Local Plasma Approximation Research Articles

Ionization of He, Ne, Ar, Kr, and Xe by proton impact: Single differential distributions in energy and angles

In this paper we report energy and angular distributions of electrons emitted in collisions of protons with $\text{neon-}({\text{F}}^{\ensuremath{-}},{\text{Ne}}^{0},{\text{Na}}^{+})$, $\text{argon-}({\text{Cl}}^{\ensuremath{-}},{\text{Ar}}^{0},{\text{K}}^{+})$, $\text{krypton-}({\text{Br}}^{\ensuremath{-}},{\text{Kr}}^{0},{\text{Rb}}^{+})$, and $\text{xenon-}({\text{I}}^{\ensuremath{-}},{\text{Xe}}^{0})$ isoelectronic series for high and intermediate impact energies. Calculations were performed within the continuum distorted wave-eikonal initial-state method using an angular expansion in spherical harmonics and a numerical evaluation of the radial functions corresponding to both: the initial (bound) and the final (continuum) states in the same central potential. The first Born approximation was calculated on equal footing. The shellwise local plasma approximation was also calculated when possible. A complete and exhaustive comparison with the available experimental data is carried out. We have spanned almost all the published experiments in our range of interest. Successes and failures of the different theoretical methods are pointed out. Possible signatures of many-electron effects are noticed.

Ionization of the He, Ne, Ar, Kr, and Xe isoelectronic series by proton impact

In this paper we report ionization cross sections of positive ${\mathrm{Li}}^{+}$, ${\mathrm{Na}}^{+}$, ${\mathrm{K}}^{+}$, ${\mathrm{Rb}}^{+}$, neutral He, Ne, Ar, Kr, Xe, and negative ${\mathrm{F}}^{\ensuremath{-}}$, ${\mathrm{Cl}}^{\ensuremath{-}}$, ${\mathrm{Br}}^{\ensuremath{-}}$, ${\mathrm{I}}^{\ensuremath{-}}$ ions by impact of protons with energies ranging from $25\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}1000\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$. Cross sections of singly charged ions are relevant to the calculation of electron yields in collisions with insulator surfaces. Calculations were performed within the continuum distorted wave--eikonal initial state method using an angular expansion in spherical harmonics and a numerical evaluation of the radial functions corresponding to both the initial (bound) and the final (continuum) states. The first Born approximation was used on an equal footing. We find that this first-order theory holds for proton energies larger than $300\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$. For comparison, we also calculate the shellwise local plasma approximation. Our results show that it gives a good account of the cross sections for neutral targets.

Theoretical and experimental study of energy loss of Li ions in Zn

We have performed a combined theoretical and experimental study of the energy loss of Li ions in Zn, on a wide range of energies, together with comparative studies for H and He ions on the same target. By using Zn films and the Rutherford backscattering technique, we were able to determine the stopping power for Li ions in the (0.3 to 5) MeV energy interval. The experimental results cover an energy range which includes the maximum of the stopping power. The values obtained agree well with previous measurements performed in a limited energy interval and with the semiempirical code SRIM 2006. On the other hand, we have performed ab initio theoretical calculations based on the extended Friedel sum rule--transport cross section formulation for the valence electrons and the shellwise local plasma approximation for the inner shells. This theoretical description reproduces reasonably well the experimental results on the whole studied energy range. The same occurs with previous measurements performed with H and He on the same target. The importance of the screened potential on the stopping power due to the valence electrons is stressed in the present description.

Inelastic interactions of low-energy electrons with biological media

A study of inelastic interactions of low-energy electrons with biological media is of fundamental importance in the understanding of radiation-induced actions leading to the biological damage. In the present work, electron energy loss properties in liquid water and solid DNA were calculated based on the dielectric response theory for valence band electrons and atomic models for inner-shell electrons. For electron interactions with the valence band, an extended Drude dielectric function was fitted to experimental optical data and then checked by sum rules. The valance band was considered as composed of many subbands with different oscillator strength, binding energy and damping coefficient. The real and imaginary parts of the dielectric function and the energy loss function were all checked. For electron interactions with inner shells, the generalized oscillator strength was calculated using the sum-rule-constrained binary-encounter model and the local-plasma approximation. The differential inverse mean free paths for the valence band and inner shells were calculated using the Born approximation. Exchange effect was estimated using an approach based on the Moller cross-section. Results of the present work were compared with similar calculations by other authors.

Total electron yields and stopping power of protons colliding with NaCl-type insulator surfaces

In this paper we report electron yields and stopping power of protons colliding with surfaces of NaCl-type insulators formed with the alkali-metal ions ${\mathrm{Li}}^{+}$, ${\mathrm{Na}}^{+}$, ${\mathrm{K}}^{+}$, and ${\mathrm{Rb}}^{+}$ and the halides ${\mathrm{F}}^{\ensuremath{-}}$, ${\mathrm{Cl}}^{\ensuremath{-}}$, ${\mathrm{Br}}^{\ensuremath{-}}$, and ${\mathrm{I}}^{\ensuremath{-}}$. We also report fitted models for the static and dynamic polarization potentials of the eight ions of interest. The calculations are carried out within the shellwise local plasma approximation using the Levine-Louie response function, instead of the usual Lindhard one, to account for the ionization energy.

Calculation of energy-loss straggling of C, Al, Si, and Cu for fast H, He, and Li ions

We present theoretical calculations of the energy-loss straggling of C, Al, Si, and Cu targets for H, He, and Li ions in the range of intermediate to high energies $(0.01--10\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}∕\mathrm{u})$. These calculations have been done by employing the dielectric formalism and by considering the different equilibrium charge states of the swift ion inside the solid as a function of its energy. Two different models are used: the Mermin energy-loss functions combined with generalized oscillator strengths (MELF-GOS) and the shellwise application of the local plasma approximation (SLPA). The MELF-GOS describes the target outer-electron excitations through a fitting to experimental data in the optical limit, employing a linear combination of Mermin-type energy-loss functions; the excitations of the inner-shell electrons are taken into account by means of generalized oscillator strengths. The SLPA employs a free-electron-gas model for the target valence electrons and the local density approximation for each shell of target electrons separately by using Hartree-Fock atomic wave functions. The results of the energy-loss straggling obtained by the two independent models show good agreement with the available experimental data. The calculated energy-loss straggling tends at high energies to the Bohr value and takes values below it at intermediate energies. The Bethe-Livingston shoulder (or overshooting) at intermediate energies does not appear in the present calculations. We find that the energy-loss straggling normalized to ${Z}_{\mathrm{P}}^{2}$ is almost independent of the ion atomic number ${Z}_{\mathrm{P}}$; therefore, the results for H, He, and Li projectiles in each target can be approximated by a universal curve at high energies.

Many-electron model for multiple ionization in atomic collisions

We have developed a many-electron model for multiple ionization of heavy atoms bombarded by bare ions. It is based on the transport equation for an ion in an inhomogeneous electronic density. Ionization probabilities are obtained by employing the shell-to-shell local plasma approximation with the Levine and Louie dielectric function to take into account the binding energy of each shell. Post-collisional contributions due to Auger-like processes are taken into account by employing recent photoemission data. Results for single-to-quadruple ionization of Ne, Ar, Kr and Xe by protons are presented showing a very good agreement with experimental data.

Mean excitation energies for the stopping power of atoms and molecules evaluated from oscillator-strength spectra

The mean excitation energy for the stopping power of matter, usually expressed by symbol I, is the only nontrivial material property in Bethe’s [Ann. Phys. 5, 325 (1930)] asymptotic stopping-power formula. It is therefore a crucial input for the evaluation of stopping power for swift charged particles. To calculate the I value of a material from its definition, it is necessary to know the oscillator-strength spectrum of the material in question over the entire range of the excitation energy. We evaluate the mean excitation energies of 32 atoms and molecules from the oscillator-strength spectra that were published by Berkowitz in 2002 [Atomic and Molecular Photoabsorption: Absolute Total Cross Sections (Academic, San Diego, 2002)]. We find that most of the present I values are consistent with those given in the literature. The I values of NO2, O3, and C60 in particular are evaluated in the present work. For buckminsterfullerene C60, an estimation of the I value is made also using the local-plasma approximation, in an attempt at understanding differences in the I values of carbon in a free atom, a C60 molecule, and graphite. Systematic trends of I values obtained in the present calculation are discussed, in the context of the Thomas-Fermi model.

K-shell ionization of low Z elements in ion–solid collisions and applicability of local plasma approximation

K-shell vacancy production cross sections are measured using X-ray technique, in collisions of highly charged fluorine ions with various solid targets such as, Cl, K, Fe and Cu, at energies from 50 to 110 MeV. The experimental data is compared with an ab initio model based on local plasma approximation (LPA) and the usually employed ECPSSR. A detailed comparison with the LPA model is presented as a function of generalized perturbation strength.

Stopping power for swift dressed ions

We present theoretical calculations of electronic stopping power, including excitation and loss of both projectile and target electrons. The energy loss due to target valence and inner-shell electrons are separately evaluated: the former in the usual dielectric formalism, and the latter by employing a shell-wise local plasma approximation. Stopping power calculations of He ions in Al and Zn are presented, including the electron-electron contribution mentioned above. The agreement with the experimental data is very good, and let us conclude that, for helium ions, projectile excitation and loss contribute to the stopping power at the most in 1%, and it is reasonable for the theoretical descriptions to neglect it.

Pressure dependence of the mean excitation energy of atomic systems

Changes in the mean ionization energy of atoms in compressed matter are estimated through cage models of atomic confinement whereby pressure is obtained in terms of the rate of change of total atomic energy with volume. Resort is taken to a recently implemented shellwise Thomas–Fermi–Dirac–Weizsacker theory for confined atoms to construct the atomic energy functional, which is self-consistently optimized for different confinement conditions. The resulting modified atomic orbital densities are then used within the Local Plasma Approximation to evaluate the corresponding orbital and total mean excitation energies. Good agreement is obtained with accurate calculations for free atoms. For compressed atoms agreement is found with a previously derived universal expression [J.M. Peek, Phys. Rev. A 36 (1987) 5429] for total mean excitation energies suggesting its adequacy for this class of studies.

Energy loss of helium ions in zinc

The energy loss of helium ions in zinc has been measured in the energy range from 37.5 to 1750 keV/ amu using the transmission technique and the Rutherford backscattering method. In addition, calculations using the extended Friedel sum rule, the unitary convolution approximation, and the local plasma approximation have been performed. The contributions of the inner-shell and valence electrons to the total energy loss are separately evaluated. The measurements and calculations are in good agreement over an extended range of energies, and both of them yield stopping values higher than those provided by SRIM 2003.

Experimental study of K-shell ionization oflow-Zsolids in collisions with intermediate-velocity carbon ions and the local plasmaapproximation

K-shell vacancy production in low-atomic-number (Zt = 17–29)solid targets has been measured in collisions of highly chargedcarbon ions with energies of 1.5–6 MeV u−1.The K-shell ionization cross sections of Cl, K, Ti, Fe and Cu are derived from themeasured K x-ray cross sections. The present data-set has been used to test thepredictions of a theoretical model based on the local plasma approximation(LPA). This theory takes into account the response of solid core electronsworking within the dielectric formalism. We find that this ab initio ion–solidmodel gives very good agreement with the measured data for Fe and Cutargets, while it tends to under-estimate the data for the most symmetriccollision systems studied here. We discuss the range of validity of the LPA interms of the symmetry parameter and the impact velocity. On the otherhand, a model based on the perturbed stationary state approximation,designed for ion–atom collisions (ECPSSR) is found to give excellentagreement with the measured data for all target elements over the wholeenergy range. All the measured cross sections for different targets arefound to follow a universal scaling rule predicted by the ECPSSR.

Antiscreening mode of projectile-electron loss

The inelastic contribution of target electrons to different electronic processes in the projectile is obtained by employing the local-density approximation as usually applied in the dielectric formalism. Projectile-electron-loss cross sections due to the electron-electron interaction are calculated and compared with those obtained by using atomic antiscreening theories. We also calculate ionization cross sections and stopping power for bare ions impinging on different gases. The good agreement with the experimental data and the simplicity of the local-density approximation make it an efficient method for describing inelastic processes of gaseous target electrons. It is expected to be useful for targets with large atomic number. In this case, the number of possible final states to be considered by the traditional atomic methods makes it a tough task to be tackled. On the contrary, the more electrons the target has, the better the local plasma approximation is expected to be.

Model calculation for energy loss in ion-surface collisions

The so-called local plasma approximation is generalized to deal with projectiles colliding with surfaces of amorphous solids and with a specific crystalline structure (plannar channeling). Energy loss of protons grazingly colliding with aluminum, SnTe alloy, and LiF surfaces is investigated. The calculations agree quite well with previous theoretical results and explain the experimental findings of energy loss for aluminum and SnTe alloy, but they fall short to explain the data for LiF surfaces.

K-shell processes in heavy-ion collisions in solids and the local plasma approximation

We have investigated K-shell vacancy production due to ionization and electron transfer processes, in collisions of highly charged oxygen ions with various solid targets such as Cl, K, Ti, Fe, and Cu at energies between 1.5 and 6.0 MeV/u. The K-shell ionization cross sections were derived from the measured K x-ray cross sections. An ab initio theoretical model based on the local plasma approximation (LPA), which is an extension of the dielectric formalism to consider core electrons, provides an explanation of the measured data only qualitatively. In case of asymmetric collisions ${(Z}_{p}{/Z}_{t}l0.35,$ ${Z}_{p},$ ${Z}_{t}$ being the atomic numbers of the projectile and target, respectively) and at higher energies, the LPA model explains the data to some extent but deviates for more symmetric collision systems. On the other hand, a perturbed-stationary-state (PSS) calculation (ECPSSR), including the corrective terms due to energy (E) loss, Coulomb (C) deflection, and relativistic (R) wave functions designed for ion-atom collisions agree quite well with the data for different combinations of target and projectile elements. In addition, we have also measured the $K(\mathrm{target})\ensuremath{-}K(\mathrm{projectile}) \mathrm{electron}$ transfer cross sections and compared them with a model based on perturbed-stationary-state approximation.

CALCULATING MEAN EXCITATION ENERGY FROM SHANNON INFORMATION ENTROPY FOR K–Xe ATOMS

The calculation of the Shannon entropy of Hartree–Fock electron density is reported for the K–Xe atoms in the fourth and fifth rows of the periodic table in the ground state. In local plasma approximation, the Shannon entropy calculated is used directly to estimate mean excitation energies. To our knowledge, the mean excitation energies of K–Xe atoms are presented here for the first time.

Dynamics of solid inner-shell electrons in collisions with bare and dressed swift ions

We analyze the dynamical interactions of swift heavy projectiles and solid inner-shell electrons. The dielectric formalism employed to deal with the free-electron gas is extended to account for the core electrons, by using the local plasma approximation. Results for stopping power, energy straggling, and inner-shell ionization in collisions of bare ions with metals are displayed, showing very good accord with the experimental data. Simultaneous excitations of projectile and target electrons are also analyzed. In the high-energy range we find a similar contribution of target core and valence electrons to the probability of projectile-electron loss. The problem of no excitation threshold within the local plasma approximation and the possibility of collective excitations of the shells are discussed.

Shell corrections in stopping powers

One of the theories of the electronic stopping power S for fast light ions was derived by Bethe. The algorithm currently used for the calculation of S includes terms known as the mean excitation energy I, the shell correction, the Barkas correction, and the Bloch correction. These terms are described here. For the calculation of the shell corrections an atomic model is used, which is more realistic than the hydrogenic approximation used so far. A comparison is made with similar calculations in which the local plasma approximation is utilized. Close agreement with the experimental data for protons with energies from 0.3 to 10 MeV traversing Al and Si is found without the need for adjustable parameters for the shell corrections.

Momentum-density effects upon the electronic stopping ofelemental solids

Treatment of electronic stopping via kinetic theory and the orbital local plasma approximation is extended (from free-standing ordered slabs) to include bulk crystalline targets, and hence probe their electron momentum distribution. Sensitive computational issues, important for comparison with experimental data, are addressed. A primary result is unambiguous first-principles prediction of large gas-solid and film-solid differences in Li stopping. Previous predictions had involved semi-empirical determination of mean excitation energies. Additionally, a stopping anisotropy that is separate from and much smaller than familiar channelling and related to the familiar Compton-profile anisotropy is treated, apparently for the first time. Example calculations for hexagonal Li and graphite are given.