Ion Sphere Research Articles

Highly charged ions in a dilute plasma: An exact asymptotic solution involving strong coupling

The ion sphere model introduced long ago by Salpeter is placed in a rigorous theoretical setting. The leading corrections to this model for very highly charged but dilute ions in thermal equilibrium with a weakly coupled, one-component background plasma are explicitly computed, and the subleading corrections shown to be negligibly small. This is done using the effective field theory methods advocated by Brown and Yaffe. Thus, corrections to nuclear reaction rates that such highly charged ions may undergo can be computed precisely. Moreover, their contribution to the equation of state can also be computed with precision. Such analytic results for very strong coupling are rarely available, and they can serve as benchmarks for testing computer models in this limit.

Plasma effect on the Kα group emission of He-like neon

The spectra shifts for the intercombination line (1s2p(3P1)→1s2) and the resonance line (1s2p(1P1) →1s2) of He-like neon, which are the two electronic dipole transitions in the Ｋα group emissions, are studied under dense plasma conditions by using the self-consistent field ion sphere model. The results show the two electronic dipole transitions red shift nearly linealy with the increase of plasma electron density. Moreover, the red-shift energy becomes more sensitive to the plasma electron density when the plasma electron temperature is lower. It is worthy to note that the energy discrepancy between these two spectral lines is equal to the exchange energy of state 1s2p(3P1). So, it is the first time that the exchange energy varying with plasma environment is observed both qualitatively and quantitatively. This result may be useful to dense plasma diagnosis in connection with variation of the relative position and the spectral fine structure splitting in high density plasmas.

Screening models for laser–cluster interactions

We study the applicability of various screening approaches within the context of laser–cluster interactions. Comparisons between well-known screening models, such as the static screened Coulomb, Debye–Hückel, Thomas–Fermi and ion–sphere ones, and a more elaborated approach based on the Lindhard dielectric function within the linear response theory (Gupta and Rajagopal 1982 Phys. Rep. 87 261) show that none of the simpler classical models can be used through the complete range of plasma situations encountered in laser–cluster interactions. Therefore, we have clearly specified the validity domains of the various models as well as the regions of electronic temperature and density where Friedel oscillations appear.

Spectral properties of helium‐like ions under strongly coupled plasma conditions

AbstractSystematic investigations have been performed to study the effect of strongly coupled plasma on the dynamic polarizabilities, low‐lying energy levels, oscillator strengths, and transition probabilities for the helium isoelectronic ions Li+, Be2+, B3+, C4+, N5+, O6+, F7+, and Ne8+. An ion‐sphere (IS) model of the plasma has been adopted and time‐dependent perturbation theory has been applied to calculate the energy levels and other transition properties. Systematic trend is observed for the spectroscopic properties along the isoelectronic sequence under a given plasma strength and also for a given ion under different plasma strengths. The ionization potential for a given ion is found to decrease, and the number of bound excited states has become finite under increased plasma strengths. The spectral line shifts under such plasma environment have been calculated. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006

Semi-classical collisional functions in a strongly correlated plasma

Collisions between atoms (or ions) and electrons play an important role in the interpretation of line spectra and for the modelling of stellar interiors. Plasma shielding effects due to electron and ion correlations are not negligible in the physical conditions of white dwarf atmospheres, owing to their high density. They also play a role in cool stars and for atomic transitions that are quasi-degenerate. In the standard formalism of Stark impact broadening of spectral lines and of cross sections, the electrostatic Coulomb potential is used to describe the interaction between the perturbing electrons and the emitting atom. Electronic correlations (screening effects) are usually taken into account by introducing a cut-off in the interaction when the electron-atom distance exceeds the Debye radius RD. A more consistent treatment to describe collective effects is the Debye-Huckel potential: the two-particle Coulomb field is shielded by the ensemble of the surrounding electrons. This is a good approximation only for high temperature and low density plasmas (weakly non-ideal plasmas), while for strongly non- ideal plasmas, the Coulomb cut-off potential or the ion sphere potential are more appropriate. These potentials, which can be written as the Coulomb potential with two correcting terms, are widely used in the literature. In this paper, we investigate the ion sphere model to describe the electron atom interaction in a strongly coupled plasma. New semi-classical collisional functions are derived for both the transition probability and the cross section, using the classical path approximation.

Effect of dense plasma on the spectral properties of hydrogenic ions

AbstractThe effect of strongly coupled plasma on the energy levels, dynamic polarizabilities, oscillator strengths, and transition probabilities of a number of hydrogenic ions is estimated, using the ion‐sphere (IS) model. The transition properties are calculated using time‐dependent variation perturbation theory. The variation of the atomic properties under different plasma densities are analyzed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Semi-classical collisional functions in a strongly correlated plasma

Collisions between atoms (or ions) and electrons play an important role in the interpretation of line spectra and for the modelling of stellar interiors. Plasma shielding effects due to electron and ion correlations are not negligible in the physical conditions of white dwarf atmospheres, owing to their high density. They also play a role in cool stars and for atomic transitions that are quasi-degenerate. In the standard formalism of Stark impact broadening of spectral lines and of cross sections, the electrostatic Coulomb potential is used to describe the interaction between the perturbing electrons and the emitting atom. Electronic correlations (screening effects) are usually taken into account by introducing a cut-off in the interaction when the electron-atom distance exceeds the Debye radius . A more consistent treatment to describe collective effects is the Debye-Hückel potential: the two-particle Coulomb field is shielded by the ensemble of the surrounding electrons. This is a good approximation only for high temperature and low density plasmas (weakly non-ideal plasmas), while for strongly non-ideal plasmas, the Coulomb cut-off potential or the ion sphere potential are more appropriate. These potentials, which can be written as the Coulomb potential with two correcting terms, are widely used in the literature. In this paper, we investigate the ion sphere model to describe the electron atom interaction in a strongly coupled plasma. New semi-classical collisional functions are derived for both the transition probability and the cross section, using the classical path approximation.

Screening effects on resonant charge-exchange collisions in strong coupled plasmas

Plasmas screening effects on the resonant charge-exchange processes by stripped ions from hydrogenic ions in strongly coupled plasmas are investigated using the ion-sphere model. The semiclassical straight-line trajectory analysis is applied to describe the dynamic behavior of the collision system. The plasma screening effects on the resonant charge-exchange probability in strongly coupled plasmas are found to be decreased with increasing ion sphere radius and collision energy. It is found that the maximum position of the resonant charge-exchange probability is receded from target nucleus with a decrease of the ion-sphere radius and however is almost unchanged with increasing collision energy.

Effect of the electron gas polarizability on the specific heat of phonons in Coulomb crystals.

The effect of the background polarizability on the thermodynamic properties of a Coulomb crystal of ions is studied. The response of electrons is treated using the Thomas-Fermi (TF) and random phase approximations (RPA). For the case of ions fixed at their lattice sites, the energy of bcc and fcc crystals is calculated to first order in the screening parameter (kappa(TF)a)(2) (kappa(TF) is the TF wave number and a is the ion sphere radius). It is shown that in the RPA there exist domains of parameters (mass density rho and charge number Z) where energy of fcc crystal is lower than that of bcc. The effect of ion vibrations is studied using harmonic lattice approximation. It is shown that phonon modes are nearly identical in the RPA and in the TF approximation. The latter allows one to apply the Ewald technique to the construction of the dynamical matrix, which speeds up all calculations considerably. The main thermodynamic quantities of phonons are calculated as functions of the quantum parameter T(p)/T (where T(p) is the ion plasma temperature) and the screening parameter. The electron polarizability leads to a moderate increase of the phonon thermodynamic quantities as compared to the case of one-component plasma with rigid background (by approximately 30% at kappa(TF)a=0.8). Zero-point motion of ions modifies the aforementioned domains where fcc has lower energy than bcc for static ions. The effect is profound at small Z but leaves the domains unaltered at larger Z. The thermal vibrations of ions at T greater, similar T(p) eliminate completely the domains where fcc is thermodynamically preferable at T=0. The related model of Yukawa-Wigner solid is briefly studied. It is shown that neither bcc nor fcc crystal structures are stable in this model.

Atomic diamagnetism within a dense plasma.

In this paper we have studied the influence of plasma electron polarization around a charged atomic impurity on the diamagnetic response behavior of the impurity ion, when subject to large-scale magnetic fields within high-density plasmas. As a typical example, we consider the two-electron ion C4+ (Z=6) in its ground state 1s(2):(1)S. Calculation performed within the Hartree-Fock approximation under the framework of the ion sphere model for the plasma-embedded impurity ion suggests that, in a high-density regime, the diamagnetic shift of the ground state is a bivariate function of the magnetic field and the plasma electron density. Also, it is shown that the magnitude of the diamagnetic susceptibility of the impurity ion increases with increasing plasma electron density, implying that the ion becomes more diamagnetic as a direct consequence of the increased orbital radii of its bound charges under enhanced density-induced screening.

Influence of a dense plasma on the fine-structure levels of a hydrogenic ion

We discuss the effects of plasma electron polarization surrounding a multiply charged hydrogenic impurity in a high density plasma on the fine-structure levels of the impurity ion. Calculations performed using the ion sphere model suggest that the magnitude of the fine-structure correction smoothly increases with increasing plasma electron density. The other features of the dense plasma effects include the removal of the k degeneracy of the Dirac levels, and a breakdown of the Z4 scaling of the fine-structure correction along the hydrogenic sequence of ions. The resultant outcome is a complete modification of the fine-structure multiplets in terms of the ordering and spacing between the multiplet components.

Plasma screening effects on inelastic Compton scattering of photons by hydrogenic ions in strongly coupled classical plasmas

Plasma screening effects on inelastic Compton scattering of photons by hydrogenic ions in uniformly distributed strongly coupled classical plasmas are investigated. The interaction potential in strongly coupled plasmas is given by the ion–sphere model. The screened radial atomic wave functions and energy eigenvalues for the 1s and 2p states of the hydrogenic target ion in strongly coupled plasmas are obtained by the Ritz variational and perturbational calculations. The expression for the lowest-order transition matrix element is obtained by a two photon process associated with terms quadratic in the vector potential A. The inelastic Compton scattering cross section from the 1s ground state to the 2p excited state is obtained as a function of the incident photon energy including the plasma screening effects through the ion–sphere radius. In strongly coupled plasmas, the plasma screening effect on the inelastic Compton scattering cross section is found to be stronger than that on the photoionization cross section.

Modeling the radiative properties of dense plasmas

A model aimed at describing the electronic structure of hot dense plasmas is presented. This model is first used to study the effect of the nearest neighbor interaction on the photoabsorption $K$-edge position in a dense fluorine plasma. Changes to the ionization potential lowering from the well-known ion sphere model [H. Nguyen et al., Phys. Rev. A 33, 1279 (1986)] are obtained by the present approach for plasma density above solid. We believe that this effect could be of importance in the calculation of the opacity of dense materials. The present model also provides an alternative to the treatment of line broadening in very dense plasmas where the average interionic spacing can be of the order of the spatial extent of the excited-state orbitals. To illustrate this point, we present F Lyman-\ensuremath{\beta} line shapes for various density conditions.

Two-centre bound states in hot dense plasmas

A model for describing the transient molecular behavior in hot dense plasmas is presented and applied to the case of a transient F8+/F9+ molecular ion embedded in a dense (Ne ≈ 1023 cm−3) fluorine plasma. Electron screening effects on molecular energy levels and on dipolar matrix elements are investigated for specific plasma conditions. The accuracy of the calculations is tested comparing values of the polarization shift of the FLyβ line as calculated from the present model to the ones determined in the framework of the Ion Sphere Model (ISM).

Statistical properties of the dense hydrogen plasma: An ab initio molecular dynamics investigation.

The hydrogen plasma is studied in the very high density (atomic and metallic) regime by extensive ab initio molecular dynamics simulations. Protons are treated classically, and electrons in the Born-Oppenheimer framework, within the local density approximation to density functional theory. Densities and temperatures studied fall within the strong coupling regime of the protons. We address the question of the validity of linear screening, and we find it yields a reasonably good description up to ${\mathit{r}}_{\mathit{s}}$\ensuremath{\approxeq}0.5, but already too crude for ${\mathit{r}}_{\mathit{s}}$=1 (with ${\mathit{r}}_{\mathit{s}}$=(3/4\ensuremath{\pi}\ensuremath{\rho}${)}^{1/3}$ the ion sphere radius). These values are typical of Jovian planets interiors. Finite-size and Brillouin zone sampling effects in metallic systems are studied and shown to be very delicate also in the fluid (liquid metal) phase. We analyze the low-temperature phase diagram and the melting transition. A remarkably fast decrease of the melting temperature with decreasing density is found, up to a point when it becomes comparable to the Fermi temperature of the protons. The possible vicinity of a triple point bcc-hcp(fcc)-liquid is discussed in the region of ${\mathit{r}}_{\mathit{s}}$\ensuremath{\approxeq}1.1 and T\ensuremath{\approxeq}100-200 K. The fluid phase is studied in detail for several temperatures. The structure of the fluid is found to be reminiscent of the underlying bcc (solid) phase. Proton-electron correlations show a weak temperature dependence, and proton-proton correlations exhibit a well-defined first coordination shell, thus characterizing fluid H in this regime as an atomic liquid. Diffusion coefficients are computed and compared to the values for the one-component plasma. Vibrational densities of states (VDOS) show a plasmon renormalization due to electron screening, and the presence of a plasmon-coupled single-particle mode up to very high temperatures. Collective modes are studied through dynamical structure factors. In close relationship with the VDOS, the simulations reveal the remarkable persistence of a weakly damped high-frequency ion-acoustic mode, even under conditions of strong electron screening. The possibility of using this observation as a diagnostic for the plasma phase transition to the fluid molecular phase at lower densities is discussed. \textcopyright{} 1996 The American Physical Society.

Electron–ion collisional excitations in strongly coupled plasmas using the ion-sphere model

In strongly coupled plasmas, screening effects are investigated on 1s→2p dipole transition probabilities for electron-impact excitation of hydrogenic ions. Electron–ion interaction is described by the ion-sphere model potential. Behavior of the projectile electron is represented by the semiclassical straight-line trajectory method. Variation of the transition probabilities is determined as a function of the plasma-screening strength through the size of the ion sphere. The transition probabilities are increased with an increase of the ion-sphere radius and the projectile energy. These results, in strongly coupled plasmas, are similar to the screening effects on 1s→2p dipole transition probabilities for electron–ion excitations in weakly coupled plasmas described by the classical Debye–Hückel model.

Absence of Dicke narrowing in x-ray laser plasmas?

Present x-ray laser plasmas are in the intermediate coupling regime (0.1<Γ<4, Γ≡Z2e2/kTa, with a the ion sphere radius), where the binary collision based arguments of low density plasma kinetic theory can be misleading. The difficulty of modeling the spectral output from neonlike lasers at wavelengths near 200 Å has led to the suggestion, based on a low density, electron screened, plasma model, that collisional (‘‘Dicke’’) narrowing may be important. Molecular dynamics results, which include ion collisions and screening effects, are presented here. They indicate that the free-particle Doppler approximation is still quite accurate for λ∼200 Å and Γ≲1. Collisional narrowing will become important at somewhat stronger couplings (Γ∼5) and at this wavelength the diffusion approximation is reasonable for Γ≳10. Collisional narrowing is found to be small even for the higher density (Γ≊4) nickel-like lasers operating near 45 Å.

Ion-ion interaction and equation of state of a dense plasma: Application to beryllium.

A recent model treating the structure of ``simple plasmas'' as that of high-temperature liquid metals is used here to calculate the equation of state of dense beryllium plasmas, for values of compression between 0.2 and 6, and temperatures up to 100 eV. This model gets rid of the standard simplified descriptions of ionic distributions (isolated ion sphere, uniform positive background, etc.); it applies when the electronic structure justifies the use of a binary pair interaction. This interaction is calculated, for every density and temperature, using the self-consistent electronic charge density obtained in a density-functional-theory calculation. The statistical mechanics of the ion fluid is treated via a modified hypernetted-chain integral equation. The various contributions to the equation of state are presented and discussed, and comparisons with other theories are made.

Electronic bound states of a two-ion center immersed in high-density plasmas.

In order to evaluate the simultaneous influence of a neighboring ion located at an arbitrary distance R and of free electrons on atomic bound states in high-density plasmas (${N}_{e}$\ensuremath{\gtrsim}${10}^{23}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$) we have suggested a transient molecule model that consists of a two-ion center surrounded by bound and free electrons. The Dirichlet boundary condition is laid down in such a way to make the total electrostatic potential constant over the entire molecular envelope and also to obtain the limit of two independent ion spheres or that of one united ion sphere when R\ensuremath{\rightarrow}\ensuremath{\infty} or R\ensuremath{\rightarrow}0, respectively. A closed form has been obtained for the interaction potential between bound and free electrons at the high-temperature limit. Energy levels and wave functions have been evaluated by diagonalizing the total Hamiltonian in the subspace of the lowest 40 molecular levels. A possible appearance of new spectral components and, in particular, a drastic reduction of the Stark effect are clearly shown.

The potential of average force between two ions at infinite dilution in a solvent of polarizable hard spheres

The potential of average force between two ions at infinite dilution in a solvent of polarizable hard spheres is considered. The ions are treated as hard spheres with point charges and the solvent molecules are treated as polarizable hard spheres. The diameter of ions may be different than the diameter of polarizable particles. The potential of average force rises near contact much more steeply than the primitive model would permit and also has maxima and minima vanishing at larger distances, in semiquantitative agreement with the similar results of Patey and Valleau. The oscillating character of the potential of average force is due above all to the oscillations of the radial distribution function between the ion and polarizable hard sphere.