Ground state and resonant states of helium in exponential cosine screened Coulomb potential (original) (raw)
Related papers
Ground states of helium in exponential-cosine-screened Coulomb potentials
Journal of Physics B: Atomic, Molecular and Optical Physics, 2009
Ground-state energies and wavefunctions for helium atom (He) in exponential-cosine-screened Coulomb potentials (ECSCP) with screening parameter λ, V (r) = − 1 r e −λr cos (λr) (in au), 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.
Doubly excited resonance states of helium in exponential cosine-screened Coulomb potentials
Physical Review A, 2009
We have made an investigation on the 2s 2 1 S e resonances in helium ͑He͒ in exponential cosine-screened Coulomb potentials ͑ECSCP͒. 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 and doubly excited resonance states of H−embedded in dense quantum plasmas
Journal of Physics B, 2009
We have made an investigation on the ground states and the 2s 2 1 S e 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.
Physical Review A, 2009
nonautoionizing states of helium atom with Coulomb and screened Coulomb ͑Yukawa͒ potentials in the framework of Ritz variational principle. Highly accurate correlated exponential wave functions with exponents generated by a quasirandom process are used to represent the correlation effect. For the Coulomb case, the metastable bound-excited 2pnp 1 P e ͑3 Յ n Յ 5͒, 2pnp 3 P e ͑2 Յ n Յ 5͒, 2pnd 1,3 D o ͑3 Յ n Յ 9͒, and 2pnf 1,3 F e ͑4 Յ n Յ 9͒ states energies are reported. Our upper-bound results for the 2pnd 1 D o ͑3 Յ n Յ 7͒, 2pnf 1 F e ͑4 Յ n Յ 8͒, 3 D o and 3 F e states are the lowest values up to this date. For the screened Coulomb case, the lower-lying metastable bound states energies for different screening parameters and for each spin states are also reported.
Complex-scaling treatment for high-lying doubly excited resonances for screened Coulomb helium atom
The European Physical Journal D-Atomic, …, 2008
This work presents an investigation on the doubly excited 1 S e autoionizing states of screened helium atom lying below the n = 4 threshold of the He + ion. The potential generated in this system is represented by a Yukawa type potential. We have employed complex-coordinate rotation method, as it is a powerful scheme to study high lying resonances. Hylleraas type wave function is used to consider the correlation effect between all the charged particles. Our resonance parameters for the resonances lying below the He + (n = 2) threshold agree well with those of the existing calculations by using the stabilization method. Resonances associated with higher thresholds are new calculations. All the present results are well converged with basis length N = 444.
Ground states and doubly excited resonance states of H − embedded in dense quantum plasmas
Journal of Physics B: Atomic, Molecular and Optical Physics, 2009
We have made an investigation on the ground states and the 2s 2 1 S e 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.
Doubly excited bound and resonance (^{3}P^{e}) states of helium
Physical Review A, 2009
Highly precise energy values for the first 14 3 P e bound states of helium arising out of two electrons having equal azimuthal quantum number are being calculated by using Ritz variational method. The present calculated upper bound energies are lowest yet obtained. Resonance energies and widths for a wide range of resonance states ͑ 3 P e ͒ of helium below N =3-5 ionization threshold of He + have also been evaluated by using stabilization method. The present resonance parameters for the region below N =3-5 ionization threshold of He + are in excellent agreement with the few available accurate theoretical results. Moreover in the present paper, the resonance parameters of 3 P e resonance states below N = 6 and 7 ionization thresholds of He + are also reported.
Computation, 2021
The energy eigenvalues of the ground state helium atom and lowest two excited states corresponding to the configurations 1s2s embedded in the plasma environment using Hulthén, Debye–Hückel and exponential cosine screened Coulomb model potentials are investigated within the variational Monte Carlo method, starting with the ultracompact trial wave functions in the form of generalized Hylleraas–Kinoshita functions and Guevara–Harris–Turbiner functions. The Lagrange mesh method calculations of energy are reported for the He atom in the ground and excited 1S and 3S states, which are in excellent agreement with the variational Monte Carlo results. Interesting relative ordering of eigenvalues are reported corresponding to the different screened Coulomb potentials in the He ground and excited electronic states, which are rationalized in terms of the comparison theorem of quantum mechanics.
Improvement to wave functions and energy values of the ground state of helium
Nonrelativistic wave functions and energy values for the ground state of helium are calculated accurately by using the conventional Rayleigh-Ritz technique. However, the trial wave functions used are more general than those used by Hylleraas and others. They contain interelectronic separation coordinates in the exponential function beside the variational parameters. Groups of three-and four-parameter wave functions are obtained with comparatively smaller energies. Also, improved wave functions and energies have been obtained by solving determinants of orders 7, 13, 22, 34, 50, 70, 95, and 125, using a simple model. The last determinant yields an energy value of — 2.903 724 371 a.u. as compared with-2.903 724 370 a.u. obtained by Pekeris by solving a determinant of order 715. The first determinant (ten parameters) yields an energy value of ,-2.903425 858 a.u. , as compared with the recent value of — 2.9022 a.u. computed by Tweed with the use of a 41-parameter wave function.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2012
In the presence of an environment of mobile charges, the bound-state Schrödinger Hamiltonian for an embedded He atom differs from its vacuum form. The central problem of incorporating screening in the nucleus-bound-electron and bound-electron-bound-electron terms of this Hamiltonian is investigated here for the He ground-state in a comparative manner by using two models, and the same product form of 1s-type parametric hydrogenic functions to perform exploratory variational calculations. Both models employ induced charge densities in the corresponding Poisson's equations with a fixed point-like nucleus, but the underlying charge-density response of the host system is generated by differently chosen perturbations. These are the point-charge nucleus and the nucleusbound-electron charge distribution as external perturbations. The repulsive bound-electron-boundelectron interaction in the Hamiltonian is modeled by a parametric Yukawa-type potential. Using the consistent variational results for the binding energies and wave functions, the charge-state dependent stopping power of a metallic target for slowly moving He is briefly discussed.