Ground state energy of hydrogen-like ions in quantum plasmas (original) (raw)
Related papers
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.
Ranges and stopping power of KeV electrons in the solid hydrogens
Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 1988
l-3 keV electron ranges and stopping power in the solid hydrogens have been investigated by the Monte Carlo simulation method on the basis of experimental thin film measurements. In the simulation, elastic scattering cross sections are calculated exactly using the single-atom crystalline potentials. Inelastic processes for gold are treated by modifying Gryzihski's semiempirical expression for each core and valence electron excitation. For H, the ionization cross section from Green and Sawada is applied together with the gas phase stopping power from Parks et al. Simulations of electron penetration in a layer of solid hydrogen on a gold substrate with normal incidence and reflection from bulk hydrogen with different angles of incidence are fitted to experimental measurements by adjusting the stopping power of electrons in solid hydrogen. It is found to be 0.75 times the stopping power for the gas phase. The mean path length and mean penetration depth of electrons in solid hydrogen are determined from the simulations with this modified stopping power. Also the full penetration depth distributions are presented as well as their Gaussian parametrizations. The previously determined measured projected range is almost equal to the calculated mean path length.
Confined hydrogenlike ions in plasma environments
Physical Review A
The behavior of H-like ions embedded in astrophysical plasmas in the form of dense, strongly and weakly coupled plasmas is investigated. In these, the increase and decrease in temperature are impacted by a change in confinement radius r c. Two independent and generalized scaling ideas have been applied to modulate the effect of the plasma-screening constant λ and ion charge Z on such systems. Several relations are derived to interconnect the original Hamiltonian and two scaled Hamiltonians. In the exponential-cosine-screened Coulomb potential (ECSCP; dense) and weakly coupled plasma (WCP) these scaling relations have provided a linear equation connecting the critical screening constant λ (c) and Z. Their ratio offers a state-dependent constant beyond which a particular state vanishes. Shannon entropy has been employed to understand the plasma effect on the ion. With an increase in λ, the accumulation of opposite charge surrounding the ion increases, leading to a reduction in the number of bound states. However, with a rise in ionic charge Z, this effect can be delayed. The competing effect of plasma charge density n e and temperature in WCP and ECSCP is investigated. A recently proposed simple virial-like theorem was established for these systems. Multipole (k = 1-4) oscillator strength and polarizabilities for these are studied considering 1s, 2s states. As a bonus, analytical closed-form expressions are derived for f (k) and α (k) (k = 1-4) involving 1s and 2s states for the free H-like ion.
Negative ion of hydrogen in dense semi-classical plasmas: Stability and zero-energy resonances
Physics of Plasmas, 2021
The effects of dense semi-classical plasma (DSCP) on the ground state of the negative ion of hydrogen (H À) and on the dynamics of electron-hydrogen scattering have been investigated. DSCP is described by an effective potential which takes care of the collective effects of the plasma at large distances as well as the quantum mechanical effects of diffraction at small distances. An elaborative wave function is employed in the Rayleigh-Ritz variational method to compute the ground state energy of H À for various values of the plasma parameters. In particular, critical values of the plasma parameters are calculated accurately to make a detailed study on the stability of the ion embedded in DSCP. Furthermore, parameters related to the ground state of H À and H are used in the effective range theory to study the effects of DSCP on the dynamics of low-energy e À H(1s) scattering. Special emphasis is given to investigate the phenomenon of zero-energy resonances by computing the singlet scattering length near the critical values of the plasma parameters.
Laser and Particle Beams, 2002
In this work, the Saha equation is solved using atomic data provided by means of a new relativistic-screened hydrogenic model based on analytical potentials to calculate the ionization state and ion abundance for LTE iron plasmas. The plasma effects on the atomic structure are taken into account by including the classical continuum lowering correction of Stewart and Pyatt. For high density, the Saha equation is modified to consider the degeneration of free electrons using the Fermi–Dirac statistics instead of the Maxwellian distribution commonly used. The results are compared with more sophisticated self-consistent codes.
A Classical Description of the Electrons in Plasma
حوليات العلوم و التكنولوجيا, 2013
In this work, we calculated the effective potential of an electron in a plasma. This potential, which is obtained by solving a non-linear integral equation, is a sum of three contributions: the first is the interaction energy between the electron plasma and a test charge regarded as an impurity. We have taken this interaction equal to screened "Kelbg". The second is the Coulomb interaction energy between the electron in question and the other electrons plasma, that we calculate using a Maxwell-Boltzmann distribution. The third is Coulomb interaction energy between the electron and ions plasma uniformly distributed. The effective potential, is obtained, in the first stage, we have calculated the distribution of electric microfield created by the electrons on the impurity. In the second stage we calculated the time autocorrelation function of the electric microfield. The results are compared with those given by molecular dynamics simulation.
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.
Energy spectrum of hydrogen atoms in dense plasmas
Physical Review E, 1995
From the Bethe-Salpeter equation for the two-particle (proton-electron) Green function, an effective Schrodinger wave equation can be derived for a hydrogen atom in a hydrogen plasma, which describes the perturbation of atomic energy levels and eigenstates by many-particle plasma effects (Pauli blocking, exchange and dynamic self-energy, and interaction-potential correction due to dynamic screening). Taking full account of dynamic screening by the random-phase approximation dielectric function, we solved the effective wave equation for nondegenerate plasmas. For bound atomic states, the plasma effects nearly compensate one another and the energy levels depend only weakly on density. In contrast, the lowering of the continuum edge is not diminished by such compensation, so that the bound states successively merge into the continuum with increasing plasma density. As our results show, reliable calculations have to incorporate dynamic screening, since the use of static screening (which greatly facilitates calculations) may lead to substantial errors, even at low densities.
On the self-energy of electrons in metals
Solid State Communications, 1987
The electron self-energy of unoccupied states is investigated taking into account dynamical screening and nonlocal exchange. To obtain agreement with experiment it is crucial to go beyond the framework of the homogeneous electron gas and include the nonlocal exchange with electrons in valence and core shells. This contribution of atomic origin gives rise to a considerable, almost linear energy dependence of the self-energy over a wide energy range in agreement with experimental findings for many substances and in disagreement with the local density approximation. Quantitative results are presented for Ag.
Stability of hydrogen atom in non-ideal classical plasmas
Physics of Plasmas
The stability of a hydrogen atom embedded in classical nonideal plasma has been investigated. The interaction potential between the proton and the electron has been modeled by a pseudopotential, which is obtained from a sequential solution of Bogolyubov chain equations. The critical values of the plasma screening parameters have been determined quite accurately within the framework of the Rayleigh-Ritz variational method by employing an extensive wave function following a definitive prescription. Convergence of the results has been corroborated by increasing the number of terms in the wave function. A detailed study has been carried out on the effects of nonideality of plasma on the bound states for the density and temperature lying in the ranges of 2.7 Â [10 23-10 26 ] m À3 and [10 4-10 5 ] K, respectively. It is found that the atom remains bound in the aforementioned density and temperature ranges.