Improved analytical formulae for correcting elastic-scattering effects in X-ray photoelectron spectroscopy

We present new predictive formulae for the correction parameters Q_x and β_eff that are used to account for the effects of elastic scattering in quantitative X-ray photoelectron spectroscopy. These formulae were derived from an analysis of published calculations of Q_x and β_eff from extensive Monte Carlo simulations for a group of elemental solids. Two formulae are given for each parameter. One formula is a function of the single-scattering albedo and the photoelectron emission angle, and is useful for emission angles between 0° and 80°. The other formula is a function only of the single-scattering albedo and is useful for emission angles between 0° and 50°. The single-scattering albedo is in turn a simple function of two material parameters, the inelastic mean free path and the transport mean free path. The latter parameters can be determined readily from available predictive formulae for any material or from databases. The root-mean-square and mean deviations of the Monte Carlo values of Q_x and β_eff from those found with the new formulae are comparable to or smaller than those found with formulae published by Seah and Gilmore.     

Elastic photoelectron-scattering effects in quantitative X-ray photoelectron spectroscopy

We present improved formulae for the correction parameters Q_x and β_eff that are used to account for elastic scattering of photoelectrons in quantitative X-ray photoelectron spectroscopy (XPS). The new formulae are based on new Monte Carlo simulations for 584 photoelectrons in 39 elemental solids that could be excited by Mg Kα and Al Kα X-rays in 315 different XPS configurations. The new simulations differed from similar earlier calculations in that differential elastic-scattering cross sections calculated from the Dirac–Hartree–Fock potential were utilized rather than those from the Thomas–Fermi–Dirac potential, a smaller analyzer acceptance angle was chosen, and the number of trajectories in each simulation was an order of magnitude larger. New values of Q_x and β_eff were obtained for each photoelectron line, each X-ray source, and each XPS configuration. These Q_x and β_eff values could be fitted to simple two-parameter expressions, each a function of the single-scattering albedo and the photoelectron emission angle. Values of Q_x from the new predictive formula differed from the previous expression by less than 1%. Larger deviations in the values of β_eff, up to 2.5%, were found from the new fit to the β_eff parameter. The new expressions for Q_x and β_eff provide a convenient means for correction of elastic-scattering effects in XPS.     

Electron IMFPs in bulk Cd0.88Mn0.12Te crystals determined by EPES

The inelastic mean free path (IMFP) of electrons is a basic parameter for surface-sensitive electron spectroscopies (AES, XPS, EELS) in quantitative analyses.Cd_1−xMn_xTe mixed crystals are currently of great interest due to their magnetic and magneto-optical properties. Since information on electron transport processes in these semimagnetic compounds is scarce, their systematic studies are highly desirable.In the present work, the IMFPs in Cd_0.88Mn_0.12Te (1 1 0) crystal samples were obtained from EPES with use of the Ni standard in the electron energy range 500-2000 eV. In addition, we also explored the effect of bulk Mn content in the determination of the IMFP. Relative EPES measurements were carried out using the MICROLAB 350 spectrometer. The sample surface was sputter cleaned and amorphized by Ar⁺ ions. Surface composition of the samples was monitored in situ by XPS and AES. The measured IMFPs were uncorrected for surface excitations and compared with those predicted from the TPP-2M and G-1 formulae. Also, the values of the IMFPs determined here were compared with those evaluated from the expression of Sekine et al. However, accuracy of this expression is rather poor except the case of pure CdTe (x = 0). In general, good agreement was found between the measured IMFPs in Cd_0.88Mn_0.12Te and the corresponding predicted IMFPs. The root-mean-square deviation from IMFP values predicted from the TPP-2M formula was 1.2 Å. The mean percentage deviation from the TPP-2M IMFPs was 9.3%.     

Theory for strong-coupling superconductivity in transition-metal alloys

Strong-coupling superconductivity in transition-metal alloys of the type A_xB_1?x is treated by applying the coherent-potential approximation to the Eliashberg theory of superconductivity. Expressions are given for the average electron-phonon coupling constant λ_eff, the average Coulomb-pseudopotential μ¹_eff, the superconducting transition temperature T_c, and the order parameter.     

Electric quadrupole moments and strong interaction effects in pionic atoms of 165Ho, 175Lu, 176Lu, 179Hf and 181Ta

The effective quadrupole moments Q_eff of the nuclei of ¹⁶⁵Ho, ¹⁷⁵Lu, ¹⁷⁶Lu, ¹⁷⁹Hf and ¹⁸¹Ta were accurately measured by detecting the pionic atom 5g-4f X-rays of the elements. The spectroscopic quadropole moments, Q_spec, were obtained by correcting Q_eff for nuclear finite size effect, distortion of the pion wave function by the pion-nucleus strong interaction, and contribution to the energy level splittings by the strong interaction. The intrinsic quadrupole moments, Q₀, were obtained by projecting Q_spec into the frame of reference fixed on the nucleus. The shift, ε₀, and broadening, Γ₀, of the 4f energy level due to the strong interaction between the pion and the nucleons for all the elements were also measured. Theoretical values of ε₀ and Γ₀ were calculated and compared to the experimental values. The measured values of Q₀ were compared with existing results in muonic and pionic atoms. The measured values of ε₀ and Γ₀ were also compared with existing values.     

Relative intensities in X-ray photoelectron spectra. Part IX. Estimates for photoelectron mean free paths taking into account elastic collisions in a solid

By means of the Monte Carlo method the angular dependences of photoelectron peak intensities have been calculated for substrates covered with films of various thicknesses D. The calculations have been carried out for several sets of parameters of the elastic and inelastic interactions of electrons with solids and for various experimental geometries. On the basis of numerical theoretical results, analytical expressions are derived for estimating the difference between the effective mean free path of photoelectrons (λ_eff) and the inelastic mean free path (λ_n) in solids. These expressions are used to analyse experimental data for the determination of thin-film thicknesses by means of ESCA. It is concluded that the values determined experimentally are apparently D/λ_eff ratios — not D/λ_n, as is usually assumed. The importance of the results obtained is discussed with reference to the determination of photoelectron mean free paths in solids and of thin-film thicknesses by means of ESCA.     

Nonisotropic L-conversion-electron — X-ray directional correlations in160Dy

The directional correlations betweenL-conversion electrons andL x-rays have been measured. The electrons were emitted in the 86.78keV 2⁺→0⁺ transition in¹⁶⁰Dy, in the decay of¹⁶⁰Tb. The experimental results areA ₂₂(e _L -x _Li )=0.085 (22),A ₂₂(e _L -x _Lα )=0.0066 (29),A ₂₂(e _L -x _Lβ )=0.0000 (27), andA ₂₂(e _L -x _Lγ )=0.0096 78). These results are in disagreement with published theoretical values. It is suggested that the discrepancy is due to a phase inconsistency in the internal conversion matrix elements and there is good agreement withA ₂₂ values calculated in this work.     

Anomalous cross section for photon-photon scattering in gauge theories

We consider the deep inelastic structure functions of the photon in an asymptotically free gauge theory. In contrast to the case of a hadronic target, we find that the shortdistance analysis determines the shape and magnitude and not merely the Q² dependence of the structure functions. The structure functions of the free quark theory are renormalized by finite, calculable factors. For example, at x = 0.1, we find that F₂ will, at large Q², exceed the free quark result by a factor 1.751, while for x = 0.5, F₂ is suppressed asymptotically, relative to the free quark theory, by a factor 0.964, and at x = 0.8, by a factor 0.611.     

On the effective cross-section for recombination of free carriers with dipole centres

An approximate calculation of the effective cross-section for recombination δ_eff of free charge carriers with dipole centres for small mean path lenght l of free carriers and not very small gas-kinetical cross-section of recombination σ_k is conducted. A formula for the σ_eff suitable also for larger l and small σ_k is suggested.     

Effective Mode Volume of Nanoscale Plasmon Cavities

The controlled squeezing of electromagnetic energy into nanometric volumes via surface plasmon-polariton excitations in plasmonic nanoresonators is analyzed using the concept of an effective electromagnetic mode volume V _eff, while taking careful account of the plasmon-polariton dispersion and the electromagnetic energy stored in the metal. Together with the quality factor Q of the cavity resonance, this enables a comparison with dielectric optical cavities, where V _eff is limited by diffraction. For a Fabry–Perot type planar metallic cavity, a one-dimensional analytic model as well as a three-dimensional finite-difference time-domain simulation reveal that V _eff is not bounded by diffraction, and that Q/V _eff increases for decreasing cavity size. In this picture, matter–plasmon interactions can be quantified in terms of Q and V _eff, and a resonant cavity model for the enhancement of spontaneous Raman scattering is presented.     

Site selective optical spectra of free base porphin in anthracene

The low temperature optical spectra of free base porphin in crystalline anthracene have been observed in the visible region of the spectrum. Quasilines and broad components were observed in the region of the forbidden Q bands. Site selection techniques were used to separate the spectra of inequivalent site species, and vibronic frequencies were assigned in the ground state and excited Q states. The relative strengths of the broad and quasiline components of the spectra in the Q_x and Q_y states indicated that the host lattice may affect the relative transition strengths of Q_x and Q_y. These results indicated that the strength of the transition to Q_x is greater than that of Q_y for a free porphin molecule.     

Twist-4 gluon recombination corrections for deep inelastic structure functions

We calculate twist-4 coefficient functions for the deep inelastic structure function F₂(x,Q²) associated to 4-gluon operator matrix elements for general values of the Bjorken variable x and study the numerical effect on the slope ∂F₂(x,Q²)/∂logQ². It is shown that these contributions diminish the strongly rising twist-2 terms towards small values of x.     

Quasielastic versus inelastic and deep inelastic lepton scattering in nuclei at x > 1

We have made a thorough investigation of the nuclear structure function W_2A in the region of 0.8 < x < 1.5 and Q² < 20 GeV², separating the quasielastic and inelastic plus deep inelastic contributions. The agreement with present experimental data is good giving support to the results for both channels. Predictions are made in yet unexplored regions of x and Q² to assert the weight of the quasielastic or inelastic channels. We find that at Q² < 4 GeV² the structure function is dominated by the quasielastic contributions for x < 1.5, while for values of Q² > 15 GeV² and the range of x studied the inelastic channels are over one order of magnitude bigger than the quasielastic one. The potential of the structure function at x > 1 as a source of information on nuclear correlations is stressed once more.     

Metal carbide-induced negative flatband voltage shift in TaCx and HfCx/HfO2 gate stacks

We systematically investigated the role of the top interface for TaC_x and HfC_x/HfO₂ gate stacks on the effective work function (Φ_m,eff) shift by inserting a SiN layer at the gate/HfO₂ top interface or HfO₂/SiO₂ bottom interface. We found that Φ_m,eff of the TaN gate electrode on HfO₂ was larger than that on SiO₂ because of the HfO₂/SiO₂-bottom-interface dipole. On the other hand, we found that Φ_m,eff values of the TaC_x and HfC_x gate electrodes on HfO₂ agree with Φ_m,eff on SiO₂. This is because the potential offset of the opposite direction with respect to the bottom interface dipole appears at the metal carbide/HfO₂ interface. It is thus concluded that the top interface in the metal carbide/HfO₂ gate stacks causes the negative Φ_m,eff shift.     

Beta-decay energies and nuclear masses of very neutron-rich Rb and Cs isotopes

Theβ-endpoint energies of very neutron-rich Rb and Cs isotopes with mass numbers 94≦A≦98 and 142≦A≦146, respectively, have been measured with a plastic scintillatorβ-telescope at the on-line mass separator OSTIS. From these,Q _β-values and mass excesses are calculated and compared with the results obtained in direct mass determinations.     

Electron inelastic mean free paths in solids: A theoretical approach

In the present paper, the inelastic mean free path (IMFP) of incident electrons is calculated as a function of energy for silicon (Si), oxides of silicon (SiO2 ), SiO, and Al2O3 in bulk form by employing atomic/molecular inelastic cross sections derived by using a semi-empirical quantum mechanical method developed earlier. A general agreement of the present results is found with most of the available data. It is of great importance that we have been able to estimate the minimum IMFP, which corresponds to the peak of inelastic interactions of incident electrons in each solid investigated. New results are presented for SiO, for which no comparison is available. The present work is important in view of the lack of experimental data on the IMFP in solids.     

Nuclear structure effects in the mass region aroundA=100, derived from experimentalQ β -values

The endpoint energies ofβ-transitions in 15 neuron-rich nuclei with mass numbers 101≦A≦106 have been measured with a plastic scintillator telescope in coincidence with a large Ge(Li)-detector at the on-line mass separator LOHENGRIN. From theQ _β -values obtained in these experiments, nuclear structure effects in this region of the nuclear chart are deduced. Finally, nuclear masses derived from theseQ _β -values are compared with the predictions of different theoretical mass calculations.     

Beta-decay energies of neutron-rich nuclei in the mass region 142≦A≦150

The β-endpoint energies of 6 neutron-rich nuclei with mass numbersA=146 andA=147 have been measured with a plastic scintillator telescope at the on-line mass separator OSTIS. With theQ _β-values derived from these experiments and with those obtained in earlier studies, nuclear structure effects in this part of the nuclear chart are investigated. In addition, nuclear masses derived from the experimentalQ _β-values are compared with the predictions of theoretical mass calculations.     

Total cross section for inclusive electron scattering in the lowQ 2 region

Absolute cross sections for inclusive electron scattering on H, D, Be, Al, and Si have been measured in the kinematical region 0.08 (GeV/c)²<Q ²<1.0 (GeV/c)² and 0.3 GeV<v<6.5 GeV. The measurements have been performed at incident energies of 3, 5, 6, and 7 GeV and at the fixed scattering angle of 10°. A careful treatment of radiative corrections due to elastic electron nucleus scattering, quasielastic and inelastic scattering on the bound nucleons has been applied to the measured cross sections. The comparison of the nuclear cross sections with the elementary ones leads to a value ofA _eff<A with a rapid onset of this effect at small values of the scaling variablex′.     

A comparison of πππ, Kππ, πKKKK system produced in the reactions meson +p→3 mesons + p

A comparison is made of the low-mass three-meson systems (πππ), (Kππ), $\text{(π}\text{K}\text{K}\text{)}$ and $\text{(}\text{K}\text{K}\text{K}\text{)}$ diffractively produced in the reaction meson + proton → three mesons + proton. Several striking similarities and a few important differences are observed: (i) the reactions are consistent with the assumption that the three mesons decay entirely into a 0^? meson and a 0⁺, 1^? or 2⁺ resonance; (ii) the three-meson mass spectra have a peak ≈ 250 MeV above the effective threshold M_eff of the dominant decay mode and then fall off approximately as (mass)^?3;(iii) the average spin 〈J〉 = 0.55 + 1.1 Q_eff, where Q_eff = M - M_eff; (iv) the average orbital angular momentum 〈l〉 increases according to 〈l〉 = 0.75 Q_eff; (v) the three-meson states are produced dominantly in unnatural spin-parity states and no evidence for their being resonant is found; (vi) the only natural spin-parity states found are the well-established 2⁺ resonances A₂ and K¹ (1420); they have similar properties to the non-resonant unnatural parity states except for a dip at t = 0 in the dσ/dt distributions; (vii) both the unnatural and natural spin-parity states are produced mostly by an exchange of natural parity; (viii) there is evidence for two types of production mechanism with different polarization properties, one approximately conserving helicity in the t-channel and the other in the s-channel.