Generalized Oscillator Strengths Research Articles

Electron impact excitation of bismuth

Abstract The present study investigates the electron impact excitation of bismuth from the ground state 6p3 4S3/2 to the excited state 6p27s 4P1/2. Motivated by the latest measurements by Marinković et al [J. Phys. B, 49 23 520 (2016)], relativistic distorted wave calculations are performed to obtain the differential and integrated cross sections for incident electron energies at 10, 20, 40, 60, 80, and 100 eVs. These results are compared with the available experimental data and a good agreement is observed. Our results represent the first theoretical work to provide such a comparison. Additionally, we report the generalized oscillator strengths derived from our calculated differential cross sections.

Theoretical study of valence excitations in fluoromethanes by high energy electron impact

We report a theoretical study of the electron-impact electronic excitation of fluoromethanes. Generalized oscillator strengths (GOSs) are calculated for the molecules at the equation-of-motion coupled-cluster singles and doubles level. To clarify the influence of nuclear dynamics on the electronic excitations, the effects of internal molecular vibrations are included in the calculation. Comparison with experimental data resolves some inconsistencies in the assignment of the transition bands. Furthermore, it is shown that the lengthening of the CH bond enhances the excitation from the highest occupied orbital to the 3s Rydberg orbital for CHF3, CH2F2, and CH3F, and that the CH stretching vibrations thus have a significant influence, especially at small momentum transfer where electric dipole transitions are dominant. Since the 2 1A1 state of CHF3 dissociates into CF3 + H, the result indicates that the CH stretching vibration causes an increase in the production of CF3 by electron collision and by photoabsorption.

Vibronic effect study of 1A2 state of H2O and D2O

The generalized oscillator strengths of the dipole-forbidden excitations of the 1A2 of H2O and D2O were calculated with the time dependent density functional theory, by taking into account the vibronic effect. It is found that the vibronic effect converts the dipole-forbidden excitation of the 1A2 into a dipole-allowed one, which enhances the intensities of the corresponding generalized oscillator strength in the small squared momentum transfer region. The present investigation shows that the vibronic effect of H2O is slightly stronger than that of D2O, which exhibits a clear isotopic effect.

Generalized oscillator strengths and integral cross sections of krypton studied by high-energy electron scattering

Absolute generalized oscillator strengths of the valence-shell excitations of krypton have been determined with an incident electron energy of 1500 eV and an energy resolution of about 80 meV. By employing the relative flow technique with a dilute target, the pressure effect is excluded and the accuracy of the measured generalized oscillator strengths is improved. By comparing the present generalized oscillator strengths with the previous experimental and theoretical results, it is found that the first Born approximation is not reached at the squared momentum transfer larger than 1 a.u.. The optical oscillator strengths have been obtained by extrapolating the measured generalized oscillator strengths to zero squared momentum transfer, which cross-checks the previous electron impact and photoabsorption results. With the aid of the BE-scaling method, the integral cross sections of krypton have been determined from the excitation threshold to 5000 eV. The present oscillator strengths and integral cross sections supplement the fundamental database of the electron scattering of krypton and provide a benchmark for the theoretical methods.

Velocity Form Calculations of Generalized Oscillator Strengths for 3s→ (3p, 4p, 5p, 6p) Dipole Transitions of Atomic Sodium in Debye Plasma

Velocity Form Calculations of Generalized Oscillator Strengths for 3s→ (3p, 4p, 5p, 6p) Dipole Transitions of Atomic Sodium in Debye Plasma

Electronic cross section, stopping power and energy-loss straggling of metals for swift protons, alpha particles and electrons

Understanding and quantifying the electronic inelastic interactions of swift ions and electrons in metals is fundamental for many applications of charged particle beams. A common theoretical approach is moreover desirable for the case of both types of projectiles, as large numbers of secondary electrons arise as the result of ion interaction with metals. The electronic cross section, stopping power and energy-loss straggling resulting from the interaction of swift protons, alpha particles and electrons when moving through the metals aluminum, iron, copper, molybdenum, platinum and gold, are calculated theoretically for a wide energy range of the projectiles. The model is based on the dielectric formalism, which realistically accounts for the excitation spectrum of each metal through the Mermin Energy-Loss Function–Generalized Oscillator Strength (MELF-GOS) methodology. The impact of the complexity of the excitation spectrum of each metal (encompassing interband transitions and collective excitations), as well as the different sources of (sometimes conflicting) optical data is analysed in detail. Specific interactions are considered for each projectile, such as electron capture/loss and electron cloud polarisation for ions, and indistinguishability, exchange and low-energy corrections for electrons. An estimate of possible contributions of surface excitations to the interaction probabilities of low energy electrons is given. Comparison of our results with a large collection of available experimental data shows good agreement. As a practical and useful outcome of the work, we provide analytical expressions fitting all our calculated quantities, which can be applied for simulation or comparison purposes.

Investigation of the valence-shell excitations of molecular carbon disulfide by high-energy electron scattering

Absolute generalized oscillator strengths of the valence-shell excitations of carbon disulfide have been determined by a joint investigation of a fast electron impact experiment and equation of motion coupled cluster with singles and doubles (EOM-CCSD) calculations. Based on the present experimental and theoretical results, the transition nature of the excitations are elucidated, and some controversies about the transition assignments are resolved. By extrapolating the generalized oscillator strengths to zero momentum transfer, the corresponding optical oscillator strengths were determined, which provide a cross-check to the previous experimental and theoretical results. Moreover, the integral cross sections of the valence-shell excitations from their excitation thresholds to 5000 eV have been obtained by means of the BE-scaling method. The oscillator strengths and integral cross-sections complement the fundamental data of carbon disulfide and supply important applications in astrophysics and atmospheric physics.

Electromagnetic interaction models for Monte Carlo simulation of protons and alpha particles

Electromagnetic interactions of protons and alpha particles are modeled in a form that is suitable for Monte Carlo simulation of the transport of charged particles. The differential cross section (DCS) for elastic collisions with neutral atoms is expressed as the product of the DCS for collisions with the bare nucleus and a correction factor that accounts for the screening of the nuclear charge by the atomic electrons. The screening factor is obtained as the ratio of the DCS for scattering of the projectile by an atom with a point nucleus and the parameterized Dirac–Hartree–Fock–Slater (DHFS) electron density, calculated from the eikonal approximation, and the Rutherford DCS for collisions with the bare point nucleus. Inelastic collisions, which cause electronic excitations of the material, are described by means of the plane-wave Born approximation, with an empirical simple model of the generalized oscillator strength (GOS) that combines several extended oscillators with resonance energies and strengths determined from the atomic configurations and from the empirical mean excitation energy of the material. The contributions from inner subshells are renormalized to agree with realistic ionization cross sections calculated numerically from the DHFS self-consistent model of atoms by means of the plane-wave Born approximation. The resulting DCS allows analytical random sampling of individual hard inelastic interactions.

On the photoinduced degradation of tamsulosin: The simpler the better

In this work, we present a comprehensive investigation of the decomposition of tamsulosin. Experiments were performed in an aqueous solution through photolysis with a 254 nm light source. In general, tamsulosin degradation was observed (presenting a rate of 35.4%, in 180 min), demonstrating that direct photoinduced decomposition is efficient. The simpler uncatalyzed process worked while previous experiments using solid catalysts showed negligible degradation. The kinetic constant of the photolysis process (17.6 ×10−3 min−1) was determined, considering first order kinetics, by fitting plots of ln([Tam]t −[Tam]∞)/ln([Tam]0 −[Tam]∞) versus irradiation time, where [Tam]t is the concentration of tamsulosin at time t, and [Tam]∞ is the limiting concentration of the reacting system. In addition, physical insights regarding tamsulosin photoexcitation and photolysis were obtained through quantum chemistry computations. Density functional theory (DFT) was used to investigate the ground state while its time-dependent formalism (TD-DFT) was used for determining vertical excitation energies and generalized oscillator strengths (GOSs). All the computations were undertaken at the CAM-B3LYP/6-311++G(d,p) level of theory, in water. Regarding the excited states, all five lowest-lying states were determined to have non-zero GOSs, with S3 (found at 5.73 eV (∼216 nm) at the TD-DFT/CAM-B3LYP/6–311++G(d,p) level of theory) presenting the highest GOS (0.1157) among all. Hence, these accessible states may be assigned as those responsible for the photoinduced degradation observed experimentally. Moreover, the computational results suggest tamsulosin undergoes photodecomposition through excited state chemical reaction rather than via a direct photolysis path.

Oscillator Strengths and Cross Sections of the Valence-Shell Excitations of HBr Studied by Fast Electron Impact.

The oscillator strengths and cross sections of the valence-shell excitations of HBr were determined by fast electron scattering with an incident electron energy of 1500 eV and an energy resolution of 80 meV. The momentum transfer dependence behaviors of the generalized oscillator strengths have been used to elucidate the transition characteristics. The present results show that the strong spin-orbital interaction results in the observation of some triplet states in the (Λ, S) coupling and the constant generalized oscillator strength ratios for the pair states with the same electronic configuration and quantum number Ω, and the quantitative spin-orbit coupling coefficients of b3Π1(v = 0) and C1Π(v = 0) are determined. The optical oscillator strengths of the valence-shell excitations were obtained by extrapolating the generalized oscillator strengths to the limit of zero squared momentum transfer. The present optical oscillator strengths give an independent cross-check of the previous experimental and theoretical results, and the comparison shows that the line-saturation effect is more severe for the high Rydberg states with large intensities and narrow natural widths. The integral cross sections of the valence-shell excitations of HBr were obtained from the excitation threshold to 5000 eV by the BE-scaling method. The present oscillator strengths and cross sections supplement the fundamental molecular database of HBr and can be used for modeling in the semiconductor industry, astrophysics, and atmospheric chemistry.

Oscillator strength and cross section study of the valence-shell excitations of NO2 by fast electron scattering

Abstract Oscillator strengths and cross sections of the valence-shell excitations in NO2 are of great significance in testing the theoretical calculations and monitoring the state of ozone layer in the earth’s atmosphere. In the present work, the generalized oscillator strengths of the valence-shell excitations in NO2 were obtained based on the fast electron scattering technique at an incident electron energy of 1.5 keV and an energy resolution of about 70 meV. By extrapolating the generalized oscillator strengths to the limit of a zero squared momentum transfer, the optical oscillator strengths for the dipole-allowed transitions have been obtained, which provide an independent cross check to the previous experimental results. Based on the BE-scaling method, the corresponding integral cross sections have also been derived systematically from the excitation threshold to 5000 eV. The present dynamic parameters can provide the fundamental spectroscopic data of NO2 and have important applications in the studies of atmospheric science.Oscillator strengths and cross sections of the valence-shell excitations in NO2 are of great significance in testing the theoretical calculations and monitoring the state of ozone layer in the earth’s atmosphere. In the present work, the generalized oscillator strengths of the valence-shell excitations in NO2 were obtained based on the fast electron scattering technique at an incident electron energy of 1.5 keV and an energy resolution of about 70 meV. By extrapolating the generalized oscillator strengths to the limit of a zero squared momentum transfer, the optical oscillator strengths for the dipole-allowed transitions have been obtained, which provide an independent cross check to the previous experimental results. Based on the BE-scaling method, the corresponding integral cross sections have also been derived systematically from the excitation threshold to 5000 eV. The present dynamic parameters can provide the fundamental spectroscopic data of NO2 and have important applications in the studies of atmospheric science.

Plasma-relevant fast electron impact study of difluoromethane

Difluoromethane () is a commonly used etching gas in manufacturing very-large-scale integrated circuits as the fluorine source. Electron impact excitation cross sections for are important input data for modeling the reactive etching plasmas. In this work, we present the experimental generalized oscillator strengths for the , , and transitions on the absolute scale. The measurement was realized by employing the crossed-beam based relative flow technique at an angle-resolved electron energy loss spectrometer, operating at an incident energy of 1500 eV and a resolution of 80 meV. The dipole-forbidden transition at around 9.7 eV is identified for the first time. The measured data are fitted with the well-known Lassettre formula to yield analytical expressions and optical oscillator strengths at for dipole-allowed transitions. The analytical expressions enable integrations over momentum transfer to obtain the Born integral cross sections for electron impact excitations from the threshold to 5000 eV. The integral cross sections for dipole-allowed transitions are scaled to a more reliable level by using the BE-scaling method. The experimental data can benchmark theoretical calculations and supplement the molecular database for plasma modelers.

Oscillator strengths and cross sections of the valence-shell excitations of CH[formula omitted]I studied by fast electron scattering

Oscillator strengths and cross sections of the valence-shell excitations in CH3I are important for studying molecular photodissociation and monitoring the destruction of ozone in the Earth’s atmosphere. Based on the relative flow technique, absolute generalized oscillator strengths of the valence-shell excitations in CH3I have been determined by using an angle-resolved electron energy loss spectrometer. The measurement was carried out at an incident electron energy of 1.5 keV and an energy resolution of 80 meV. Optical oscillator strengths for the dipole-allowed transitions have been obtained at the zero limit of the squared momentum transfer, providing an independent cross check with the previous experimental results. The integral cross sections from the excitation threshold to 5000 eV have also been obtained by means of the BE-scaling method. The present experimental oscillator strengths and cross sections can supplement the fundamental spectroscopic data of CH3I and will play an important role in the studies of molecular photodissociation dynamics.

Theoretical Study of Valence Shell Excitation by Electron Impact in CCl4

This paper reports a theoretical study of valence shell excitation in CCl4 by high-energy electron impact. Generalized oscillator strengths are calculated for the molecule at the equation-of-motion coupled-cluster singles and doubles level. To elucidate the influence of nuclear dynamics on electron excitation cross-sections, the effects of molecular vibration are included in the calculation. Based on a comparison with recent experimental data, several reassignments of spectral features are made, and it is found that excitations from the Cl 3p nonbonding orbitals to σ* antibonding orbitals, 7a1 and 8t2, play dominant roles below the excitation energy of ∼9 eV. Furthermore, the calculations reveal that distortion of the molecular structure due to the asymmetric stretching vibration significantly affects the valence excitations at small momentum transfers, where contributions from dipole transitions are dominant. It indicates that vibrational effects have a considerable influence on Cl formation in the photolysis of CCl4.

Oscillator strengths and cross sections of the valence shell excitations in nitrous oxide studied by high-energy electron scattering

Generalized oscillator strengths (GOSs) of the valence shell excitations to the A1Σ−+B1Δ, C1Π, D1Σ+ and 21Π states in nitrous oxide have been determined by employing an angle-resolved electron energy loss spectrometer operated at an incident energy of 1500 eV and an energy resolution of about 80 meV. Detailed comparisons with the previous data indicate that the higher-order Born terms play a significant role in the GOSs of C1Π and D1Σ+ states at either low impact energies or large momentum transfers, and the GOSs of A1Σ−+B1Δ and C1Π states measured with the gas cell may suffer from the pressure effect. The measured GOS data are fitted with the Lassettre formula to determine the corresponding optical oscillator strengths (OOSs) and calculate the integral cross sections (ICSs) based on the BE-scaling method. The oscillator strengths and cross sections in this work provide a cross check on the previous data and can serve as a benchmark for testing the developed theoretical models and computational codes.

Electron-Impact Ionization of Carbon

We present ionization cross-sections of collisions between electrons and carbon atoms using the classical trajectory Monte Carlo method. Total cross-sections are benchmarked against the reported experimental data and the predictions of numerically intensive theoretical methods as well as pioneering calculations for this collision system. At impact energies greater than about 100 eV, the present results are in very good agreement with the generalized oscillator strength formulation of the Born approximation as well as with the experimental data. Limitations inherent to a purely classical description of the electron impact ionization process at low impact energies are detected and analyzed, suggesting a clear route for future studies.

Calculated energy loss of swift light ions in platinum and gold: importance of the target electronic excitation spectrum

Understanding and predicting the energy loss of swift ions in metals is important for many applications of charged particle beams, such as analysis and modification of materials, and recently for modelling metal nanoparticle radiosensitisation in ion beam cancer therapy. We have calculated the stopping power of the transition metals Pt and Au for protons and alpha particles in a wide energy range, using the dielectric formalism, which realistically accounts for the excitation spectrum of each metal through the Mermin Energy Loss Function - Generalised Oscillator Strength methodology. For each combination of projectile, energy and target, we have considered: (i) the equilibrium charge state of the projectile through the target, (ii) the energy-loss due to electron capture and loss processes, and (iii) the energy loss resulting from the polarisation of the projectile’s electronic cloud due to the self-induced electric field. Our calculated stopping powers show a fairly good agreement with the available experimental data for platinum and gold, particularly the most recent ones around the stopping power maximum, which validates the methodology we have used to be further extended to other transition metals. For the materials studied (platinum and gold), two commonly used and different sources of the experimental excitation spectrum yield comparable calculated stopping powers and mean excitation energies, the latter being closer to the most recent data provided in a recent ICRU Report than to previous compilations. Despite the small differences in the sources of excitation spectra of these metals, they lead to practically the same stopping power results as far as they reproduce the main excitation features of the material and fulfil physically motivated sum rules.

Bethe stopping-power formula and its corrections

The classical and quantum theories leading to the asymptotic Bethe formula of the stopping power of matter for charged particles heavier than the electron are briefly reviewed. Models and approximations for the practical calculation of various corrections that extend the validity range of the formula are described. The asymptotic formula and the associated shell correction were determined previously from an extensive database of atomic generalized oscillator strengths, calculated for an independent-electron model with the Dirac-Hartree-Fock-Slater (DHFS) self-consistent potential, with due account for relativistic departures from the Bethe sum rule. The nonrelativistic Bloch correction is extended to the relativistic domain by means of the Lindhard-S\o{}rensen formulation, and an accurate parametrization for point projectiles with small charges is proposed. The density-effect correction and the Barkas correction are obtained from a semiempirical model of the optical oscillator strength (OOS), built from the calculated DHFS contributions of inner electron subshells plus the OOS of outer-shell electrons represented by an analytical expression, which is determined by the composition, mass density, and empirical mean excitation energy, or $I$ value of the material. Inclusion of the shell, density-effect, Lindhard-S\o{}rensen, and Barkas corrections into the asymptotic formula leads to the corrected Bethe formula. A general strategy is proposed to determine the stopping power in terms of only the $I$ value of the material. It is shown that, with the empirical $I$ values recommended in Report 37 of the International Commission on Radiation Units and Measurements, the stopping powers calculated numerically from the corrected formula are in close agreement with available measurements of the stopping power of elemental materials for protons and alpha particles with energies higher than 0.75 and 5 MeV, respectively.

Oscillator strengths and cross sections of high Rydberg states in ammonia studied by fast electron scattering

We report the experimental generalized oscillator strengths (GOSs) for transitions from the ground state to the Rydberg states , , , and an ‘undefined’ state in ammonia. The experiment was performed using an angle-resolved electron energy loss spectrometer operated at an incident energy of 1500 eV and an energy resolution of about 80 meV. The experimental observation confirms the recent theoretically predicted appreciable vibrational effects on the GOS for the transition (2021 J. Phys. B: At. Mol. Opt. Phys. 54 135202). The measured GOS data are fitted with the Lassettre formula to determine the corresponding optical oscillator strengths for dipole-allowed transitions. Furthermore, the fitted curves enable the integrations of GOSs over the momentum transfer squares to obtain the Born excitation cross sections. The integral cross sections are scaled to an accurate scale by using the BE-scaling method. The data in this work can supplement the molecular database and deepen our understanding of the scattering mechanism.

Generalized oscillator strength of the core-excited states of molecular nitrogen studied by nonresonant inelastic x-ray scattering

Fast electron impact was used to study the generalized oscillator strengths of the inner-shell excitations in atoms and molecules previously. In this work, a nonresonant inelastic x-ray scattering technique is extended to determine the generalized oscillator strengths of $(1{\ensuremath{\sigma}}_{g}\ensuremath{\rightarrow}1{\ensuremath{\pi}}_{g})+(1{\ensuremath{\sigma}}_{u}\ensuremath{\rightarrow}1{\ensuremath{\pi}}_{g})$ inner-shell excitations of molecular nitrogen in the squared momentum transfer range of 0.86 to 14.40 a.u. at a photon energy of about 10 keV and an energy resolution of about 1.3 eV. The present generalized oscillator strength strictly follows the first Born approximation and thus provides a rigorous test to the previously calculated results and the experimental ones measured by the electron energy loss spectroscopy. The presently extrapolated optical oscillator strength at zero momentum transfer is in accord with most experimental results and the theoretical data with the correlation effect considered carefully. This work indicates that the nonresonant inelastic x-ray scattering technique is a powerful tool to study the core excitation mechanism in atoms and molecules.