Effects of multi orbital contributions in the angular-dependent ionization of molecules in intense few-cycle laser pulses

We outline the details of our new method to calculate angular-dependent ionization probabilities based on electronic structure theory for diatomic and larger systems. To demonstrate its abilities, we compare our calculations to measured ionization probabilities of the four molecules D₂, N₂, O₂ and CO in the strong-field regime. The calculated angular distributions yield better agreement with the experimental data than those obtained from the widely used MO-ADK theory. For CO the measured angular distributions of ionic fragments indicate contributions to the ionization from both the HOMO and the HOMO-1 orbital, an effect that is addressed by the theory.     

Relative intensities in photoelectron spectroscopy of atoms and molecules

The relative intensities of photoelectron lines is discussed. The relationship of observed intensities to angle of observation is considered as are the errors introduced by ignoring the fact that different lines may have different angular distributions. Tables of theoretical results for the angular distribution asymmetry parameter, β, are presented for incident Al K_α, Mg K_α, and Zr M_ζ radiation for all atomic ground state subshells of non-zero angular momentum. The application of these results to molecules is discussed.     

Relative intensities in X-ray photoelectron spectra: Part VII. The effect of elastic scattering in a solid on the angular distribution of photoelectrons escaping from samples covered with thin films of various thicknesses

The angular distributions of X-ray photoelectron peak intensity for (1) a semi-infinite sample, (2) a substrate sample covered with a film, and (3) an overlayer sample are calculated by the Monte-Carlo method. The elastic as well as the inelastic scattering of electrons in a solid is taken into account. In all cases the elastic scattering is shown to have a significant effect on both the absolute value of peak intensity and the angular distribution of photoelectrons. The electron mean free paths without inelastic collisions (λ_n) calculated using formulas derived without taking account of elastic scattering are shown to differ significantly from the real values. Moreover, the λ_n values calculated in this way are not physical constants at all, but depend for example on the film thickness and the intervals of photoelectron take-off angles under consideration. The elastic scattering effect is shown capable of explaining some difficulties which arise in the interpretation of experimental data reported in the literature on the basis of expressions derived taking into account only the inelastic interactions of photoelectrons with a solid.     

Temperature dependence of azimuthal X-ray Photoelectron Diffraction (XPD) from Cu2p32 core level of Cu(001): Experiment and single scattering cluster calculations

The temperature dependence of X-ray photoelectron diffraction (XPD) affects in azimuthal distributions of $\text{Cu}\text{2p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ core level intensities from a clean copper (001) single crystal has been measured in the range from ambient to 1010 K and for polar angles of emission relative to the surface of θ = 7° (corresponding to very high surface sensitivity) and θ = 45°. The XPD anisotropy ΔI/I_max at θ = 7° shows a decrease of 42.5% between ambient temperature and 1010 K while that for θ = 45° shows a 22.7% decrease over the same temperature range. Single scattering cluster calculations including Debye-Waller factors very well predict the variation of anisotropy with temperature at θ = 7°, while at θ = 45° theory significantly underestimates the decrease in ΔI/I_max, probably due to multiple scattering effects. The effective surface Debye temperature of 202 K deduced from theory and experiment for θ = 7° agrees well with prior determinations. The 7° XPD data give no evidence for surface melting effects on Cu(001) at temperatures up to T/T_melting = 0.74.     

Vibrationally resolved K-shell photoionization cross sections of methane

We use an extension of the static-exchange density functional theory (DFT) method, previously reported in [E. Plésiat et al., Phys. Rev. A 2, 023409 (2012), E. Plésiat, P. Decleva, F. Martín, Phys. Chem. Chem. Phys. 31, 10853 (2012)], to evaluate vibrationally resolved (total and angular) K-shell photoelectron cross sections of methane. The calculated cross sections are in very good agreement with the existing experimental measurements at low photoelectron energies. We show that, in contrast with the rich interference patterns previously observed in molecular frame C(1s) photoelectron angular distributions of methane at both low and high photoelectron energy, no interference effects are observed in the calculated β parameters, even at high photon energies.     

Characterization of 1T-TiSe2 surface by means of STM and XPD experiments and model calculations

Scanning tunneling microscopy (STM) and X-ray photoelectron diffraction (XPD) are applied to study the surface of layered dichalcogenide 1T-TiSe₂. XPD pattern simulation for the 1T-TiSe₂ surface is performed in the approach of electron multiple scattering within the EDAC code: considered are models of structural defects in the 1T-TiSe₂ lattice, relaxation contraction (expansion) of surface layers and van der Waals gap, and deviation of the 1T-TiSe₂ surface geometry from the basal plane (001). The atomic structure of 1T-TiSe₂ surface layers is reconstructed from the XPD pattern on Se(LMM) and Ti2p core level using the photoelectron holography scattering pattern extraction algorithm with maximum entropy method (SPEA-MEM). The results of the 3D reconstruction are in agreement with the XPD pattern simulation data. In both cases, the TiSe₂ surface corresponds to 1T polytype; an increase is observed in the parameter a₀ and in the van der Waals gap between two surface slabs. It is assumed that similar structural distortions of the 1T-TiSe₂ lattice lead to the formation of an energy gap between the valence band and the conduction band of titanium diselenide, which was observed earlier by photoemission spectroscopy and follows from the theoretical calculations.     

Stoßdissoziation von H 2 + -Ionen

Inelastic collisions between the hydrogen molecule ion and the hydrogen molecule leading to dissociation are investigated experimentally in the energy range between 3 and 20 keV. The velocity distributions of the protons produced in these processes are compared with calculated distributions using a Born approximation formula. The calculation takes into account the excitation of the 2pσ _u state of the H ₂ ⁺ and a possible simultaneous excitation of the target. It can be shown, that the quantitative knowledge of these processes makes possible a satisfying explanation of the measured distributions. In general a good agreement is obtained between theory and experiment concerning both energy and angular dependence of the velocity distributions.     

The total reaction cross section for α-induced deuteron break-up in the energy range 20–28 MeV

Alpha-particle spectra resulting from the bombardment of douterons with α-particles have been measured at energies of 20.4, 24.2 and 28.1 MeV for all kinematically possible scattering angles θ_1ab > 5°. Angular distributions for the break-up cross section have been obtained by integration over the α-particle energy. The total reaction cross section is computed by extrapolating the angular distributions to 0°. The results are compared with predictions calculated from α-d phase shifts and Faddeev theory.     

Three-jet distributions ine + e − annihilation: Electromagnetic and weak production

Hard gluon bremsstrahlung off quarks ine ⁺ e ^? annihilation is expected to produce three-jet events. The angular distributions of the jets are calculated for electromagnetic and weak production in the high energy region (Z resonance decay included). Numerical estimates are presented for the vectoraxialvector interference terms within the Weinberg-Salam theory. We discuss (i) angular correlations between jets, (ii) semiinclusive pion distributions and (iii) we comment on angular asymmetries of leptons originating from heavy quark decays.     

Investigation of the reaction 208Pb(18O, f): Fragment spins and phenomenological analysis of the angular anisotropy of fission fragments

The average multiplicity of gamma rays emitted by fragments originating from the fission of ²²⁶Th nuclei formed via a complete fusion of ¹⁸O and ²⁰⁸Pb nuclei at laboratory energies of ¹⁸O projectile ions in the range E _lab = 78–198.5 MeV is measured and analyzed. The total spins of fission fragments are found and used in an empirical analysis of the energy dependence of the anisotropy of these fragments under the assumption that their angular distributions are formed in the vicinity of the scission point. The average temperature of compound nuclei at the scission point and their average angular momenta in the entrance channel are found for this analysis. Also, the moments of inertia are calculated for this purpose for the chain of fissile thorium nuclei at the scission point. All of these parameters are determined at the scission point by means of three-dimensional dynamical calculations based on Langevin equations. A strong alignment of fragment spins is assumed in analyzing the anisotropy in question. In that case, the energy dependence of the anisotropy of fission fragments is faithfully reproduced at energies in excess of the Coulomb barrier (E _c.m. ? E _B ≥ 30 MeV). It is assumed that, as the excitation energy and the angular momentum of a fissile nucleus are increased, the region where the angular distributions of fragments are formed is gradually shifted from the region of nuclear deformations in the vicinity of the saddle point to the region of nuclear deformations in the vicinity of the scission point, the total angular momentum of the nucleus undergoing fission being split into the orbital component, which is responsible for the anisotropy of fragments, and the spin component. This conclusion can be qualitatively explained on the basis of linear-response theory.     

Investigation of giant E3 resonances by (N, γ) reactions

Effects related to the presence of giant E3 resonances are investigated by nucleon radiative capture according to the direct-semidirect model. The γ-ray angular distributions from the ²⁰⁸Pb(N, γ₀) reactions are calculated in the energy region above the giant dipole resonance and the influence of the E1–E3 and E2–E3 interferences is discussed. The results provide indications of an appreciable effect on the 90° photon emission when a collective isovector E3 excitation is present.     

Quasielastic transfer reactions in 238U + 197Au and 197Au + 197Au collisions near the Coulomb barrier

Differential cross sections as a function of cm angle were measured for 1n- and 2n-transfer reactions in ²³⁸U + ¹⁹⁷ Au and¹⁹⁷ Au + ¹⁹⁷ Au collisions in the energy range from 0.881 V_c to 1.093 V_c and 0.825 V_c to 0.964 V_c, respectively. For ¹⁹⁸Au and ¹⁹⁹Au from the ²³⁸U + ¹⁹⁷Au collisions, for reduced distances of closest approach d _o 1.55 fm, the angular distributions at all bombarding energies are well described by the semiclassical theory. Equivalently, the transfer probabilities show the expected exponential decrease with increasing d _o over many orders of magnitude. For all other transfer products from ²³⁸U + ¹⁹⁷Au collisions, and for all transfer products from ¹⁹⁷Au + ¹⁹⁷Au collisions, markedly reduced cross sections relative to the semiclassical theory are observed for central collisions at all bombarding energies, even for values of d _o that are well outside the region where absorption is known to set in. Only for the more peripheral collisions, one observes agreement of the angular distributions (transfer probabilities) with the semiclassical expectations. The deviations for central collisions are absent for reactions with positive Q _gg values and scale roughly with increasingly negative values of Q _gg, i.e. with increasing Q-value mismatch. Channel coupling is proposed as the relevant mechanism.     

Angular distributions in quasi-fission reactions

Angular distributions for fission-like fragments were measured in the systems ⁵⁰Ti, ⁵⁶Fe + ²⁰⁸Pb by applying an off-line K X-ray activation technique. The distributions d²σ/dθdZ exhibit forward-backward asymmetries that are strongly Z-dependent. They result from a process (quasi-fission) which yields nearly symmetric masses in times comparable to the rotational period of the composite system. A method for obtaining the variance of the tilting angular momentum, K₀², from these skewed, differential angular distributions is described. The results indicate that the tilting mode is not fully excited in quasi-fission reactions. The results are compared to the sum of the variances of all statistical spin components, measured via γ-multiplicities. Integration of the angular distributions d²σ/dθdZ over all values of Z yields the integral angular distributions dσ/dθ and dσ/dΩ symmetric around 90°. The associated unusually large anisotropies do not at all provide an adequate basis for tests or modifications of the transition-state theory. A deconvolution of d²σ/dθdZ is performed with gaussian distributions depending on rotational angles Δθ extending over a range of up to 540°. From the mean values 〈Δθ〉 a time scale for the evolution of K₀ is calculated.     

High spin selectivity in α-particle induced reactions

Distinct maxima have been observed in the spectra of protons emitted from the ²⁴Mg(α, p)²⁷Al reaction in the region of the excitation energies of ²⁷Al between 5 and 15 MeV, where continuous spectra are expected according to the statistical model. To investigate the reaction mechanism responsible for the selective excitation of several states of ²⁷Al, angular distributions of protons in the angular range from 20° to 170° in the lab system were measured at the α-particles energies E_lab = 25.4 25.8 and 26.2 MeV. Thirteen out of thirty levels observed in proton spectra, exhibit symmetry of their angular distributions around 90° the c.m. system, when averaged over energy. The contribution of preequilibrium emission was calculated and found to be negligible. A Hauser-Feshbach analysis was carried out to determine spins of states of ²⁷Al whose angular distributions were symmetric around 90° in the c.m. system. Results of this analysis indicated high spin selectivity in the ²⁴Mg(α, p)²⁷Al reaction.     

O(1D)和CD4反应的准经典轨线

在新的全域势能面上, 用准经典轨线方法细致地研究了O(¹D)+CD₄多通道化学反应的动力学．这个势能面是用交换不变多项式方法基于MRC+Q/aug-cc-pVTZ从头算点拟合得到的．通过计算得到了产物OD+CD₃、D+CD₂OD/CD₃O和D₂+DCOD/D₂CO的分支比、平动能分布以及角度分布,结果显示理论与实验吻合得较好, 从而说明了这个反应的同位素取代效应很小． 研究表明,O(¹D)+CD₄反应是经过陷入的抽取机理发生的： 最初主要通过D原子的抽取,并不是之前人们认为的直接C-D键的插入形成CD3OD中间物后再进而解离成各个产物通道．     

Beiträge von direkten und Compoundprozessen zur Reaktion40Ca(d, α)38K beiE d =5–10 MeV

For the reaction⁴⁰Ca(d,α)³⁸K differential cross sections for the excitation of the low lying states in³⁸K have been measured at bombarding energies between 5 and 10 MeV. Total cross sections have been calculated using the statistical theory. It was found, that in the whole energy region the isotropic background of the angular distributions gives a good estimation of the compound contribution to the reaction cross section.     

Excited-state photoelectron spectra of the one-photon forbidden C3IIg rydberg state of molecular oxygen

The Rydberg C³II_g, state of molecular oxygen, which is one-photon forbidden from the ground electronic state, has been studied by means of (2 + 1) multiphoton ionization (MPI) ion-current and photoelectron spectroscopic techniques in the laser wavelength region 287–289 nm. Excitedstate photoelectron spectra have been observed at different rotational levels of the C³Π_gv' = 2 state of O₂, and show marked deviation from the Franck-Condon distribution generally expected in ionization of Rydberg electrons. Namely, in addition to main photoelectron peaks due to Δv = 0 transitions, other vibrational peaks are also observed with considerable intensities. The v⁺= 2 photoelectron peak shows different angular dependence from the other vibrational peaks. The rotational structure in the MPI ion-current spectrum of O₂ is well interpreted in terms of the rotational constants of the X²Π_g ground electronic state of O₂⁺.     

Optical potential for 12C + 28Si scattering

¹²C + ²⁸Si elastic scattering angular distributions are smooth functions, relatively easily fit by optical potential predictions, at laboratory bombarding energies, E_1ab, within ≈ 10 MeV of the Coulomb barrier (i.e. up to E_1ab ≈ 27 MeV). Between E_1ab = 27 and 36 MeV the angular distributions show pronounced oscillatory structure which is not easily fit with an optical potential. No optical potential has been found to give a very good account of all the angular distributions simultaneously; the best simultaneous fit to all the data was achieved with a surface-transparent potential whose real and imaginary well depths are energy dependent.