas. Exponential-cosine-screened Coulomb potentials (ECSCP) are used to represent the effective potential for a test charge in dense quantum plasmas. Ground-state energies and wavefunctions are determined within the framework of Ritz's variational principle by employing highly correlated wavefunctions to take into account the correlation effect of the charged particles. Ground-state energies are shown to converge with the increase of terms in the wavefunctions. We also report various expectation values of the coordinates of electrons in H−. Resonance energies and widths for the doubly excited H− for various values of the screening parameter are determined using the stabilization method by calculating the density of the resonance states. Results for resonance energies and widths are reported for the screening parameter in the range 0.0–0.15. Such a calculation for H− is reported for the first time in the literature.

Ratios of double-to-single photoionization cross sections of helium atom embedded in dense quantum plasmas at high nonrelativistic photon energies

An investigation on the asymptotic ratios of double-to-single photoionization cross sections of the helium atom (He) embedded in dense quantum plasmas at very high nonrelativistic photon energies has been made. Exponential cosine-screened Coulomb potential has been used to represent the effective potential of a test charge in a dense quantum plasma. Making use of highly correlated wave functions for the ground states of He, results of the asymptotic ratios (R) of double-to-single photoionization cross sections for the screening parameter in the range [0,0.5] a.u. are reported. The reported value of R for the unscreened case confirms its established value. A comparative study of the behavior of R in weakly coupled plasmas and in dense quantum plasmas has also been made.

Doubly excited resonance states of helium in exponential cosine-screened Coulomb potentials

We have made an investigation on the $2{s}^{2}\text{ }{^{1}S}^{e}$ resonances in helium (He) in exponential cosine-screened Coulomb potentials (ECSCP). Highly correlated wave functions are used to take into account of the correlation effect of the charged particles. Resonance energies and widths for the doubly excited He in ECSCP are determined using the stabilization method by calculating the density of the resonance states. Results for resonance energies and widths are reported for the screening parameter in the range 0.0--0.275

Ground states of helium in exponential-cosine-screened Coulomb potentials

Ground-state energies and wavefunctions for helium atom (He) in exponential-cosine-screened Coulomb potentials (ECSCP) with screening parameter λ, have been obtained for various values of λ within the framework of Ritz's variational principle. Highly correlated and extensive wavefunctions have been used to obtain energy eigenvalues. The ground-state energies of He for various values of λ have been shown to converge with the increase of the terms in the wavefunction. The ground-state energies of He+ along with the ionization potentials of He have also been reported. Our present work represents a first calculation, for the first time in the literature, of the ground-state energies of He interacting with ECSCP.

Energy bounds for the generalized exponential–cosine screened Coulomb potential

In this paper the energy eigenvalues corresponding to the generalized exponential–cosine screened-Coulomb potential, V(r) =−alr exp(−λr) cos(μr), are studied. Variational characterization of eigenvalues and the method of potential envelopes are used to determine general eigenvalue bounds and also bounds on the critical-screening parameters.

Critical screening parameters for screened Coulomb potentials

The authors develop a simple numerical method to integrate one-dimensional eigenvalue equations and apply it to the calculation of critical screening parameters for screened Coulomb potentials. The method is based on the propagation matrix for the solutions of the eigenvalue equation and its accuracy is easily and systematically improved provided the coefficients of the eigenvalue equation can be expanded in a Taylor series about every point of the grid. They show results for the static screened and exponential cosine screened Coulomb potentials.

Hypervirial solution for the generalized exponential cosine-screened Coulomb potential.

The bound-state energy spectrum of the generalized exponential cosine-screened Coulomb potential is obtained by employing the hypervirial equations with the Hellman-Feynman theorem applied to the screening parameters \ensuremath{\lambda} and \ensuremath{\mu} independently. The energy eigenvalues are obtained up to the fourth order of the screening parameters.

Perturbative results from the 1/N expansion for screened Coulomb potentials

The energy eigenvalues for the Hulthén, Yukawa, and exponential-cosine screened Coulomb potentials are calculated in the 1/N expansion. States with up to three nodes in the wave functions are considered. We obtain the perturbative results up to the order of λ8, where λ is the screening parameter.

Hypervirial 1/Nexpansion for the bound-state energy spectrum of the generalized exponential-cosine-screened Coulomb potential

The bound-state energy spectrum of an N-dimensional generalized exponential cosine-screened Coulomb potential is obtained by employing the N-dimensional hypervirial equations and the Hellman-Feynman theorem. The present method is shown to provide a useful 1/N expansion scheme which can be used as an alternative to the method of Mlodinow and Shatz [J. Math. Phys. 25, 943 (1984)] for the determination of the energy eigenvalues of the screened Coulomb potentials.

Bound-state energies of the generalized exponential cosine-screened Coulomb potential.

Bound-state energies of the generalized exponential cosine-screened Coulomb potential.

An improved calculation for screened Coulomb potentials in Rayleigh-Schrodinger perturbation theory

Earlier works on screened Coulomb potentials using Rayleigh-Schrodinger perturbation theory have been re-examined. Instead of working with the usual Hulthen potential as the unperturbed Hamiltonian, the authors propose that a scaled Hulthen potential with modified strength and screening coefficient represents the lowest-order approximation for the static-screened Coulomb and exponential cosine-screened Coulomb potentials. The scale parameter appearing in the new Hulthen potential is then determined from the notion of the virial theorem and intuitive physical arguments. It is found that the accuracy of the predicted energy eigenvalues for the bound s states improves significantly even when the screening parameter is large and quite close to its critical values for which the quantum state becomes just bound. In spite of the simplicity of the approach, the numerical results compare fairly well with those obtained from rigorous analytic approximation methods.

Group Theoretic Approach to the Exponential Cosine Screened Coulomb Potential

Perturbation method, using the properties of SO (2,1) algebra is applied to get a simple analytical formula for energy eigenvalues of the exponential cosine screened Coulomb potential.

Accurate eigenvalues and oscillator strengths for the exponential-cosine screened Coulomb potential

Energy eigenvalues accurate to eight to six significant figures are obtained for the exponentialcosine screened Coulomb (ECSC) potential with the use of a numerical method. Oscillator strengths for the $2p$ to $1s$ transition are calculated for some values of the screening parameter. Results are obtained for scattering resonances for the $1s$, $2s$, and $2p$ states. The critical screening parameter for the $1s$ state of the generalized ECSC potential has also been calculated.