Dipole Oscillator Strengths Research Articles

Atomic data for opacity calculations. XV. Fe I-IV

Photoexcitation and photoionization processes are examined for ground and excited terms of Fe I, Fe II, Fe III and Fe IV. An LS coupling R-matrix approach is used in a seventeen target term expansion for Fe I, including 3d7, 3d6(5D)4S, 3d6(5D)4p and 3d5(6S)4s2 configurations; and sixteen term expansions for Fe II, Fe III and Fe IV, including 3d6, 3d5 and 3d4 configurations respectively. Data for even and odd LS terms having S<or=3; L<or=7 and effective principal quantum numbers up to 10 are calculated. Over six thousand term energies and nearly half a million dipole oscillator strengths are calculated. The photoionization cross section is tabulated for all bound terms over a fine mesh of photon energies to elucidate the low-energy resonance structure.

Accurate variational calculations of energies of the 2 (2)S, 2 (2)P, and 3 (2)D states and the dipole, quadrupole, and dipole-quadrupole polarizabilities and hyperpolarizability of the lithium atom.

The combined configuration-interaction--Hylleraas method has been used to calculate the energies for the ground 2 $^{2}$S and the excited 2${\mathrm{}}^{2}$P and 3 $^{2}$D states of the lithium atom. The energies obtained, -7.478 060 1 a.u. for the 2 $^{2}$S state, -7.410 155 4 a.u. and -7.335 523 1 a.u. for the 2 $^{2}$P and 3 $^{2}$D states, respectively, are the lowest nonrelativistic variational upper bounds found so far. Ionization potentials, lifetimes, dipole oscillator strengths and their sums, dynamic dipole, quadrupole and dipole-quadrupole polarizabilities, and the static second hyperpolarizability are also reported and compared with experimental and other theoretical results.

Comments on the Simulation of the Passage of Fast Electrons in Water

A recent paper in this journal by Kaplan and Sukhonosov (1) uses a Monte Carlo method to simulate the passage of fast electrons in water and the subsequent radiation chemistry. In that paper the authors find a serious discrepancy between our work (2-4) and theirs regarding the dependence of the stopping of low-energy electrons on the phase of water. Figure 1 shows the stopping powers of water vapor and liquid as determined by ourselves (2-4), by Kaplan and Sukhonosov (1), and by Paretzke et al. (5). The differences between the stopping powers of Kaplan and Sukhonosov and our work are readily apparent and were attributed by them to our alleged use of the Bethe formula. This allegation is due to a misunderstanding of our procedure. We follow a method originated by Ashley' (6) for constructing the inelastic cross section for low-energy electrons which gives a significantly different result from that of Bethe even though both methods are based on the dipole oscillator strength distribution (DOSD). Ashley's method approximates the generalized oscillator strength distribution (GOSD) by a quadratic extension of the dielectric response function in the energy-momentum plane. One obtains for the imaginary part of the dielectric response function, e(q,w),

Dipole oscillator strength properties and dispersion energies for acetylene and benzene

Dipole oscillator strength distributions (DOSDs), which are globally reliable, have been constructed for the acetylene and benzene molecules, through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength and molar refractivity data. A recommended isotropic DOSD for each molecule is used to evaluate a wide variety of dipole oscillator stength sums, logarithmic dipole sums, and mean excitation energies, for C2H2 and C6H6. Also obtained are reliable results for the isotropic dipole-dipole dispersion energy coefficients C 6, for the interaction of acetylene and benzene with themselves and with forty-one other species, and for the triple-dipole dispersion energy coefficients C 9, for (C2H2)3 and (C6H6)3. Psuedo-DOSDs for acetylene and benzene are presented which greatly facilitate the evaluation of C 6's and C 9's for a variety of interactions.

The absorption coefficient spectrum of poly(methyl methacrylate) in the soft X‐ray region

AbstractThe total photoabsorption cross section for poly(methyl methacrylate) (PMMA) is measured experimentally, using synchrotron radiation, over the photon energy range 40 &lt; E &lt; 1000 eV. The experiments utilize nominally monochromatic radiation from a grazing incidence grating monochromator (the “Grasshopper” at the Canadian Synchrotron Radiation Facility) on the storage ring “Aladdin” at the University of Wisconsin. The raw experimental data are corrected for the spectral contamination of the incident radiation from the monochromator by utilizing a calculated photoabsorption spectrum for PMMA. The calculations are carried out using the “mixture” rule and reliable dipole oscillator strength distributions for smaller molecules related to PMMA.

Constrained anisotropic dipole oscillator strength distribution techniques, and reliable results for anisotropic and isotropic dipole molecular properties, with applications to H2 and N2

Constrained anisotropic dipole oscillator strength distribution techniques are discussed and applied to obtain reliable results for a wide variety of the anisotropic and isotropic dipole properties of H2 and N2. These include the dipole oscillator strength sumsS k, k=2, 1, −1/2(−1/2) −2, −3, −4, ..., the logarithmic dipole sumsL k and mean excitation energiesI k, k=2(−1) − 2, and, as a function of wavelength, the dynamic polarizability and the associated anisotropy, the total depolarization ratio, the Rayleigh scattering cross section, and the Verdet constant. The anisotropic components of the DOSD for a molecule are obtained from a given recommended isotropic DOSD by using a constrained least squares procedure and a series of known anisotropic constraints. Assuming that sufficient input is available, the constrained DOSD approach used in this paper is the only available method for the reliable evaluation ofall the relevant anisotropic and isotropic dipole properties for a wide variety of atoms and molecules.

Angle and bond-length dependent C6 coefficients for H2 interacting with H, Li, Be and rare gas atoms

Accurate new C6 dispersion energy coefficients, and their dependence on the diatom orientation and bond length, are calculated for molecular hydrogen interacting with an atom of H, Li, Be, He, Ne, Ar, Kr or Xe. They are generated from accurateab initio pseudo dipole oscillator strength distributions (DOSD) for H2, H, He and Be, and reliable semiempirical ones for Li, Ne, Ar, Kr and Xe. Compact power series expansions for the diatom bond-length dependence of these coefficients, suitable for incorporation into representations of full potential energy surfaces for these systems, are determined and assessed.

Impact parameter dependence of light-ion electronic energy loss

We have calculated the dependence of the mean electronic energy loss of light ions on impact parameter by use of the harmonic-oscillator model of atomic stopping. Results are reported for protons incident on atomic hydrogen, helium, neon, and argon at velocities v $ ̆ v o . Considerable care has been taken in selecting proper sets of dipole oscillator strengths to characterize the ensemble of harmonic oscillators. The energy transfer to an individual oscillator is known from our previous work to the three leading orders in the Bom series. Mainly first-order results have been analysed. We find a quasi-Guassian behavior at small impact parameters and a nearly exponential tail at larger impact parameters. The latter approaches Bloch's dipole limit which is asymptotically exact. A single-oscillator model is included in the comparison and turns out to be inadequate in all cases except for high-speed protons incident on hydrogen. Part of our results can be compared with those of Kabachnik et al. The overall agreement is reasonable, but discrepancies of up to a factor of 2 have been found. For atomic hydrogen, these inaccuracies are asserted to originate in their numerical procedure.

Empirical relation between linear and nonlinear dipole polarizabilities

An empirical relation between linear and nonlinear dipole polarizabilities is proposed in the form γ(0; 0, 0, 0)= Y′ S(−3) S(−4)/ S(−2). By using experimental as well as highly accurate theoretical data of the dipole oscillator strength sums S( k) and the static second hyperpolarizability γ(0; 0, 0, 0), Y′ is shown to be nearly constant for a large class of small atoms and molecules.

Absolute optical oscillator strengths for the electronic excitation of atoms at high resolution: Experimental methods and measurements for helium.

An alternative method is described for the measurement of absolute optical oscillator strengths (cross sections) for electronic excitation of free atoms and molecules throughout the discrete region of the valence-shell spectrum at high energy resolution (full width at half maximum of 0.048 eV). The technique, utilizing the virtual-photon field of a fast electron inelastically scattered at negligible momentum transfer, avoids many of the difficulties associated with the various direct optical techniques that have traditionally been used for absolute optical oscillator strength measurements. The method is also free of the bandwidth (line saturation) effects that can seriously limit the accuracy of photoabsorption cross-section measurements for discrete transitions of narrow linewidth obtained using the Beer-Lambert law [${\mathit{I}}_{0}$/I=exp(nl${\mathrm{\ensuremath{\sigma}}}_{\mathit{p}}$)]. Since the line-saturation effects are not widely appreciated and are only usually considered in the context of peak heights, a detailed analysis of this problem is presented, with consideration of the integrated cross section (oscillator strength) over the profile of each discrete peak.The suitability of the high-resolution dipole (e,e) method for general application to atomic and molecular electronic spectra is evaluated by test measurements of the absolute dipole (optical) oscillator strengths for the photoexcitation and photoionization of helium, since for this atom detailed quantum-mechanical calculations using highly correlated wave functions have been reported. The absolute scale is obtained from the Thomas-Reiche-Kuhn sum-rule normalization of the Bethe-Born transformed electron-energy-loss spectrum and does not involve the difficult determinations of photon flux or target density. The measured dipole oscillator strengths for helium excitation (1 $^{1}$S\ensuremath{\rightarrow}n $^{1}$P, n=2--7) are in excellent quantitative agreement with the calculations reported by Schiff and Pekeris [Phys. Rev. 134, A368 (1964)] and by Fernley, Taylor, and Seaton [J. Phys. B 20, 6457 (1987)]. The absolute measurements are also compared with other experimental and theoretical oscillator strength determinations for photoexcitation and photoionization processes in helium up to 180 eV, including the 2snp and 3snp autoionizing resonances in the 59--72-eV energy region.

Charge and spin transfer and optical properties in conducting porphyrin compounds

Anisotropic materials made from stacked macrocycles have potential applications as organic conductors and nonlinear optical materials. Using self-consistent-field local density theory, we have been exploring the ground and excited state electronic structures of metal substituted tetraazaporphyrins, phthalocyanines, and tetrabenzoporphyrins. The calculated and measured polarized optical absorption peaks are in satisfactory agreement. The theoretical dipole oscillator strengths provide absolute intensities for verification of transition assignments, which are helpful for identifying low-lying states and excitation mechanisms.

Absorption spectrum of doubly-ionized silicon

Energy terms, dipole oscillator strengths and photoionization cross-sections from the ground state have been calculated for doubly-ionized silicon. Energies of the autoionizing 1 P 0 states and resonance line widths in the continuum are also obtained. The configuration interaction method was used for initial and final states. The ionic orbitals were generated through angular-momentum-dependent, scaled Thomas-Fermi-Dirac-Amaldi potentials.

A calculation of the isotropic and anisotropic spectral moments of the dipole oscillator strength distribution of N2

AbstractWe calculate a range of isotropic and anisotropic spectral moments of the dipole oscillator strength distribution for N2 in the random phase approximation. The internuclear dependence of, in particular, S∥(k) is nonnegligible and vibrationally averaged moments are reported. The results are compared to other calculations and to experiment when available, and we conclude that the scheme gives reliable results. Based on our results, we predict a 10% anisotropy in the stopping power of oriented N2 molecules.

Energy loss by electrons in gaseous saturated hydrocarbons

The stopping powers, the inelastic mean free paths, the ranges, and the distributions of energy loss events for electrons in some gaseous alkanes have been calculated from experimentally based dipole oscillator strength distributions. The results show very little difference between the members of the homologous series of straight-chain hydrocarbons, C{sub n}H{sub 2n+2} where n = 2, 4, 6, and 8. For instance, the integrated path length of a 1-MeV electron in ethane of unit density is 0.38 cm and increases to 0.40 cm in octane of the same density. The stopping power of a 1-MeV electron in unit density hexane is 0.2 eV/nm, and the inelastic mean free path is 220 nm. The corresponding values for the other alkanes differ by less than 10%. The distribution of energy loss events along the track of a high-energy electron in these gaseous hydrocarbons is not significantly affected by the value of n, and it is insensitive to the incident electron energy from 10 keV to 1 MeV. The most probable energy loss along the track of a 1-MeV electron is 14 eV in ethane, 15 eV in butane and hexane, and 16 eV in octane. The mean energy loss is 25 eVmore » in butane, hexane, and octane and is 1 eV less in ethane.« less

Geometric dependence of the mean excitation energy and spectral moments of water.

The spectral moments S(k) and L(k) of the dipole oscillator strength distribution of water have been calculated in the random-phase approximation as a function of molecular geometry. Several of the moments vary quite strongly with the O−H bond distance, while the dependence on bond angle is much less pronounced

Dipole moments, transition moments, oscillator strengths, radiative lifetimes, and overtone intensities for CH and CH+ as computed by quasi‐degenerate many‐body perturbation theory

AbstractThe correlated, size‐consistent, ab initio effective valence‐shell dipole operator (μv) method is used to calculate dipole moments and transition dipole moments of the CH molecule and transition dipole moments of the CH+ ion as a function of internuclear distance. The dipole and transition dipole moments computed here compare well with those of other accurate ab initio methods. The transition dipole moments are then used to calculate oscillator strengths and radiative lifetimes for the A → X and B → A transitions of the CH+ ion and the A → X transition of the CH molecule. Comparisons are made with the best available theoretical and experimental lifetimes. Finally, the CH ground‐state dipole moment function is used to evaluate overtone intensities and to examine simple models of the CH overtone intensities in polyatomic molecules.

Absorption spectrum of singly-ionized aluminum

Energy terms, dipole oscillator strengths and photoionization cross-sections from the ground state have been calculated for singly-ionized aluminum. Autoionization 1 P 0 state-transition energies and resonance line widths in the continuum are also obtained. The configuration interaction method was used for initial and final states. The ionic orbitals are generated through angular-momentum-dependent, scaled Thomas-Fermi-Dirac-Amaldi potentials.

MCHF oscillator strength and lifetime calculations in neutral calcium

The authors report extensive multiconfiguration Hartree-Fock (MCHF) calculations, taking into account valence correlation and core-relaxation effects, of energy levels, eigenvector compositions, electric dipole and quadrupole oscillator strengths involving the n1S(n=1-4), n1PO (n=1, 2), n1D(n=1-3) and n1FO(n=1, 2) states in Ca I. On the whole, the agreement between theory and observation has been improved by their set of MCHF results. The theoretical transition probabilities allow the evaluation of the lifetimes for the levels 4s4p, 4s5p 1PO; 4s4d, 4p2 1D and 3d4p, 4s4f 1FO which are compared with previous measurements. The differences between MCHF calculations for series perturbed by doubly-excited states in Ca and Sr are discussed. It is concluded that core-polarization effects are of about the same importance in the two atoms but that the effects on the 3d (Ca) and 4d (Sr) orbitals are such that the total core-polarization effects for series and perturbers are of the same magnitude in Sr while large differences exist in Ca.

Time-dependent Hartree–Fock second-order molecular properties with a moderately sized basis set. II. Dispersion coefficients

Time-dependent coupled Hartree–Fock frequency-dependent polarizabilities are used to obtain ab initio dipole–dipole C6, dipole–quadrupole C8, and triple–dipole ν, dispersion coefficients. The moderately sized 6-31G (+sd+sp) basis set optimized for calculation of molecular static dipole polarizabilities has enabled the computation of dispersion coefficients for a wide variety of molecules containing atoms up to chlorine. Results are presented for 48 molecules including benzene, cyclohexane, SF6, and CCl4. Appropriate scaling of 6-31G(+sd+sp) results for C6 and ν enables the prediction of these coefficients to within 3% of experimental estimates that are based on dipole oscillator strength distributions. Results for the mean static quadrupole polarizability C̄(0) and C8 dispersion coefficient are presented for nondipolar molecules and the origin dependence of C8 is investigated.

Use of dipole oscillator strength in the calculation of the range of electrons in various gases

The importance of studies with synchrotron radiation for providing dipole oscillator strength distributions in the spectral region between 10 and 100 eV is discussed. Dipole oscillator strengths compiled from photo-absorption and high energy electron inelastic scattering experiments are compared with recent synchrotron measurements for gaseous C 2H 2OH and i-C 4H 8 in the v-u.v. region. The compiled dipole oscillator strength distributions for these gaseous media and for water vapor are used to calculate the inelastic mean free path, mean excitation potential and the range distribution of low-energy electrons. The density normalized ranges are found to decrease in the order H 2O > C 2H 5OH > i-C 4H 8. The actual range of a 1 keV electron in H 2O is about 3 or 4 times that in C 2H 5OH and i-C 4H 8, respectively. This difference can have a pronounced effect on track structure.