Ion-sphere Model Research Articles

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

Plasma screening effects on resonant Compton scattering of photons by bound atomic electrons from the ground state of hydrogenic ions in uniformly distributed strongly coupled plasmas are investigated. The interaction energy in strongly coupled plasmas is given by the ion-sphere model potential. The screened radial atomic wave functions and energy eigenvalues for the 1s and 2p states of the target hydrogenic ion in strongly coupled plasmas are obtained by the variation and perturbation methods. The transition matrix element near resonance is obtained by the lowest-order photon-perturbation Hamiltonian in the electronic dipole representation. The resonant Compton scattering cross section including the plasma screening effect is found to be smaller than that neglecting the plasma screening effect since the resonance frequency is increased due to the plasma screening effect.

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.

Electron‐Impact Excitations of Hydrogenic Ions in Strongly Coupled Plasmas

Plasma screening effects are investigated on electron-ion collisional excitations in strongly coupled plasmas. Scaled cross sections for 1s → 2p0(m = 0) excitation is obtained using the ion-sphere model potential with the close-encounter effects. Ground and excited bound wave functions in strongly coupled plasmas are obtained using the Ritz variation and perturbation methods. The semiclassical straight-line trajectory approximation is applied to the motion of the projectile electron in order to investigate the variation of the transition probabilities as a function of the impact parameter and ion-sphere radius. The transition probability neglecting the screening effects on the target atomic wave functions is found to be greater than that including the screening effects on the target atomic wave functions. It is shown that the target screening effects are slightly decreased with an increase of the projectile energy.

Bremsstrahlung radiation from electron–ion polarization scatterings in strongly coupled plasmas

Low energy bremsstrahlung processes in electron–ion polarization scatterings in strongly coupled plasmas described by the ion-sphere model are investigated using the classical trajectory method. The interaction between the projectile electron and the screened target ion is given by the attractive polarization interaction between the projectile electron and the induced dipole. The classical straight-line trajectory method is applied to represent the differential bremsstrahlung radiation cross section as a function of the impact parameter and ion-sphere radius. The results show that the bremsstrahlung radiation due to the component of the acceleration perpendicular to the projectile velocity is dominant for small impact parameters, especially, for soft photon radiation. However, for large impact parameters, the contribution from the component of the acceleration parallel to the velocity is almost comparable to that from the component of the acceleration perpendicular to the velocity.

K-shell photoionizations in strongly coupled plasmas

In strongly coupled plasmas, the photoionizations from the 1s ground state of hydrogenic ions are investigated using the ion-sphere model potential. The initial bound wave function and energy eigenvalue of the target ion are modified in the ion-sphere potential using the Ritz variation method. The final state of the ejected photoelectron is represented by a plane wave solution. The Coulomb correction is considered using the screened Coulomb wave function with the appropriate effective charge. The K-shell photoionization cross section is obtained for the acceleration form of the matrix element because of the convenience of the calculations. The plasma screening effect is obtained as a function of the ion-sphere radius and photon energy. The retardation correction is also considered in obtaining the total K-shell photoionization cross section in strongly coupled plasmas. The plasma screening effects on the total K-shell photoionization cross section for the ion-sphere radius, RZ⩾2aZ, are found to be less than about 25%. It is also found that the plasma screening effect is almost independent of the incident photon energy.

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).

Electron captures from hydrogenic ions by fully stripped ions in strongly coupled plasmas

In strongly coupled plasmas, plasma-screening effects are investigated on electron capture from hydrogenic ions by fully striped ion projectiles using the classical Bohr–Lindhard model. The interaction potential in strongly coupled plasmas is described by the ion-sphere model potential. The electron capture radius is obtained by the ion-sphere interaction potential and the kinetic energy of the released electron in the frame of the projectile ion. The classical straight-line trajectory approximation is applied to the motion of the projectile ion in order to visualize the electron capture probability as a function of the impact parameter, projectile energy, and ion-sphere radius. It is found that the electron capture probability is quite sensitive to the projectile velocity and the ion-sphere radius. The maximum position of the electron capture probability is shifted to the target nucleus as the projectile energy increases and is receded from the target nucleus as the ion-sphere radius increases. It is also found that the maximum value of the capture probability is increased with an increase of the ion-sphere radius. The scaling relationship for the capture cross section in the screened case and compare with the existing one for the unscreened case is also obtained.

Bremsstrahlung in electron-ion Coulomb scattering in strongly coupled plasma using the hyperbolic-orbit trajectory method.

Classical bremsstrahlung in electron-ion Coulomb scattering in strongly coupled plasmas is investigated using the classical curved trajectory method. In strongly coupled plasmas, the electron-ion interaction potential is obtained by the ion-sphere model potential. The modified hyperbolic-orbit trajectory method is applied to describe the motion of the projectile electron in order to investigate the variation of the differential bremsstrahlung radiation cross section as a function of the impact parameter and ion-sphere radius. The results show that the scaled doubly differential bremsstrahlung radiation cross sections have minima at the small impact parameter region for soft photon radiation. For hard photon radiation, the minima disappear. The impact parameter corresponding to the minimum position of the bremsstrahlung radiation cross section recedes from the center of the ion core as the ion-sphere radius increases. The radiation cross section is substantially reduced as the radiation energy increases, especially for the large ion-sphere radius. \textcopyright{} 1996 The American Physical Society.

Plasma-screening effects on bremsstrahlung in electron–ion Coulomb scatterings in strongly coupled plasmas

Plasma-screening effects are investigated for the bremsstrahlung in electron–ion Coulomb scatterings in strongly coupled plasmas using the classical trajectory method. In strongly coupled plasmas, the electron–ion interaction potential is obtained by the ion-sphere model potential. The classical straight-line trajectory approximation is applied to the motion of the projectile electron in order to investigate the variation of the differential bremsstrahlung radiation cross section as a function of the impact parameter and ion-sphere radius. The results show that the plasma-screening effects for the differential bremsstrahlung radiation cross section are increased with increasing the ion-sphere radius. The differential bremsstrahlung radiation cross sections are decreasing as the radiation energy increases. However, for a small ion-sphere radius the radiation cross sections are almost unchanged with increasing or decreasing the radiation energy.

Insights on the plasma polarization shift: A comparison of local density approximation and optimum potential methods

The plasma polarization shift computed with a local density functional approximation of an ion-sphere model is compared with results calculated using an optimum central field effective exchange potential. Indications are that the bulk of the shift is an artifact of the approximate exchange functional describing the interaction between bound and continuum orbitals in the LDA.

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.

A Static Model for the Continuum-Lowering of a Hydrogen-Like Ion as an Ultra-Dense Plasma Diagnostics

A simple formula for the density diagnostics of a plasma is proposed in the present work. The idea comes from the level-crossing feature of a hydrogen-like ion immersed in the plasma. Viewing the lowest electronic states to which the crossing between all neighboring levels takes place, the density is shown to be expressed in a tractable form as a function of the ionization-potential lowering of the emitter. The calculation performed for the ion-sphere model with the Hartree-potential turns out to be as accurate as those for the Stewart-Pyatt model. The edge-shift is discussed in connection with the ionization-potential lowering which is caused from the screening effect in the plasma.

Solar opacities based on the ion-sphere and ion-correlation models

Solar opacities based on the ion-sphere and ion-correlation models are given for the Grevesse mixture. Uncertainties connected with these models are pointed out. Although at low densities both may be realistic, at high densities when the interionic distances are comparable with the wavelengths of the bound-state wave functions, they have to be improved. Neither can give an accurate many-body representation of the plasma, and the question of which is more realistic can be answered only by more accurate computer simulation.

Photoabsorption in hot plasmas based on the ion-sphere and ion-correlation models.

In hot plasmas the theoretically predicted photoabsorption cross sections rest upon the electronic states predicted by the plasma model. We compare the theoretical photoabsorption based on two models, the ion-sphere model and the ion-correlation model. We discuss the underlying physics and present calculations for iron, aluminum, and bromine plasmas, and also for a mixture of 14 elements under conditions occurring below the convective region of the sun.

Atomic structure and process in high density plasmas.

Electronic properties of atoms in high density plasmas are reviewed. Two important features of these plasmas, i.e., pressure ionization and continuum lowering are described in classical theories based on the Debye-Huckel and ion-sphere models. The results of numerical calculations for various model potentials are also summarized. Finally we have looked over recent works on density of state of electron and many-ion-effect in plasmas.

State densities and ionization equilibrium of atoms in dense plasmas.

The semiclassical Bohr-Sommerfeld quantization condition is used to derive an approximate analytical expression for the state density of the hydrogen atom in a dense plasma. An ion-sphere model with an infinitely high potential wall is assumed. The expression leads to a universal curve that spans all values of the electron density. The curve is continuous and smooth over the entire energy range, starting from the hydrogenic state density for low-lying bound states and approaching the plane-wave state density in the high-energy limit of the continuum. The number of bound states is approximately proportional to the inverse of the square root of the electron density. Integration of the state density over the Boltzmann distribution of the electronic energy results in an ionization equilibrium relation, leading to modified Saha's equation. The correction factor for this modified equation is a function of both the electron temperature and the electron density, and is expressed as a universal function of the ion coupling parameter.

Continuum wave functions and bremsstrahlung in plasmas based on the ion-sphere and jellium models

We determine the density of states and subject the continuum wave functions to normalization and asymptotic conditions consistent with the ion-sphere and jellium models of the plasma. To illustrate the difference between the two models, we present bremsstrahlung calculations for aluminum and iron plasmas. We also compare the exact quantum-mechanical results with the predictions of the Born-Elwert approximation and with some predictions based on phase-shift calculations. Finally, we discuss briefly the effect of a non-Maxwellian electron distribution.

Average-atom quantum-statistical cell model for hot plasma in local thermodynamic equilibrium over a wide range of densities.

A method for numerically modeling hot plasma over a wide range of densities is described. The model generalizes the essential aspects of the Stewart-Pyatt model to plasmas comprising mixtures of elements and extends the treatment to include the effects of electron polarization and screening. A practical numerical prescription is provided that is a straightforward generalization of the ion-sphere cell model. In addition, exact closed-form expressions are given for the continuum lowering. The model also addresses the problem of the microfield, i.e., the plasma-potential fluctuations that perturb the upper electronic states, and provides a suitable framework for improved practical approaches to this.

Influence of attractive interaction between deuterons in Pd on nuclear fusion

It is shown that in a heavily deuterated palladium metal a pair of deuterons exhibits attractive interaction at short distances (≈0.1–0.7 A) due to strong Coulomb correlations in the ion-sphere model and due to the screening action of localized 4d electrons. This mechanism can lead to enhanced thermonuclear reactions at room temperatures some 50 orders of magnitude faster than that in a D2 molecule. Characteristic signatures of predicted nuclear reactions are described.