Atomic Subshells Research Articles

A new look at an energetic (e,2e) reaction: Binary versus recoil

We analyze the recoil-to-binary peak ratio in an energetic (e,2e) reaction on the valence ns sub-shell of noble gas atoms. Dramatic qualitative change in this ratio dependence on the ejected electron energy can be explained by variation of reflectivity of the short-range Hartree-Fock potential. The reflectivity increases profoundly from lighter (He) to heavier (Ne and Ar) noble gas atoms because of modification of the scattering phases due to occupation of the target p orbitals (Levinson theorem). This effect is further modified due to strong inter-shell correlations in Ar. These theoretical predictions are confirmed experimentally.

An energetic (e, 2e) reaction away from the Bethe ridge: recoil versus binary

We analyse the recoil-to-binary (RB) peak intensity ratio in an energetic (e, 2e) reaction performed on the valence ns sub-shell of noble gas atoms away from the Bethe ridge condition. A qualitative change in the RB ratio dependence on the ejected electron energy from He to Ar can be explained by the variation of reflectivity of the short-range Hartree–Fock potential. The reflectivity increases profoundly from lighter (He) to heavier (Ne and Ar) noble gas atoms because of modification of the scattering phases due to occupation of the target p orbitals (Levinson–Seaton theorem). This effect is further modified due to strong inter-shell correlations in Ar. These theoretical predictions are confirmed experimentally.

Photoionization of the subvalent subshells of noble gas endohedrals: interference of three resonances

We demonstrate strong interference patterns in the photoionization cross-section of the subvalent subshells of noble gas (NG) endohedral atoms NG@F. This interference is a result of common action of three factors: the effect of neighbouring atomic subshells, reflection of photoelectron waves by the fullerene F shell and resonance modification of the incoming photon beam by the complex effect under the action of the F electrons. We have considered the outer ns-subshells for Ne, Ar, Kr and Xe noble gas atoms. The polarization of the fullerene shell is expressed via the F total photoabsorption cross-section. The photoelectron reflection from the static F potential is taken into account in the frame of the so-called bubble potential which is a spherical δ-type potential. It is assumed that the NG atom is centrally located in the fullerene. It is also assumed in accordance with the available experimental data that the fullerene radius is much bigger than the atomic radius and the thickness of the fullerene shell. These assumptions permit the NG@F photoionization cross-section to be presented as a product of the NG atomic cross-section and two calculated factors that account for polarization of the F electron shell and reflection of photoelectrons by the fullerene static potential.

Extreme Ultraviolet Lithography Simulation by Tracing Photoelectron Trajectories in Resist

In order to evaluate the roughness of a resist pattern after development, photoelectron trajectories excited by extreme-ultraviolet (EUV) light are traced, and the resist pattern quality is discussed on the basis of a time-dependent resist development simulation. Binding energies of all subshells of atoms in poly(methyl methacrylate) (PMMA) and Si, and the photoionization cross section (dipole oscillator strength) are obtained by solving the Schrödinger equation with the Hartree–Fock–Slater potentials. The angular distribution of photoelectron emission is also taken into account. The photoelectron range from the generated position is around 30 nm in PMMA. If EUV light exposure has the square-wave intensity distribution, the critical dimension (CD) error and line edge roughness (LER) are almost negligible. If the aerial image is laterally sinusoidal, however, even if the contrast is unity, the pattern is seriously distorted. If the contrast is 0.5, the pattern is hardly formed for the doses less than 5.0 mJ/cm2.

Calculations of inner-shell ionization by electron impact with the distorted-wave and plane-wave Born approximations

A method is described for computing total cross sections for the ionization of inner shells of atoms and positive ions by impact of electrons and positrons with arbitrary energies. The method combines the relativistic plane-wave Born approximation (PWBA) with a semirelativistic version of the distorted-wave Born approximation (DWBA). Formal expressions for the longitudinal and transverse generalized oscillator strengths (GOSs) of closed shells are derived. Tables of GOSs for $K$ shells and for $L$ and $M$ subshells of neutral atoms have been calculated for a discrete grid of energy losses and recoil energies. A suitable interpolation scheme allows the easy evaluation of PWBA ionization cross sections from these GOS tables. The difference between the total ionization cross sections that result from the DWBA and the PWBA (considering the longitudinal interaction only) has been calculated numerically for projectiles with kinetic energies up to 16 times the ionization energy of the active shell. In this energy range, ionization cross sections with the accuracy of a distorted-wave calculation are obtained by simply adding this difference to the cross section resulting from the conventional PWBA. For higher energies, the cross section is obtained by multiplying the PWBA cross section by an energy-dependent scaling factor that is determined by a single fitted parameter. Numerical results are shown to agree with experimental data, when these are available.

Calculations of effective atomic number

We present and discuss effective atomic number ( Z eff) obtained by different methods of calculations. There is no unique relation between the computed values. This observation led us to the conclusion that any Z eff is valid only for given process. We illustrate calculations for different subshells of atom Z=72 and for M3 subshell of several other atoms.

Effect of plasma oscillations ofC60collectivized electrons on photoionization of endohedral noble-gas atoms

It is demonstrated that outer and inner electron shells, including that formed by collectivized electrons of the fullerene C{sub 60}, affects dramatically the cross section of the subvalent ns subshells of the noble-gas endohedral atoms A-C{sub 60}. The calculations are performed within the framework of a very simple, so-called ''orange skin,'' model that makes it possible, in spite of its simplicity, to take into account the modification of the ns subshell due to its interaction with inner and outer atomic shells, as well as with the collectivized electrons of the C{sub 60}. As a concrete example, we consider the Xe 5s electrons completely collectivized by the powerful action of the Xe close and remote multielectron neighboring shells.

Ratios of internal conversion coefficients

We present here a database of available experimental ratios of internal conversion coefficients for different atomic subshells measured with an accuracy of 10% or better for a number of elements in the range 26 ⩽ Z ⩽ 100. The experimental set involves 414 ratios for pure and 1096 ratios for mixed-multipolarity nuclear transitions in the transition energy range from 2 to 2300 keV. We give relevant theoretical ratios calculated in the framework of the Dirac–Fock method with and without regard for the hole in the atomic subshell after conversion. For comparison, the ratios obtained within the relativistic Hartree–Fock–Slater approximation are also presented. In cases where several ratios were measured for the same transition in a given isotope in which two multipolarities were involved, we present the mixing ratio δ 2 obtained by a least squares fit.

An extended x-ray absorption fine structure study of hydrogen storage in Ti–Hf–Nialloys

The effect of hydrogenation on the local structure of aTi40Hf40Ni20 crystalline alloy was studied by means of the extended x-ray absorption finestructure. The samples were loaded to different hydrogen-to-metal ratios,H/M, between1.2 and 1.7. The desorption process was also investigated by studying the local order in an alloy chargedto H/M = 1.85 thendesorbed to H/M = 0.8.For the non-hydrogenated alloys, the local order was very similar in Ti–Hf–Ni andTi–Zr–Ni alloys, quasicrystal or crystal. With increasing hydrogen concentration,all of the mean interatomic distances increased, except for the Ni–Hf (Hf–Ni)ones, which show an anomalous behaviour, decreasing with increasingH/M.This leads to a remarkable inversion of the atomic subshells oftitanium and nickel in the first environment of hafnium atoms aroundH/M = 1.2.The increase of distances is a maximum for the Ti–Ti and the Ti–Hf correlations, which isconsistent with the hydrogen atoms sitting preferentially near titanium and hafnium atoms.Similar conclusions were obtained previously from a study of Ti–Zr–Ni alloys.

Interchannel-coupling effects in the spin polarization of energetic photoelectrons

Effects of the interchannel coupling on the spin polarization of energetic photoelectrons emitted from atomic Ne valence subshells are examined. Like previously obtained results for cross sections and angular distributions, the photoelectron spin polarization parameters too are found considerably influenced by the coupling. The result completes a series of studies to finally conclude that the independent particle description is inadequate for the {\em entire} range of photoionization dynamics over the {\em full} spectral energy domain

PHOTOELECTRON ANGULAR DISTRIBUTION PARAMETERS FOR ELEMENTS Z=55 to Z=100 IN THE PHOTOELECTRON ENERGY RANGE 100–5000 eV

Presented here are parameters of the angular distribution of photoelectrons along with the subshell photoionization cross sections for all atoms with 55≤ Z≤100 and for atomic shells with binding energies lower than 2000 eV. The parameters are given for nine photoelectron energies in the range 100–5000 eV. Relativistic calculations have been carried out within the quadrupole approximation by the use of the central Dirac–Fock–Slater potential. The effect of the hole resulting in the atomic subshell after photoionization has been taken into account in the framework of the frozen orbital approximation.

Evolution of the localstructure with hydrogenation in Ti-Zr-Ni quasicrystals andapproximants

The effect of hydrogenation on the local structure of Ti-Zr-Nialloys has been studied by means of extended x-ray absorptionfine structure. The alloys were either icosahedralquasicrystals or crystalline approximants. They were loaded todifferent hydrogen-to-metal ratios 1.2⩽ H/M ⩽1.7.The desorption process was also investigated by studying thelocal order in an alloy charged to H/M = 1.2 then desorbed toH/M =0.84. The local structure was identical in the crystallineand quasicrystalline alloys with the same H/M ratio (0 or 1.2) and that of the desorbed sample was intermediate between that ofthe non-hydrogenated samples and that of the samples chargedto 1.2. Therefore, it is possible to follow the evolution of thelocal structure with hydrogenation from H/M = 0 to 1.7. Ageneral increase of all the mean first distances was foundexcept for the Zr-Ni (Ni-Zr) one. There is a remarkable inversion of the atomic subshells of titanium and nickel in thefirst environment of zirconium atoms around H/M = 1. For the1.56 hydrogenated sample, the effect of adding a small amountof lead, which stabilizes the icosahedral phase, was studiedand it was demonstrated that lead atoms substitute for thenickel atoms and are, therefore, incorporated into the quasilattice.

Determination of level widths and fluorescence yields of some atomic sub-shells for Th and U

The level widths and fluorescence yields of some atomic sub-shells were determined using L1, L2 and L3 sub-shell fluorescence yields and linewidths of some L X-rays. For this measurement, the L3l, L3α, L3β, L2β, L2γ, L1β, L1γ, Lβ, Lγ, L1x, L2x and L3x X-ray production cross sections in U and Th have been measured using the 59.5 keV incident photon energy. The measurements were performed using Am-241 radioisotopes as photon sources and a Si(Li) detector. The L X-rays are resolved with a new analytical method. The obtained L3l, L3α, L3β, L2β, L2γ, L1β, L1γ, Lβ, Lγ, L1X, L2X, and L3X X-ray production cross sections were compared with the theoretical calculations using the most reliable theoretical values of Li (i = 1, 2, 3) sub-shell photoionisation cross sections, fluorescence yields, X-ray emission rates and Coster–Kronig transition probabilities. The measured Li, Mi and Ni sub-shell fluorescence yields were compared with the semi-empirical and theoretical values. Further, obtained level widths were compared with the other experimental and theoretical values. The results in the present paper are found to be in good agreement with calculated values.

K-SHELL, L-SUBSHELL, AND TOTAL INTERNAL CONVERSION COEFFICIENTS FOR SUPERHEAVY ELEMENTS

Internal conversion coefficients (ICC) were calculated for all atomic subshells of the elements with 104≤Z≤126 for E1–E4 and M1–M4 multipolarities and 20 transition energies between 10 keV and 5 MeV. Presented here are the K-shell, L-subshell, and total ICC. For the higher shells and transition energies 10–1000 keV, the ICC have been deposited at the LANL preprint server (http://xxx.lanl.gov/e-print/nucl-th/0004003).

Polarization studies in the photoionization of atoms using agraphical technique

An alternative method to the density matrix formalism and based on thegraphical technique of angular momentum theory is applied to derive theexpression for the photoionization cross section of atoms. This expressionis suitable for calculating the polarization parameters of the remainingion and photoelectron in the case of the ionization of polarized atomsexposed to polarized radiation. The atom and ion are described by thequantum numbers LSJ and LSJIF (I is nuclear spin). The expressionsare verified by the calculation of the asymmetry parameter β of theangular distribution of photoelectrons in single and shake-upphotoionization of the 2p subshell of Na atoms.

Nondipole parameters in angular distributions of electrons in photoionization of noble-gas atoms

The parameters that determine the nondipole $(E1\ensuremath{-}E2)$ corrections to the photoelectron angular distribution have been investigated for the $s\ensuremath{-}$ and p-subshells of the noble-gas atoms through comparing results calculated in the Hartree-Fock (HF) approximation and taking into account multielectron correlations, using the random-phase approximation with exchange. Our results cover the photoelectron energy range $\ensuremath{\epsilon}$ from the photoionization thresholds to 1.6 keV. We find the interesting result that near the photoionization thresholds these parameters are generally characterized by an oscillatory behavior as a function of $\ensuremath{\epsilon},$ exclusive of the parameter for the He $1s$ subshell. These oscillations are sensitive to multielectron correlations, except those of the Ar $3p$ subshell. This finding supports once more that the photoprocesses in these atomic subshells are of a collective character. We conclude that their correct description cannot be achieved within the framework of a one-electron approximation such as the HF approximation. Results are presented and discussed.

PHOTOELECTRON ANGULAR DISTRIBUTION PARAMETERS FOR ELEMENTS Z=1 TO Z=54 IN THE PHOTOELECTRON ENERGY RANGE 100–5000 eV

Parameters of the angular distribution of photoelectrons along with the subshell photoionization cross sections calculated for all subshells of atoms with 1 ≤ Z ≤ 54 are presented in the Table for nine photoelectron energies in the range 100–5000 eV. Relativistic treatment of the photoeffect is used. The calculations have been performed within the quadrupole approximation with the central Dirac–Fock–Slater potential. The hole left by the emitted electron has been taken into account in the framework of the frozen orbital approximation. Applications of nondipolar parameters to photoelectron angular distribution in solids, to quantitative x-ray photoelectron spectroscopy analysis, and to the x-ray standing wave method are discussed.

Qualitative modification of the high energy atomic photoionization cross section

It is demonstrated that the nonrelativistic high energy omega-->infinity behavior of the photoionization cross section of an nl atomic subshell, sigma(nl)(omega), for l>0 is independent of l and is given by sigma(nl)(omega) approximately 1/omega(9/2), rather than the previously generally accepted sigma(nl)(omega) approximately 1/omega(l+7/2). Furthermore, for l = 1, although the exponent does not change, the coefficient is significantly altered. This modification of sigma(nl)(omega) is due to the interchannel interaction between ns photoionization channels and l not equal0 channels in the atom. As a result, for the photoionization of l not equal0 electrons, the single-particle approximation is never correct in the omega-->infinity limit. This has important consequences for sum rule calculations.

Time-dependent close-coupling calculations for the electron-impact ionization of carbon and neon

A time-dependent close-coupling method is used to calculate the electron-impact ionization cross section for the outer 2 p subshell of both carbon and neon atoms. The inner 1s and 2s subshells are treated using pseudopotentials, while interaction with the remaining 2 p core electrons is handled in a configuration-average approximation. When the time-dependent ionization cross section for the 2 p subshell of carbon is combined with distorted-wave ionization cross sections for the 2 s subshell, the resulting total cross section is in reasonable agreement with previous experimental measurements. However, when the time-dependent ionization cross section for the 2 p subshell of neon is combined with distorted-wave ionization cross sections for the 2 s subshell, the resulting total cross section is substantially higher than all previous experimental measurements. Further LS term-dependent distorted-wave ionization cross sections for the 2 p subshell of neon suggest the need for extending the time-dependent close-coupling method to include a full Hartree-Fock interaction with the remaining 2p core electrons. PACS number~s!: 34.80.Kw

Energy linearity of high-purity germanium detectors in the region of the Ge K-absorption edge: experimental results

Non-linearities in the energy response of gas detectors in the regions of the absorption edges of the detection medium are well documented. Monte Carlo calculations show that the non-linearity results from differences in efficiencies for converting absorbed radiation into ionisation for different atomic sub-shells. Energy non-linearity in germanium-based solid-state detectors in the region of the germanium 11.104-keV K-edge is not well documented, although a 1% non-linearity has been previously reported in a Ge(Li) detector. This relatively high value is of practical concern since high-purity germanium (HPGe) is often the detector of choice for α- and X-ray spectrometry down to a few keV. In this paper, we present the experimental results for the energy response of a HPGe detector in the 8–15-keV energy region of the germanium K-edge. Within the accuracy of our measurements, we conclude that there is no measurable non-linearity effect in germanium at the K-edge.