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The oscillator strengths and integral cross sections of the valence-shell excitations of HCl have significant applications in the studies of planetary atmospheres and interstellar gases. In the present work, the generalized oscillator strengths of the valence-shell excitations of HCl have been measured at an incident electron energy of 1500 eV and an energy resolution of 70 meV, and their momentum transfer dependence behaviors have been elucidated. It is observed that the generalized oscillator strength ratios of the b3Π1(ν' = 0) state to the C1Π(ν' = 0) state are a constant and independent of the squared momentum transfer, and this typical behavior in the momentum space is explained by the intraconfiguration mixing of the b3Π1 and C1Π states due to the spin-orbital interaction. The optical oscillator strengths of the valence-shell excitations have been 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 to the previous experimental and theoretical results, and it is found that most of the photoabsorption measurements are limited by the line saturation effect. The integral cross sections of the valence-shell excitations of HCl have been obtained systematically from the threshold to 5000 eV with the aid of the BE-scaling method.

The integral cross sections (ICSs) of the electron scattering of nitrogen molecule are of great importance to the understanding of many different aspects of atmospheric physics. In the present work, the generalized oscillator strengths (GOSs) of the valence-shell excitations of b1Πu, b′1Σu+, c31Πu, c4′1Σu+, and o31Πu of nitrogen have been determined by fast-electron scattering at an incident electron energy of 1500 eV and an energy resolution of 70 meV. By crosschecking strictly the present results with the previous electron scattering and inelastic x-ray scattering (IXS) ones, the accuracy and reliability of the GOSs for the corresponding dipole-allowed transitions of nitrogen are tested stringently. Based on the accurate GOSs of these dipole-allowed transitions, their ICSs are obtained systematically from the threshold to 5000 eV for the first time with the aid of the BE-scaling method, and the corresponding ICSs at the moderate and high energies are the only available data to the best of our knowledge.

Dissociative photoionization of 1,2-epoxyoctane was investigated by synchrotron radiation vacuum ultraviolet photons in the energy region of 9.8–16.6 eV under ultrasonic molecular beam. Dissociative fragment ions were measured with reflection time-of-flight mass spectrometer at different photon energies. Appearance potentials of the dominative ion fragments were determined through photoionization efficiency curves. The structures and energies of the parent, ionized and neutral radicals were obtained with G3 calculations. Through comparing the experimental results with the theoretical calculations, we proposed the dissociative channels for the photoionization of 1,2-epoxyoctane.

The generalized oscillator strengths of the valence-shell excitations from the ground state to 3p5(4s, 4s', 4p, 4p', 3d, 3d', 5p, 5p', 5s, 4d) of argon have been determined at an incident electron energy of 1500 eV and an energy resolution about 90 meV. The accuracy of the present generalized oscillator strengths is improved by the adopted relative flow technique. The comprehensive comparison of the present results with the previous experimental and theoretical ones shows that the first Born approximation is satisfied in the lower squared momentum transfer region for the electric dipole excitations, while the deviations from the prediction of the first Born approximation and the inelastic X-ray scattering measurements near the minimum and in the larger K2 region are obvious, which can be attributed to the failure of the first Born approximation in this K2 region. The invalidity of the first Born approximation has also been observed for the electric monopole transitions even at a high impact electron energy of 2500 eV.

For the inelastic electron scattering of atoms and molecules, a consensus has been reached that the first Born approximation is easily approached by decreasing the momentum transfer at the same impact electron energy or increasing the impact electron energy at the same momentum transfer. Although this consensus is applicable for the elastic electron scattering of most atoms and molecules, it is violated for helium where the experimental differential cross sections deviate from the first Born approximation prediction gradually with the decrease of squared momentum transfer at the same impact electron energy. Since this anomalous phenomenon was observed more than 40 years ago, the intrinsic mechanism is not explicit. In the present work, using the high-resolution x-ray scattering, we isolate the scattering contribution from the nucleus and directly obtain the pure electronic structure of helium. Then, the anomalous asymptotic behavior of the elastic electron scattering of helium has been elucidated, i.e., in the small squared momentum transfer region, the scattering contribution from the target's electrons is counteracted by the one from the atomic nucleus, which results in the residual contribution beyond the first Born approximation being drastically enlarged.

A joint experimental and theoretical investigation of the valence-shell excitations of hydrogen has been performed by the high-resolution inelastic x-ray scattering and electron scattering as well as the multireference single- and double-excitation configuration-interaction method. Momentum-transfer-dependent inelastic squared form factors for the vibronic series belonging to the $B{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+},\phantom{\rule{0.28em}{0ex}}C{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}$, and $EF{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}$ electronic states of molecular hydrogen have been derived from the inelastic x-ray scattering method at an impact photon energy around 10 keV, and the electron energy-loss spectra measured at an incident electron energy of 1500 eV. It is found that both the present and the previous calculations cannot satisfactorily reproduce the inelastic squared form-factor profiles for the higher vibronic transitions of the $B{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$ state of molecular hydrogen, which may be due to the electronic-vibrational coupling for the higher vibronic states. For the $C{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Pi}}}_{u}$ state and some vibronic excitations of $EF{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}$ state, the present experimental results are in good agreement with the present and previous calculations, while the slight differences between the inelastic x-ray scattering and electron energy-loss spectroscopy results in the larger squared momentum-transfer region may be attributed to the increasing role of the higher-order Born terms in the electron-scattering process.

We report a comparative study of low-lying valence electronic states of carbon dioxide by high-resolution inelastic x-ray and electron scattering. Momentum-transfer-dependent inelastic squared form factors for the two states ${}^{1}{\mathrm{\ensuremath{\Sigma}}}_{\mathrm{u}}^{+}$ and ${}^{1}{\mathrm{\ensuremath{\Pi}}}_{\mathrm{u}}$ and generalized oscillator strength for the 9 eV feature from the ground state ${X}^{1}{\mathrm{\ensuremath{\Sigma}}}_{\mathrm{g}}^{+}$ have been derived from the inelastic x-ray scattering method at an impact photon energy around 10 keV, and the electron energy-loss spectra measured at an incident electron energy of 1500 eV. It is found from the comparison between the present results and the previous outcomes that the recent calculations taking the vibronic effects into consideration satisfactorily reproduce the inelastic squared form-factor profile for the ${}^{1}{\mathrm{\ensuremath{\Sigma}}}_{\mathrm{u}}^{+}$ transition and the generalized oscillator strength profile for the 9 eV feature. However, the vibronic effects seem to play no role in the ${}^{1}{\mathrm{\ensuremath{\Pi}}}_{\mathrm{u}}$ transition. The difference existing between the inelastic x-ray scattering and electron energy-loss spectroscopy results in the larger momentum-transfer squared region may be attributed to the increasing role of the higher-order Born terms. Furthermore, the controversy concerning the designations of electronic states around 11 eV is solved by assigning the two peaks centered at 10.98 and 11.05 eV to the vibrational progression ${}^{1}{\mathrm{\ensuremath{\Sigma}}}_{\mathrm{u}}^{{+}^{\ensuremath{'}}}$ and ${}^{1}{\mathrm{\ensuremath{\Sigma}}}_{\mathrm{u}}^{+}$, and the peak centered at 11.16 eV to the forbidden transition ${2}^{1}{\mathrm{\ensuremath{\Delta}}}_{\mathrm{u}}$ based on the present results.

The dipole (γ,γ) method, which is the inelastic X-ray scattering operated at a negligibly small momentum transfer, has been developed to determine the absolute optical oscillator strengths of the valence-shell excitations of atoms and molecules. This new method is free from the line saturation effect, and its Bethe-Born conversion factor varies much more slowly with the excitation energy than that of the dipole (e, e) method. Thus the dipole (γ,γ) method provides a reliable approach to obtain the benchmark optical oscillator strengths of the valence-shell excitations for gaseous atoms and molecules. In this paper, we give a review of the dipole (γ,γ) method and some recent measurements of absolute optical oscillator strengths of gaseous atoms and molecules.

The generalized oscillator strengths of the low-lying valence-shell excitations of N2, O2, and C2H2 have been studied by the high-energy electron scattering, the high-resolution inelastic X-ray scattering, and the multireference single- and double-excitation configuration-interaction methods. Good agreement between the present electron-scattering results and the X-ray-scattering ones for the a′′1Σg+v′=0 and a′′1Σg+v′=1+b1Πuv′=0 excitations of N2 and the A′3Δu excitation of O2 is achieved in the small squared momentum transfer region, while obvious discrepancies among them are observed in the large squared momentum transfer region. This phenomenon indicates that the first Born approximation is satisfied in the small squared momentum transfer region, while it does not hold in the large squared momentum transfer region at an incident electron energy of 1500 eV, in view of the fact that the first Born approximation is satisfied in the X-ray scattering. In addition, the present calculation for the a′′1Σg+ excitation shows that the traditional assigned v′ = 0 and 1 of the a″1Σg+ excitation correspond to v′ = 9 and 13 of the 21Σg+ excitation and reproduces the X-ray-scattering results of the a′′1Σg+v′=0 excitation very well except the ones in the small squared momentum transfer region. We also report the generalized oscillator strengths of the A + B excitations of C2H2, and its profile shows that the bending geometry has great influence on the transition feature.The generalized oscillator strengths of the low-lying valence-shell excitations of N2, O2, and C2H2 have been studied by the high-energy electron scattering, the high-resolution inelastic X-ray scattering, and the multireference single- and double-excitation configuration-interaction methods. Good agreement between the present electron-scattering results and the X-ray-scattering ones for the a′′1Σg+v′=0 and a′′1Σg+v′=1+b1Πuv′=0 excitations of N2 and the A′3Δu excitation of O2 is achieved in the small squared momentum transfer region, while obvious discrepancies among them are observed in the large squared momentum transfer region. This phenomenon indicates that the first Born approximation is satisfied in the small squared momentum transfer region, while it does not hold in the large squared momentum transfer region at an incident electron energy of 1500 eV, in view of the fact that the first Born approximation is satisfied in the X-ray scattering. In addition, the present calculation for the a′′1Σg+ exci...

The vibrationally resolved generalized oscillator strengths of the first and strongest singlet excitation AA2″1← X1A1 of ammonia have been determined at an impact electron energy of 1500 eV with an energy resolution of 80 meV. The comprehensive comparison of the present results with the previous experimental and theoretical ones shows that the high-energy limit, where the first Born approximation holds, has been reached at an impact electron energy of 1500 eV in K2 1 a.u. even at 1500 eV. It is also observed that the minimum position of the generalized oscillator strength of the vibronic state shifts toward the larger squared momentum transfer with the increasing vibrational quantum number. By extrapolating the generalized oscillator strength to the zero momentum transfer, the optical oscillator strength of the AA2″1 state has been obtained, which gives an independent cross check to the previous results. The integral cross sections of the AA2″1 state have been obtained systematically from the threshold to 5000 eV with the aid of the BE-scaling method.

The dipole (γ, γ) method, which is the inelastic x-ray scattering operated at a negligibly small momentum transfer, is proposed and realized to determine the absolute optical oscillator strengths of the vanlence-shell excitations of atoms and molecules. Compared with the conventionally used photoabsorption method, this new method is free from the line saturation effect, which can seriously limit the accuracies of the measured photoabsorption cross sections for discrete transitions with narrow natural linewidths. Furthermore, the Bethe-Born conversion factor of the dipole (γ, γ) method varies much more slowly with the excitation energy than does that of the dipole (e, e) method. Absolute optical oscillator strengths for the excitations of 1s2 → 1 snp(n = 3 − 7) of atomic helium have been determined using the high-resolution dipole (γ, γ) method and the excellent agreement of the present measurements with both those measured by the dipole (e, e) method and the previous theoretical calculations indicates that the dipole (γ, γ) method is a powerful tool to measure the absolute optical oscillator strengths of the valence-shell excitations of atoms and molecules.

The generalized oscillator strengths for the valence-shell excitations of A2Σ+, C2Π, and D2Σ+ electronic-states of nitric oxide have been determined at an incident electron energy of 1500 eV with an energy resolution of 70 meV. The optical oscillator strengths for these transitions have been obtained by extrapolating the generalized oscillator strengths to the limit that the squared momentum transfer approaches to zero, which give an independent cross-check to the previous experimental and theoretical results. The integral cross sections for the valence-shell excitations of nitric oxide have been determined systematically from the threshold to 2500 eV with the aid of the newly developed BE-scaling method for the first time. The present optical oscillator strengths and integral cross sections of the valence-shell excitations of nitric oxide play an important role in understanding many physics and chemistry of the Earth’s upper atmosphere such as the radiative cooling, ozone destruction, day glow, aurora, a...

Using the inelastic x-ray scattering with a high resolution of 70 meV, squared form factors of molecular carbon monoxide have been determined from the ground state X-1 Sigma(+) to the vibronic states of A(1)Pi and B-1 Sigma(+). Since the first Born approximation is satisfied in inelastic x-ray scattering, the inelastic squared form factors of the valence-shell excitations of carbon monoxide measured by this work not only provide the experimental benchmark data but also serve as the high-energy limit for the electron impact method. Based on the present experimental results, the validity conditions of the previous electron impact works are discussed. It is found that for the excitations of A(1)Pi(v' = 0-6) the first Born approximation is reached in the region of q(2) < 0.7 a.u. at an impact electron energy of 1.5 keV, while for B-1 Sigma(+)(v' = 0) the first Born approximation does not fully hold at the impact electron energy of 1.5 keV except for the q(2) < 0.15 a.u. The large discrepancies between the present inelastic x-ray scattering results and the theoretical calculations for most transitions suggest that the formerly reported calculations are not accurate enough.

The Compton profiles of methane and ethane molecules have been determined at an incident photon energy of 20 keV based on the third generation synchrotron radiation, and the statistical accuracy of 0.2% is achieved near pz = 0. The density functional theory with aug-cc-pVTZ basis set was used to calculate the Compton profiles of methane and ethane. The present experimental Compton profiles are in better agreement with the theoretical calculations in the whole pz region than the previous experimental results, which indicates that the present experimental Compton profiles are accurate enough to serve as the benchmark data for methane and ethane molecules.

The integral cross sections (ICSs) of the electron scattering of nitrogen molecule are of great importance to the understanding of many different aspects of atmospheric physics. Based on the generalized oscillator strengths (GOSs) of these dipole-allowed transitions crosschecked by the high-energy electron scattering and high-resolution X-ray scattering, their ICSs are obtained systematically from the threshold to 5000 eV for the first time with the aid of the BE-scaling method, and the corresponding ICSs at the moderate and high energies are the only available data to the best of our knowledge.

Vibronically resolved squared form factors of ${a}^{\ensuremath{'}\ensuremath{'}}{\phantom{\rule{0.16em}{0ex}}}^{1}{{\ensuremath{\Sigma}}_{g}}^{+}$, $b{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Pi}}_{u}$, ${b}^{\ensuremath{'}}{\phantom{\rule{0.16em}{0ex}}}^{1}{{\ensuremath{\Sigma}}_{u}}^{+}$, ${c}_{3}{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Pi}}_{u}$, ${c}_{4}^{\ensuremath{'}}{\phantom{\rule{0.16em}{0ex}}}^{1}{{\ensuremath{\Sigma}}_{u}}^{+}$, and ${o}_{3}{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Pi}}_{u}$ of molecular nitrogen are determined by inelastic x-ray scattering with a high resolution of 70 meV. Through a comparison with the previous results measured by electron energy loss spectroscopy, it is found that the first Born approximation is satisfied at an incident electron energy of 300 eV in the small momentum transfer region for a dipole-allowed transition of $b{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Pi}}_{u}$, but the first Born approximation is not reached at an impact energy of 500 eV for the dipole-forbidden transition of ${a}^{\ensuremath{'}\ensuremath{'}}{\phantom{\rule{0.16em}{0ex}}}^{1}{{\ensuremath{\Sigma}}_{g}}^{+}$. It is also observed from the present experimental results that the momentum transfer dependence behavior of the excitations to $b{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Pi}}_{u}({\ensuremath{\nu}}^{\ensuremath{'}}=3,4)$ is different from that of the excitations to $b{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Pi}}_{u}({\ensuremath{\nu}}^{\ensuremath{'}}=1,2)$, which can be attributed to the perturbation of ${c}_{3}{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Pi}}_{u}$ to $b{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Pi}}_{u}$. The present results provide experimental benchmark data of inelastic squared form factors of molecular nitrogen.

The high-resolution x-ray-scattering technique is used to study the elastic scattering of atoms and molecules in the gas phase. The elastic squared form factor, which is the square of the Fourier transformation of the electron density distribution in position space and reveals the pure electronic structure of atoms and molecules in the ground state, of molecular hydrogen is measured at an incident photon energy of about 9889 eV and an energy resolution of about 70 meV. Although it is generally thought that the x-ray-scattering technique is identical to high-energy electron scattering, at least for elastic scattering these two techniques have an apparent difference, i.e., the pure electronic structure of a molecule in the ground state can be determined by x-ray scattering while it cannot be obtained by the high-energy electron impact method due to the interference between the scattering of separate nuclei and of the electrons in the target. The present experimental results match the theoretical calculations very well, which demonstrates that high-resolution x-ray scattering is a powerful tool to study the electronic structure of atoms and molecules in the ground state.

The oscillator strengths of the valence-shell excitations of molecular nitrogen have significant applicational values in studies of the Earth's atmosphere and interstellar gases. In this work, the absolute oscillator strengths of the valence-shell excitations of molecular nitrogen in 12.3?13.4 eV were measured by the novel dipole (?, ?) method, in which the high-resolution inelastic X-ray scattering is operated at a negligibly small momentum transfer and can simulate the photoabsorption process. Because the experimental technique used in the present work is distinctly different from those used previously, the present experimental results give an independent cross-check to previous experimental and theoretical data. The excellent coincidence of the present results with the dipole (e, e) and those that were extrapolated indicates that the present oscillator strengths can serve as benchmark data.

The optical oscillator strengths of the 3p54s and excitations of argon are of crucial importance in determining the elemental abundance of argon from astronomical observations. Substantial efforts have been made to determine the optical oscillator strengths of the 3p54s and transitions of argon, however, significant discrepancies among the reported values still exist. In this work, the absolute optical oscillator strengths of the 3p54s and transitions of argon have been measured by a newly developed high-resolution dipole (γ, γ) method. A comprehensive comparison with the previous experimental and theoretical data was then made as a cross-check.

The dipole(γ, γ) method based on the inelastic x-ray scattering (IXS) technique is proposed and realized to measure the absolute optical oscillator strength (OOSs) for the valence-shell excitations of atoms and molecules. The OOSs of valence- shell excitations of helium are determined, and the good agreement with the previous results is observed.

Using the high-resolution fast-electron energy loss spectrometer, the generalized oscillator strengths (GOSs) of the valence-shell excitations of xenon were determined at a high resolution of 70 meV and a high incident electron energy of 1500 eV, and the momentum transfer dependence behaviors of GOSs of the 6s[3/2]1 and 6s'[1/2]1 excitations of xenon are discussed.

The Compton profile of molecular hydrogen has been determined at an incident photon energy of 20 keV based on the third generation synchrotron radiation, and the statistical accuracy of 0.2% is achieved at pz = 0. Different theoretical methods, i.e., the density functional method, and the Hartree?Fock method, were used to calculate the Compton profiles of hydrogen with different basis sets, and the theoretical calculations are in agreement with the experimental observation in the whole pz region. Compared with the HF calculation, the DFT-B3LYP ones are in better agreement with the present experiment, which indicates the electron correlation effect is very important to describe the wavefunction in the ground state of hydrogen.

The ionization and ionic dissociation of the superexcited state of N2O are studied by using electron energy loss spectroscopy and positive ion time-of-flight mass spectroscopy at different momentum transfers; that is, 0 and 0.23 a.u. (atomic unit). The transitions at 13.8 eV and 14.0 eV are reassigned as 3pπ(000) and 3pσ(000) converging to A2Σ+, respectively. The competition between the main decay pathways of superexcited states at different momentum transfers is revealed. It is found that 3dσ converging to C2Σ+ mainly decays into N2O+ while 4dσ can decay into both N2O+ and NO+.

The decay pathways of the structured ionization region of oxygen at different momentum transfers, i.e., 0, 0.23 a.u. (atomic unit), and 0.91 a.u., are studied by measuring the ion and the scattered electron coincidently. It is found that the dipole-forbidden superexcited states of (2σu)−1(c4Σ−u)npσu 3Σ−g ← X3Σ−g decay into different channels according to the principal quantum number n. The broad ridge above 35 eV, which may be due to inner-valence excited states of (2σg)−1nλ or multiply excited states, is observed both at small and large momentum transfers, and its decay channel of O++O is dominant.

The valence-shell excitations of nitrous oxide are studied by fast electron energy loss spectroscopy. From the spectra measured at 2.5 keV and scattering angles of 3.5°–8.5°, it is found that the asymmetric peak of the transition B1Δ can be well fitted by Haarhoff-Van der Linde function, while the symmetric peaks of the transitions of C1Π and D1Σ+ can be well fitted by the Voigt function. The parameters of the peak profiles of B1Δ, C1Π and D1Σ+, i.e., their energy level positions and linewidths, are determined. With the aid of these parameters, the overlapping spectra measured at the low-energy electron impact can be deconvolved, which provides the possibility to determine the quantitative differential cross sections. The present results also show that the peak profiles of the transitions of B1Δ, C1Π and D1Σ+, are independent of the momentum transfer.