Absolute Generalized Oscillator Strength Research Articles

Electron scattering from trans 1,3-butadiene molecule: cross-sections, oscillator strength and VUV photoabsorption cross-sections

Electron energy-loss spectra for the butadiene molecule were measured in the scattering angular range of 2.0° to 8.0°, in an energy-loss range from 2 to 50 eV, using 1000 eV incident electrons. The absolute generalized oscillator strength (GOS) and inelastic cross section have been determined for the \hbox{$\tilde{\rm X}^{1}$}˜X1A g → 11B u transition. The absolute elastic differential cross section was also determined spanning an angular range from 2.0° to 40.0°. From a small angle electron energy-loss spectrum, the optical oscillator distribution (photoabsorption spectrum) for the butadiene molecule was obtained in the 2 to 100 eV photon energy range. Accurate ab initio calculations have been performed, within the First Born Approximation, for generalized oscillator strength (GOS) and excitation energies for the \hbox{$\tilde{\rm X}^{1}$}˜X1A g → 11B u and \hbox{$\tilde{\rm X}^{1}$}˜X1A g → 21A g transitions. Our results emphasize the importance of using highly correlated wavefunctions and accurate methodologies in the calculation of the GOS for electron impact-induced electronic transitions in molecules.

Cross sections for elastic and inelastic electron scattering from carbon disulfide

Electron energy-loss spectra, measured as a function of the scattering angle, have been obtained for a carbon disulfide molecule, CS2, in the excitation energy range from 0 to 45 eV. The incident electron energy was 1000 eV. The absolute generalized oscillator strength (GOS) and absolute inelastic differential cross section have been determined as a function of the square of the momentum transfer (K2) for the intense allowed transition 1Σ+u ← 1Σ+g, centred at 6.3 eV. The absolute elastic differential cross section was also determined spanning an angular range from 1.5° to 10°. It is well known that at high incident energies and small scattering angles electrons behave like pseudo photons. The CS2 photoabsorption spectrum was consequently obtained by extrapolation from the measured small angle electron energy-loss spectrum. The result shows a good resemblance to the atmospheric spectrum of Jupiter, following comet impact.

Absolute Generalized Oscillator Strength Profile of NegativeIon Resonance at 8.9 eV in C2F6

A temporary negative ion resonance at 8.9 eV in C2F6 has beenclearly identified using angle-resolved electron energy lossspectroscopy at 2.5 keV impact energy, and can be attributed toelectron capture into 12a1u, 12a1g, 22a2u, and12eg virtual molecular orbitals. The corresponding absolutegeneralized oscillator strength profile is found to have a shapecharacteristic of non-dipole interaction with the maximum K~0.8 a.u. of momentum transfer.

Absolute differential cross sections for elastic and inelastic electron scattering from benzene with 1 kev impact energy

The absolute generalized oscillator strength and absolute inelastic differential cross section have been determined, as a function of the momentum transfer, for the 1E1u + 1B1u ← 1Ag transition in the benzene molecule. A previously described electron energy-loss spectrometer, featuring a Wien-filter velocity analyser, has been used. Employing 1000 eV incident electron energy and 1.0 eV energy resolution, absolute oscillator strength distribution as a function of electron energy loss was obtained in the 2–8° scattering angle range. The absolute elastic differential cross section was also determined spanning an angular range of 2°–14°. The photoabsorption spectrum converted from the electron energy-loss spectrum was compared with the interstellar extinction curve where we confirm the proportionality between the cross section and extinction.

Absolute Generalized Oscillator Strength Profiles of RydbergTransitions in C2F6

Absolute generalized oscillator strengths (GOSs) for the twoRydberg excitations at 12.1 eV and 13.5 eV in C2F6 have beendetermined as functions of energy loss andmomentum transfer (K) at impact energy of 2.5 keV. The GOS profiles forthese two Rydberg transitions to 3 p Rydberg orbital have thecharacteristic dipole-dominated shapes with a strong maximum at K = 0.

Reinterpretation of the recently measured absolute generalized oscillator strength for theAr3p−4ptransition

The recent experimental observation of the absolute generalized oscillator strength (GOS) for the Ar $3p\ensuremath{-}{(4p,4p}^{\ensuremath{'}})$ nondipole transition has been interpreted as a manifestation of quadrupole excitation [X. W. Fan and K. T. Leung, Phys. Rev. A 62, 062703 (2000)]. Contrary to the experimentalists' assignment, on the grounds of our random-phase-approximation with exchange (RPAE) calculation, we attribute the measured GOS to combined monopole, the dominant component, and quadrupole contributions. Our RPAE GOS's for the Ar dipole $3p\ensuremath{-}4s$ and $3p\ensuremath{-}3d,5s$ and the lowest nondipole transitions are compared with the measurements. The results could have significant implications for other similar transitions, previously interpreted as quadrupole excitation and for interpreting other discrete transitions.

Generalized oscillatorstrength and inelastic cross sections for the Xe 4d resonances

Electron energy-loss spectra for the Xe atom were measured for agiven set of scattering angles (1.5°-20.0°), inan energy-loss range from 40 to 180 eV using an incidentelectron energy of 1045 eV and an energy resolution of 1.0 eV.The absolute generalized oscillator strength (GOS) and crosssection have been determined for the intense shape resonance(4d→εf) and for the discrete resonance4d(1S0)→6p(2D5/2) in the Xe atom.The GOS curve as a function of the square of the momentumtransfer for the shape resonance presents a well-definedminimum. In order to obtain the optical oscillator strength for our data normalization, the electron energy-loss spectrum(1.5°) was converted to a photoabsorption spectrum. Abroad band has also been observed in the energy-loss spectra,centred at 80.0 eV. According to previous analysis, it hasbeen assigned to double excitations (4d-15p-1).

Angle-resolved electron energy loss spectroscopy of valence-shell and Si 2p pre-edge excitation of SiF4: Bethe surface and absolute generalized oscillator strength measurement

Absolute generalized oscillator strengths (GOSs) of discrete transitions in the preionization-edge region of the valence and Si 2p inner shells of SiF4 have been determined as functions of energy loss and momentum transfer by using angle-resolved electron energy loss spectroscopy at 2.5 keV impact energy. The GOS profiles of the pre-edge features are generally consistent with the spectral assignments based on the term values of the virtual and Rydberg states from earlier valence and inner-shell studies. In particular, the GOS profiles for these low-lying preionization-edge features in the valence shell are found to be dominated by a strong maximum at zero momentum transfer, consistent with the proposed assignment of predominantly dipole-allowed Rydberg and mixed valence-Rydberg transitions. In the case of the lowest-lying preionization-edge 1t1→6a1 feature, which is formally dipole-forbidden, the present work shows that such a shape for the GOS profile is, however, not exclusive to just dipole-allowed transitions. In the Si 2p shell, the GOS profiles for the well resolved, intense σ* resonance and three higher-lying Si 2p pre-edge features have been determined and are found to be largely dominated by dipole-allowed (Rydberg) excitations. Differences in and between the GOS profiles for the valence-shell and Si 2p pre-edge features in SiF4 are identified. No discernible secondary extrema can be found in any of these GOS profiles. The present GOS results for SiF4 are compared with those reported for other cage-like molecules, including CF4 and SF6.

Absolute generalized oscillator strength profiles of Si 2p shape resonances in SiF 4

Absolute generalized oscillator strengths (GOSs) of the Si 2p shape resonances in silicon tetrafluoride (SiF 4) have been determined as functions of momentum transfer by angle-resolved electron energy loss spectroscopy at 2.5 keV impact energy. These GOS profiles reveal subtle details about the spectral nature of the underlying dipole-allowed Si 2p →2 e and Si 2p →7 t 2 continuum transitions, particularly with respect to the pre-edge Si 2p →6 a 1 σ ∗ resonance. The GOS profiles of the Si 2p shape resonances in SiF 4 are compared with those of the corresponding S 2p →2 t 2 g and S 2p →4 e g resonances in SF 6.

Valenceelectronic excitation of the SiF4 molecule: generalized oscillatorstrength for the 5t2 → 6a1 transition and ab initiocalculation

The electronic excitation of the silicon tetrafluoride (SiF4) moleculehas been studied using the angle-resolved electron energy-loss technique,at 1.0 keV incident electron energy, in the 0-50 eV energy range with anangular range of 1.5°-20.0°. The absolute generalizedoscillator strength (GOS) for the 5t2→6a1 electronictransition, located at 13.0 eV, has been determined. A minimum has beenobserved in the GOS for this transition at K2 = 1.4 au. We have alsodetermined the absolute elastic and inelastic differential cross sectionsat 1 keV. In order to help in the interpretation of the experimentalresults, ab initio calculations have been performed for the verticalvalence transitions and ionization energies for the SiF4 molecule.Configuration-interaction calculations, including single and doubleexcitations (CI-SD) and the symmetry-adapted-cluster expansion (SAC)were used. The CI-SD approach was also employed to obtain the opticaloscillator strength for the 5t2→6a1 transition.

Valence and inner shell non-dipole excitation spectroscopy of polyatomic molecules by angle-resolved inelastic electron scattering at high energy

Abstract High energy (>2 keV) electron scattering has been used extensively in the past three decades as an effective method to simulate equivalent photon-impact experiments under dipole-dominated small-angle scattering conditions (the so-called pseudo-photon experiments). More recent studies have focused on its application as a unique spectroscopic tool that provides distinct information about those parts of the electronic structure that are not easily accessible by optical techniques. The capability to excite not just the dipole-allowed transitions but also the dipole-forbidden ones gives electron impact a special advantage for probing electronic excitations and for studying non-dipole phenomena. Indeed, the control of the scattering angle, or equivalently the momentum transfer, provides a powerful means to manipulate electron-induced chemical processes if the excited-state electronic structure can be better understood. This review will give a description of angle-resolved electron energy loss spectroscopy and highlight some of its spectroscopic applications that offer specific information about the electronic structure of the valence and inner shells in polyatomic molecules. Some of the novel aspects of this non-optical technique, including the determination of absolute generalized oscillator strength for non-dipole transitions, will be illustrated by examples drawn from recent studies on CF 3 Cl and other related chlorofluorocarbons and hydrochlorofluorocarbons.

Electron-impact excitation of low-lying preionization-edgen→σ* and Rydberg transitions of CHF2Cl and CHFCl2: Absolute generalized oscillator strength measurement

Angle-resolved electron energy loss spectroscopy has been used to determine the absolute generalized oscillator strengths (GOSs) of valence-shell electronic transitions of difluorochloromethane (CHF2Cl) and dichlorofluoromethane (CHFCl2) as functions of energy loss and momentum transfer at an impact energy of 2.5 keV. Absolute GOS profiles of the prominent low-lying preionization-edge energy loss features of CHF2Cl and CHFCl2 were determined and found to be consistent with the previous assignments of the underlying transitions made by VUV photoabsorption spectroscopy. In particular, the lowest-lying features at 8.0 eV in CHF2Cl and at 7.5 eV in CHFCl2 have been attributed predominantly to electronic excitations from the Cl 3p nonbonding (n) orbitals to the C–Cl σ* antibonding orbital, in good accord with single-excitation configuration interaction (CI) excited-state calculations. The corresponding GOS profiles of these n(Cl 3p)→σ*(C–Cl) (HOMO→LUMO) transitions revealed an interesting trend of increased dipole character with increasing Cl content, i.e., from an essentially quadrupole-dominated profile, characterized by a maximum at K2∼0.9 a.u., in CHF2Cl to a mixed dipole-quadrupole profile in CHFCl2 and CHCl3. The CI calculations further showed that some of the underlying n(Cl 3p)→σ*(C–Cl) transitions in CHF2Cl, CHFCl2, and CHCl3, like the other chlorofluorocarbons: CF3Cl, CF2Cl2, CFCl3, and CCl4, could lead to dissociation of the C–Cl bond. In addition, the GOS profiles of the remaining low-lying preionization-edge features at 9.8 and 11.2 eV in CHF2Cl and at 9.4, 10.7, and 11.6 eV in CHFCl2 were also determined. These features have been previously assigned as Rydberg transitions originated from the nonbonding HOMOs. In particular, these experimental GOS profiles were found to be dominated by a strong maximum at K=0, which is indicative of strong dipole interactions. The weak secondary maxima observed at K2∼2.8–3.5 a.u. could be interpreted qualitatively in terms of the spatial overlaps between the initial-state and final-state orbital wave functions. Together with our earlier work on CHF3 and CHCl3, the present work on the remaining members of the CHFmCl3−m (m=0–3) series, CHF2Cl and CHFCl2, provides further evidence for the empirical trends on the preionization-edge structures observed in the CFnCl4−n (n=0–4) series.

Accurate determination of H2, He, and D2 Compton profiles by high energy electron impact spectroscopy

The effective nonrelativistic Compton profiles J (q,K) of H2 and He {defined in terms of the absolute generalized oscillator strength (GOS), df (K,E)/dE, as J (q,K) = (2K3/E)[df (K,E)/dE], where q is (E−K2)/2K, with K the momentum transfer and E the energy loss} have been studied as a function of scattering angle by means of high energy electron impact spectroscopy (HEEIS) with an incident energy of 25 keV over an angular range of 3°–10°. It was found that the binary encounter limit is not reached until the x-ray incoherent scattering factor reaches its large K asymptotic limit N, the number of target electrons. At 10° , the results of the Compton profiles of He and H2 were fitted by least squares to a polynomial of the form Σmn=1{an/[1+(q/ζn)2]n+2}, which leads to analytic expressions for the one electron momentum density and its integer powered moments. The fits proved to be radically different for He and H2. The experimental values for the moments of the momentum density function were found to be in excellent agreement with the best available theoretical results. In addition, the Compton profile of D2 at 8° was measured and no significant deviations from the Compton profile for H2 were observed. The new results reported here for H2 clear up a disagreement between theory and experiment and suggest that quoted uncertainties in the previous studies were unrealistically small owing to improper analysis of systematic experimental errors.

Observation of a new electronic transition in N2 at 31.4 eV by means of high energy electron impact spectroscopy

A new transition in molecular nitrogen at an energy loss of 31.4±0.5 eV has been observed by high energy electron impact spectroscopy at momentum transfers larger than 2 a.u. The absolute generalized oscillator strength was measured over the momentum transfer range 0.5?K2?5.08 a.u. using 25 and 33 keV electrons. The observed angular behavior of this line suggests that it may be due to a dipole forbidden quadrupole allowed process. The term symbol 1Πg with the electronic configuration (2sσg)−1 (2pπg)1 is tentatively assigned to this transition and it is suggested that this state may decay into the D 2Πg state of N+2 by Auger cascade.

The absolute generalized oscillator strength for the Lyman–Birge–Hopfield band of N2 as determined by high energy electron impact spectroscopy

The absolute generalized oscillator strength for the dipole forbidden quadrupole allowed Lyman–Birge–Hopfield band [a 1Πg ← X 1Σ+g] in molecular nitrogen at an energy loss of 9.35 eV is observed by electron impact spectroscopy using 25 keV electrons over the momentum transfer range 0.04?K2?10 a.u. The results agree in the zero angle (zero momentum transfer) limit with the previous observations of Skerbele and Lassettre, but are in disagreement with previous theoretical and experimental results for K2≳0.5.

Absolute Generalized Oscillator Strength of 11S→21P Transition in Helium

Absolute Generalized Oscillator Strength of 11S→21P Transition in Helium