Generalized Oscillator Strength Densities Research Articles

Fast-electron-impact ionization process by 3p of hydrogen-like ions in Debye plasmas**Project supported by the National Basic Research Program of China (Grant No. 2013CB922200) and the National Natural Science Foundation of China (Grant Nos. 11005049, 11025417, and 10974021).

The plasma screening of fast-electron-impact-ionization by excited state (3p) of Hydrogen-like ions was investigated in the first Born approximation with a plasma screening length δ varying from 1000a0 to 10a0. The generalized oscillator strength densities showed dramatic changes: some accessional minima occurred along with a remarkable enhancement in certain continuum-energy domains. The double-differential cross sections exhibit not only the same structures as the Bethe surface for moderate and large momentum transfers, but also a broadened enhancement for small momentum transfers. The single-differential cross sections exhibit a near-zero-energy-enhancement and prodigious multiple-shape resonances, depending on the continuum energy and the plasma screening length. These features are analogous to those of the photo-ionization cross section. These findings, for both types of cross section, can be explained by processes associated with continuum electrons, as long as the potential has a short-range character.

The ionization and dissociation of nitrous oxide studied by fast electron impact

Using the high-resolution fast electron energy loss spectrometer, the generalized oscillator strength densities (GOSDs) of the ion fragments of N2O at different momentum transfers were determined at a high resolution (80meV), and the momentum transfer dependence behavior of the ioniza-tion and dissociation of N2O has been studied.

Absolute oscillator strength densities below 100eV of N 2

The absolute optical oscillator strength density (OOSD) and generalized oscillator strength densities (GOSDs) below 100eV of N2 are determined with an incident electron energy of 2500eV and an energy resolution of 100 meV. The absolute generalized oscillator strengths (GOSs) for two transitions to the superexcited states at 23 and 31.4eV are determined and their momentum transfer dependence behaviours are discussed.

A relativistic optical-data model for inelastic scattering of electrons and positrons in condensed matter

A relativistic optical-data model for the calculation of non-radiative inelastic scattering of electrons and positrons in condensed matter is presented. The scattering is described within the first Born approximation, in terms of longitudinal and transverse interactions. Differential cross sections are determined by a generalized oscillator strength density, which is generated by extending a semi-empirical optical oscillator strength density to non-zero momentum transfers using a modified δ-oscillator as the extension algorithm. The Fermi density-effect correction is obtained from the optical oscillator strength and a simple approximation is proposed to account for its effect on the cross section differential in energy loss. The differential cross sections take relatively simple analytical forms, and various quantities of interest, such as total cross section, stopping power, straggling parameter and restricted inelastic transport cross section are evaluated by a single quadrature. Results are presented for electron and positron energies between 10eV and 1GeV.

Theoretical investigations on the dynamical correlation in double excitations of helium by theR-matrix method

The momentum transfer dependence of double excitations of helium were studied theoretically in order to compare with our previous experimental work [Phys. Rev. Lett. 91, 193203 (2003)]. The calculation was carried out by a series of modified R-matrix codes. We elucidate the dynamical correlations in terms of the internal correlation quantum numbers K, T, and A. The generalized oscillator strength densities and Fano profile parameters q, f{sub a}, f, and S of doubly excited states {sub n}(1,0){sub 2}{sup +} {sup 1}S{sup e}, {sub n}(1,0){sub 2}{sup +} {sup 1}D{sup e}, and {sub n}(0,1){sub 2}{sup +} {sup 1}P{sup o} were reported as functions of the momentum transfer squared K{sup 2}. The present theoretical work accompanied by our previous experiment leads to a deep understanding of the optically allowed and optically forbidden double excitations of helium.

Momentum Transfer Dependence of Two Types of the BroadEnhancement Phenomena: CO Spectra in the Valence Energy Region

Partial generalized oscillator strength densities of CO moleculesrelated to the excitation of a 5σ or 1π electron arecalculated by using multi-scattering self-consistent-field methods.Momentum transfer dependence of two types of the broad enhancementphenomena above the threshold with one-electron character, i.e. shaperesonance and non-resonance enhancement, is studied. Our calculationsshow that the energy position of a non-resonance enhancement is relatedto the momentum transfer K. Therefore, electron impact basedexperiments can be used to identify the two types of the broadenhancement phenomena.

INELASTIC COLLISION PROCESS OF Rb ATOM BETWEEN INITIAL AND FINAL CHANNELS

Based on the quantum defect theory, the infinite Rydberg states and its adjacent continue states with the same angular moment property will form a channel. Previous studies have considered the collision-induced transitions from a single initial state to a final channel. Here we extend these thoery to include all possible transitions between two channels. By defining a renormalized generalized oscillator strength density (GOSD) which varies smoothly across threshold, the inelastic collisions from an initial channel to a final channel can be treated in a unified manner. As an example, we present the renormalized GOSD of the Rb atom from s-initial to p-final channel, and also from s-initial to s-final channel.

7356. Monte Carlo simulation of energy dissipation in electron beam lithography including secondary electron generation: Kang-Yoon Lee et al, J Appl Phys, 67, 1990, 7560–7567

A new Monte Carlo simulation including secondary electron generation has been performed to study energy dissipation in electron beam lithography. The simulation of inelastic scattering is calculated from the model of the generalized oscillator strength density distribution determined by a set of resonance energies and oscillator strengths. Varying the polymethylmethacrylate film thickness, the energy dissipation profiles for various electron beam energies are evaluated. The effects of backscattered electrons from the silicon substrate and secondary electrons are studied with respect to film thicknesses and electron beam energies. The backscattered electrons from the Si substrate broaden the profile, especially near the bottom layer, and the secondary electrons broaden the profiles over the whole film.

Monte Carlo simulation of energy dissipation in electron beam lithography including secondary electron generation

A new Monte Carlo simulation including secondary electron generation has been performed to study energy dissipation in electron beam lithography. The simulation of inelastic scattering is calculated from the model of the generalized oscillator strength density distribution determined by a set of resonance energies and oscillator strengths. Varying the polymethylmethacrylate film thickness, the energy dissipation profiles for various electron beam energies are evaluated. The effects of backscattered electrons from the silicon substrate and secondary electrons are studied with respect to film thicknesses and electron beam energies. The backscattered electrons from the Si substrate broaden the profile, especially near the bottom layer, and the secondary electrons broaden the profiles over the whole film.

NODAL-CURVE OF MATRIX ELEMENT FOR GENERALIZED OSCILLATOR STRENGTH DENSITY

Generalized oscillator strength density from an initial atomic state nl to final states n＇l＇ or ∈＇l＇ forming a final channel is a function of the energy transfer ∈ and the momentum transfer q. We report our study on the nodal curves in the ∈-q plane, where the matrix element for the generalized oscillator strength density vanishes. For high momentum transfer, the positions of the nodal curves can be obtained by scaling the hydrogenic results. For low momentum transfer, the nodal curves depend strongly on the difference of the quantum defects △μ of the initial and final channels; the topology of the nodal curves for △μ>0 is completely different from the topology for △μ<0.

ELECTRONIC IMPACT EXCITATION CROSS SECTIONS AND RATES (I)——SPIN ALLOWED EXCITATION PROCESSES

Based on two properties of the generalized oscillator strength densities: (1) continuity in an excitation channel and (2) quasiscaling relation along an isoelectronic sequence, the corresponding parameters in the Bethe's formula (namely the Bethe's physical parameter set) have similar behaviors. According to the Bethe's formula, excitation cross sections for spin allowed processes can be easily calculated in terms of the Bethe 's physical parameter set which characterizes the excitations of target atoms. In the present article, we introduce corrected functions defined as the ratios between the exact cross sections and the Bethe's cross sections. The corrected functions reveal a nice universal scaling feature within 50%. Thus, various cross sections as well as rates, which correspond to electron impact excitations from an initial state to infinite final states-forming a so called "excitation channel", can be obtained conveniently.

Simple generalized oscillator strength density model applied to the simulation of keV electron-energy-loss distributions

Monte Carlo calculations of keV electron-energy-loss distributions have been performed using a simple model of the generalized oscillator strength density to simulate inelastic collisions. The model, which rests partly on the use of empirical data (primarily the atomic mean ionization potential) expresses the generalized oscillator strength density as a sum of terms ( j) of the form [ fjδ(W−Wj), Q<Wj; fjδ(W−Q), Q>Wj] where W is energy transfer, fj and Wj ( j=1,2,3,...) are a sequence of oscillator strengths and resonance energies, respectively, and Q=ℏ2q2/2m, where ℏq is the momentum transfer and m the electron mass. Comparison is made with experimental results reported for 2an transmission through Al, and 7.3-keV internal conversion electrons transmitted through surface layers of Fe.

SCALING RELATION OF GENERALIZED OSCILLATOR STRENGTH DENSITY ALONG ISOELECTRONIC SEQUENCE

The differential cross section and total cross section of high-energy electron impact excitation can be calculated by Born approximation. The differential cross section is propotional to the so called generalized oscillator strength. The target atom or ion may be excited to infinite number of bound states and adjoint continuum states which can be treated in an unified manner by Quantum Defect Theory. Thus, we define generalized oscillator strength density (GOSD) as the generalized oscillator strength per unit of excitation energy. We have calculated the GOSD's of the lithium-like isoelectronic se-quence(Li, Be+, B++, C3+, Ne7+, Na8+, K16+) for excitation from the ground state to S, P, D and F channels. The scaling relation along isoelectronic sequence is discussed.

GENERALIZED OSCILLATOR STRENGTH DENSITY

The total cross section and differential cross section of high-energy electron impact excitation can be calculated with Born approximation. The differential cross section is proportional to the so called generalized oscillator strength. The target atom or ion may be excited to infinite bound states, auto-ionizing states and adjoint continuum states which can be treated in an unified manner by Multichannel Quantum Defect Theory. Thus, we can define the generalized oscillator strength density as the strength per unit excitation energy. Taking the lithium atom as an example, we present here a summary of the variations of the generalized oscillator strength density with respect to excitation energy as well as momentum transfer. Comparing with recent accurate experimental data, the validity of Born approximation is discussed.

Inter-shell correlations in the inelastic scattering of fast electrons of the outer subshells in Ar and Xe

The influence of neighbouring subshells on the density of the generalized oscillator strength (GOS) of the outer ns2 subshells has been studied for argon and xenon. Many-electron correlations within a single subshell and inclusion of inter-shell interactions have been considered in the random-phase approximation with exchange. The calculations were performed with energies omega transferred to the atom in the range from the ionization threshold up to 14 Ryd and transferred momenta q from 0 up to 2.5 au. The monopole, dipole and quadrupole components of the GOS densities have been taken into account. It was demonstrated that ns2 subshell ionization by fast electrons is, for small transferred momenta, entirely collective, and is totally determined by the influence of the neighbouring-shell electrons. With an increase in the transferred momentum, the main contribution to the total GOS density comes from the monopole and quadrupole components which are much less affected by many-electron correlations than the dipole component.

The role of many-electron correlations in fast electron-atom inelastic collisions

The effect of many-electron correlations in the inelastic electron-atom scattering at high energies is investigated. The importance of these correlations is shown by comparison of the results of calculations with the best possible independent particle model and the experimental data. Many-electron correlations are included in the random phase approximation with exchange (RPAE) and the corresponding integral equation for the effective interaction is displayed. This equation has been solved numerically for argon, and generalized oscillator strength densities as well as the differential cross section were calculated. The results agree with the experiment quite well, showing thus the very important role the many-electron correlations play in the inelastic electron-atom scattering. The calculations confirm the relative importance of the monopole and the quadrupole transitions in the process under consideration.