Electron Subshells Research Articles

Hyperfine structure parametrisation in Maple

In hyperfine structure examinations, routine high resolution spectroscopy methods have to be combined with exact fine structure calculations. The so-called magnetic A and electric B factor of the fine structure levels allow to check for a correct fine structure analysis, to find errors in the level designation, to find new levels and to probe the electron wavefunctions and its mixing coefficients. This is done by parametrisation of these factors into different contributions of the subshell electrons, which are split further into their radial and spin–angular part. Due to the routine with which hyperfine structure measurements are done, a tool for keeping the necessary information together, performing checks online with the experiment and deriving standard quantities is of great help. Maple [Maple is a registered trademark of Waterloo Maple Inc.] is a highly-developed symbolic programming language, often referred to as the pocket calculator of the future. Packages for theoretical atomic calculation exist ( Racah and Jucys) and the language meets all the requirements to keep and present information accessible for the user in a fast and practical way. We slightly extended the Racah package [S. Fritzsche, Comput. Phys. Comm. 103 (1997) 51] and set up an environment for experimental hyperfine structure calculations, the Hfs package. Supplying the fine structure and nuclear data, one is in the position to obtain information about the hyperfine spectrum, the different contributions to the splitting and to perform a least square fit of the radial parameters based on the semiempirical method. Experimentalist as well as theoretical physicist can do a complete hyperfine structure analysis using Maple. Program summary Title of program: H fs Catalogue number: ADXD Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADXD Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: none Computers for which the program is designed: All computers with a license of the computer algebra package Maple Installations: University of Kassel (Germany) Operating systems under which the program has been tested: Linux 9.0 Program language used: Maple, Release 7, 8 and 9 Memory required to execute with typical data: 5 MB No. of lines in distributed program, including test data, etc.: 34 300 No. of bytes in distributed program, including test data, etc.: 954 196 Distribution format: tar.gz Nature of the physical problem: Atomic state functions of an many configuration many electron atom with several open shells are defined by a number of quantum numbers, by their coupling and selection rules such as the Pauli exclusion principal or parity conservation. The matrix elements of any one-particle operator acting on these wavefunctions can be analytically integrated up to the radial part [G. Gaigalas, O. Scharf, S. Fritzsche, Central European J. Phys. 2 (2004) 720]. The decoupling of the interacting electrons is general, the obtained submatrix element holds all the peculiarities of the operator in question. These so-called submatrix elements are the key to do hyperfine structure calculations. The interaction between the electrons and the atomic nucleus leads to an additional splitting of the fine structure lines, the hyperfine structure. The leading components are the magnetic dipole interaction defining the so-called A factor and the electric quadrupole interaction, defining the so-called B factor. They express the energetic splitting of the spectral lines. Moreover, they are obtained directly by experiments and can be calculated theoretically in an ab initio approach. A semiempirical approach allows the fitting of the radial parts of the wavefunction to the experimentally obtained A and B factors. Method of solution: Extending the existing csf_LS() and asf_LS() to several open shells and implementing a data structure level_LS() for the fine structure level, the atomic environment is defined in Maple. It is used in a general approach to decouple the interacting shells for any one-particle operator. Further submatrix elements for the magnetic dipole and electric quadrupole interaction are implemented, allowing to calculate the A and B factors up to the radial part. Several procedures for standard quantities of the hyperfine structure are defined, too. The calculations are accelerated by using a hyper-geometric approach for three, six and nine symbols. Restrictions onto the complexity of the problem: Only atomic state functions in nonrelativistic LS-coupling with states having l ⩽ 3 are supported. Typical running time: The program replies promptly on most requests. The least square fit depends heavily on the number of levels and can take a few minutes.

Electron loss in MeV/u collisions between many-electron projectiles and targets

Ionization cross-sections have been measured for MeV/u, low-charge-state, heavy ions colliding with many-electron targets. Single and multiple electron removal from the projectile are compared for these low-charge-state ions with similar data obtained using more highly charged projectiles. It is shown that although there are large differences in magnitudes and behavior as a function of incoming charge state between the low and high charge state data, strong similarities exist when the charge state fractions are plotted as a function of the number and type of outermost subshell electrons.

Relativistic corrections to the nuclear Schiff moment

Parity and time invariance violating ($P,T$-odd) atomic electric dipole moments (EDM) are induced by interaction between atomic electrons and nuclear $P,T$-odd moments which are produced by $P,T$-odd nuclear forces. The nuclear EDM is screened by atomic electrons. The EDM of a non-relativistic atom with closed electron subshells is induced by the nuclear Schiff moment. For heavy relativistic atoms EDM is induced by the nuclear local dipole moments which differ by 10-50% from the Schiff moments calculated previously. We calculate the local dipole moments for ${^{199}{\rm Hg}}$ and ${^{205}{\rm Tl}}$ where the most accurate atomic and molecular EDM measurements have been performed.

Photon-Induced L3 Subshell x-ray Intensity Ratios for Re, Au, Tl and Pb

The relative intensities of L3 subshell x-rays were measured for the elements Re, Au, Tl and Pb by photoionization of L3 subshell electrons. The L3 subshell electrons are excited by the K x-rays of the elements used as the primary targets and fluorescent L3 subshell x-ray intensities are measured with a Si(Li) detector. The primary targets were chosen such that their K x-rays excited the L3 subshell of the element concerned but did not excite the L2 and L1 subshells. Ge, Se, Br and Rb K x-rays were used to excite the L3 subshells of Re, Au, Tl and Pb, respectively. The Ge, Se, Br and Rb K x-rays, for this purpose, were obtained by irradiating the targets of these elements by 59.54 keV gamma rays from an Am-241 source. The theoretical L3 subshell intensity ratios were calculated using radiative transition rates based on the Dirac–Fock (DF) model and the Dirac–Hartree–Slater (DHS) model. The calculated results were compared with the experimentally measured relative intensities to check the applicability of emission rates based on the DF and DHS models.

Nuclear Schiff moment and time-invariance violation in atoms

Parity- and time-invariance-violating $(P,T$-odd) nuclear forces produce $P,T$-odd nuclear moments. In turn, these moments can induce electric dipole moments (EDMs) in atoms through the mixing of electron wave functions of opposite parity. The nuclear EDM is screened by atomic electrons. The EDM of an atom with closed electron subshells is induced by the nuclear Schiff moment. Previously the interaction with the Schiff moment has been defined for a pointlike nucleus. No problems arise with the calculation of the electron matrix element of this interaction as long as the electrons are considered to be nonrelativistic. However, a more realistic model obviously involves a nucleus of finite size and relativistic electrons. In this work we have calculated the finite nuclear size and relativistic corrections to the Schiff moment. The relativistic corrections originate from the electron wave functions and are incorporated into a ``nuclear'' moment, which we term the local dipole moment. For ${}^{199}\mathrm{Hg}$ these corrections amount to $\ensuremath{\sim}25%.$ We have found that the natural generalization of the electrostatic potential of the Schiff moment for a finite-size nucleus corresponds to an electric-field distribution which, inside the nucleus, is well approximated as constant and directed along the nuclear spin, and outside the nucleus is zero. Also in this work the ${}^{239}\mathrm{Pu}$ atomic EDM is calculated.

Final-ion-charge spectra produced by cascading decay of hollow argon and krypton atoms

Abstract Yields of multiply charged Arq+ and Krq+ ions produced in the process of cascading de-excitations of the initial hollow ions with several inner-shell vacancies are calculated via straightforward construction of de-excitation trees of the decay cascades. Respective final-ion-charge spectra are found to be sensitive both to the number of initial inner-shell vacancies and to their distribution among electron subshells.

Electron-impact single ionization of Kr10+ and Kr11+ ions

Cross sections for electron-impact single ionization of ground state Kr10+ and Kr11+ ions have been calculated in the distorted-wave approximation including both direct ionization and excitation-autoionization processes. The direct ionization cross sections are calculated for the ejection of 3s, 3p and 3d subshell electrons and the excitation-autoionization cross sections are calculated for the inner-shell excitations of the type 3p nl (n = 4,5,6;l = 0,1,2,3) and 3s n´l´ (n´ = 4,5;l´ = 0,1,2,3). In addition, the inner-shell excitation of the type 2p3d, 4l (l = 0,1,2,3) is included for Kr11+. The radiative decay effect has been found to be negligible by carrying out explicit calculations of the radiative rates and autoionizing rates. The present results show that the direct process dominates the total ionization cross section for the two ions and that the contributions of excitation-autoionization are about 15% and 13% of the total cross sections for Kr10+ and Kr11+ ions, respectively. The present results are in good agreement with the experimental measurement of Oualim et al.

Synchrotron X-ray analysis of the electron density in HoFe2.

Structure factors for a small holmium diiron HoFe(2) Laves crystal were measured with focused lambda = 0.75 Å synchrotron X-radiation using a fast avalanche photodiode (APD) counter. The deformation electron density (Deltarho) maps are remarkable for significant excess electron density midway between the Ho atoms, which is not dissimilar to the peaks attributed to classic 'covalent bonding' in C and Si crystals. These residual electrons accumulate at the centres of the kagomé net hexagons and form, with the Fe atoms, a triangular lattice which is characterized by more stable magnetic order than the kagomé net. Similar peaks occur along the Ho-Fe and Fe-Fe contacts. These results confirm the hypothesis that 5d electrons of the rare-earth atoms are important in the spin-coupling mechanism for HoFe(2)-type compounds. The 5d electrons are far less localized than the 4f electrons, and considerable 5d-5d and 5d-3d orbital overlap occurs between neighbouring atoms. Aspherical electron density near the Ho nuclei can be associated with the Ho 4f subshell electrons. Strong depletions of the Deltarho near the atoms along the Ho-Ho, Ho-Fe and Fe-Fe vectors are indications of exchange repulsion. The effect of anharmonicity on the Deltarho is insignificant.

Photoelectron spectroscopy on atomic Pr and Nd in the 4d giant resonance region

The photoionization of atomic Pr and Nd in the region of the f giant resonances has been investigated with the use of monochromatized synchrotron radiation. The kinetic energy of the photoelectrons has been analysed, in part, with a high-resolution electron spectrometer to resolve the complex multiplet splitting. The partial cross sections for photoionization in the different electronic subshells 6s, 5p, 5s, 4f, and 4d have been determined. The character of the resonances is found to be of highly intermediate f-type, i.e. discrete and continuum transitions are almost in equilibrium. The direct photoionization is discussed in terms of a tunnel model for atomic shape resonances.

Demonstrations on Paramagnetism with an Electronic Balance

The paramagnetism of inorganic compounds is related to the number of unpaired electrons of the atoms. Thus, can be used to stablish oxidation states and bonding properties. A simple set-up made with a powerful neodymium magnet over the plate of an electronic balance allows measuring the force of attraction over a solid substance or a solution in a test tube. The lack of paramagnetism of salts whose elements have complete electronic subshells and the comparison of the force of attraction over compounds of the same metal in different oxidation state (as potassium ferro and ferricianide, or salts of Cu(I) and Cu(II)), allows to confirm that paramagnetism is associated to the number of unpaired electrons. The splitting of the five d orbitals according to the ligand field theory allows to justify the different behavior of some Fe(II) or Fe(III) compounds. The graph of the force of attraction over each mole versus the number of unpaired electrons fits to the second grade polynomial k(N2+2N) predicted by the the...

Simultaneous ionization and excitation of B and Al atoms in the ground and excited states by photons

The cross sections of simultaneous photoionization and excitation of the outermost inner closed subshell electrons of boron and aluminium atoms are calculated within a relaxed-orbital Hartree-Fock framework in the dipole approximation. The atoms in the ground and excited states ns2n's 2S and ns2n'd 2D are considered. Large differences are found between the cross sections near the threshold of photoionization calculated in the average of configuration, term-dependent and MCHF approximations. A very strong enhancement of the ratio of the cross sections of simultaneous photoionization and excitation to those of the direct photoionization of the atoms in the excited state as compared to the same processes for the atoms in the ground state was obtained. A very low probability of shake-up process for B and Al atoms in the ground state was noted.

0 degrees binary encounter electron production in 30-MeV Oq++H2, He, O2, Ne, and Ar collisions.

Double-differential cross sections (DDCS's) for the production of binary encounter electrons (BEE's) were measured for collisions of 30-MeV ${\mathrm{O}}^{\mathit{q}+}$ projectiles with ${\mathrm{H}}_{2}$, He, ${\mathrm{O}}_{2}$, Ne, and Ar targets with q=4--8 and an electron ejection angle of \ensuremath{\theta}=0\ifmmode^\circ\else\textdegree\fi{} with respect to the beam direction. Particular interest focused on (a) the evaluation of the contributions of the different electron subshells of the multielectron targets, ${\mathrm{O}}_{2}$, Ne, and Ar; (b) the study of the well-known enhancement of the BEE DDCS's with decreasing projectile charge-state q; here this dependence was tested for higher collision energies and new targets; (c) the study of the dependence of the BEE peak energy on the particular target and projectile charge state. Results were analyzed in terms of the impulse approximation, in which target electrons in the projectile frame undergo 180\ifmmode^\circ\else\textdegree\fi{} elastic scattering in the field of the projectile ion. The electron scattering calculations were performed in a partial-wave treatment using the Hartree-Fock model. Good agreement with the data was found for the ${\mathrm{H}}_{2}$ and He targets, while for the multielectron targets ${\mathrm{O}}_{2}$, Ne, and Ar only electrons whose velocity was lower than the projectile velocity needed to be included for good agreement. All measured BEE DDCS's were found to increase with decreasing projectile charge state, in agreement with other recent BEE results. The BEE peak energies were found to be independent of the projectile charge state for all targets utilized. \textcopyright{} 1996 The American Physical Society.

Relative intensities of shake-up satellites in photoionization of potassium atoms from 3p64s and 3p64p

Photoionization cross sections for the 3p subshell electrons, correlation shake-up and conjugate shake-up satellite transitions in a relaxed-orbital Hartree-Fock framework within the dipole approximation are calculated. The potassium atom in the ground and first excited state 3p64p2P is considered. The single-configuration approach using pure LS and intermediate coupling of electron momenta is applied. The strong enhancement of the relative intensity of the shake-up correlation satellites in 3p inner-shell photoionization of the 3p64p2P excited state was obtained with respect to similar processes for the K atom in the ground state.

Electronic structures and properties of microclusters: cadmium and mercury

Recently obtained experimental results on the size dependence of ionization potentials (IP), photoelectron spectra, photoionization cross-sections, and optical absorption cross-sections for mercury Hg x and cadmium Cd x clusters are presented. While small mercury clusters are weakly bound, larger mercury clusters gradually assume with increasing size (between about 13 and 70 atoms) metallic-like properties, as indicated by the trend of IPs, photoelectron spectra, as well as by the apperance of a surface-plasmon resonance excitation at 5.93 eV. A similar, but much more pronounced electronic transition is exhibited by molecular beam isolated clusters of cadmium. For instance, IP(Cd 1)IP(Cd 10)= 3.1 eV, compared with the much smaller value IP(Hg 1) IP( Hg 10) = 2.2 eV. Photoelectron spectra of mass specified neural Cd 10-clusters revealed the existence of discrete electronic shells and subshells. The electronic shell structure in neutral cadmium clusters clearly dominates mass spectrometric Cd x +-intensity distributions. Pronounced shell closings are observed for Cd 10 (with 20 valence electrons), for Cd 20, Cd 35, Cd 46, and Cd 69.

Electron-impact single and double ionization of Ba2+ and Ba3+ ions.

Experimental cross sections for single and double ionization of ${\mathrm{Ba}}^{2+}$ and ${\mathrm{Ba}}^{3+}$ ions are presented for an electron-impact energy range from threshold up to 1000 eV. By the alternative use of a ``hot'' electron-cyclotron-resonance ion source and a ``cold'' Penning ion source, beams of ions with and without metastable content could be employed. A fast energy-scanning technique with step widths of about 40 meV and an energy resolution of 0.4 eV revealed fine details in the cross sections, and in particular resonant contributions to single and double ionization could be observed. The data are interpreted on the basis of calculations of energy levels and distorted-wave calculations of direct ionization from various electron subshells. Influences of giant-resonance phenomena are discussed.

Absolute Electron Impact Cross Sections for Single Ionization of Metastable Atoms of H, He, Ne, Ar, Kr, Xe and Rn

AbstractCross sections for single ionization of metastable atoms of H, He, Ne, Ar, Kr, Xe and Rn by electrons with impact energy E (threshold < E < 200 eV) are determined using a recently developed semiclassical formula. The formula consists of an energy dependent term (classical binary encounter approximation) and a term containing the weighted sum of the squared radii of maximum charge density of the outer electron subshells (Born Bethe approximation). Although this formula was originally devised and applied for ground state atoms, a comparison of the present calculations with previous calculations and measurements indicates that this formula can also be used successfully in case of metastable atoms.

Electron-impact ionization of Laq+ ions (q=1,2,3).

Experimental cross sections for single ionization of ${\mathrm{La}}^{+}$, ${\mathrm{La}}^{2+}$, and ${\mathrm{La}}^{3+}$ ions as well as for double ionization of ${\mathrm{La}}^{+}$ and ${\mathrm{La}}^{2+}$ ions and for triple ionization of ${\mathrm{La}}^{2+}$ ions are presented in an electron-impact energy range from threshold up to 1000 eV. By using a fast energy-scanning technique with step widths of about 40 meV and an energy resolution of 0.4 eV, fine details in the cross sections and especially resonant contributions could be observed. Resonant excitation of ${\mathrm{La}}^{2+}$ at 95 eV with subsequent emission of three electrons appears in our interpretation to account for 30% of the total measured double-ionization cross section. The data are interpreted on the basis of calculations of energy levels and distorted-wave calculations of direct ionization from various electron subshells and of excitation-autoionization processes. A detailed analysis of the ${\mathrm{La}}^{3+}$ single ionization both for ground-state and 5${p}^{5}$4f metastable ions is presented.

Independent electron approximation in collisions of nuclei with atoms

The process of a multielectron transition in an atom taking place during scattering, from an atom, of a structureless charged particle moving at a velocity v is treated in the model of independent particles taking into account antisymmetrisation. In the impact parameter representation, expressions for the probabilities W( rho ) of multielectron transitions between various electronic subshells, multiple ionisation processes and also ionisation transitions leading to excitation of the atomic residual have been obtained. On the basis of the probability formulae, the cross sections for the ionisation of helium atoms resulting in the excitation of the atomic residual to the 2s, 2p, 3s, 3p and 3d states have been calculated. The cross sections obtained are compared with similar cross sections taken from the work of Dalgarno and McDonald and Mapleton.

Entropy Estimates for Some Silicates at 298°K from Molar Volumes

Third law entropies for silicates of Be, Mg, Ca, Zn, Na, and K containing the same anion group, for example, SiO(4) or SiO(3) or AlSi(3)O(8), are found to be linearly related to their molar volumes. The relationship between the molar volume and the entropy of silicates of Fe and Mn, atoms with unfilled d electron subshells, is different from that of other silicates. The linear correlations yield a useful method of estimating the entropies of ortho-, meta-, and framework silicates (feldspars and feld-spathoids). The estimated entropies of pyrope and almandine at 298 degrees K are 47.47 and 68.13 gibbs per mole, respectively.

Effects of phase transitions upon some physical properties of the compound Ti3Al and its alloys

1 At 150°C and in the temperature ranges 250–350 and 500–650°C the physicomechanical properties of the compound Ti3Al and its alloys vary with temperature in an irregular manner. In view of the fact that these anomalies exhibit no hysteresis on heating and cooling and also that the high-temperature modification cannot be preserved in an overcooled condition, the phenomena observed may be regarded as manifestations of isomorphic tr ans for mations. 2 The nature of the isomorphic transformations taking place in the compound Ti3Al and its alloys in the temperature ranges 250–350 and 500–650°C is linked with changes in the SWASC in the titanium and aluminum sublattices and s(p)⇄d electron exchange between the atoms in the aluminum and titanium sublattices during the thermal excitation of their outer electron subshells. 3 The variation of the physical properties of the compound at temperatures above 800°C is attributable to the nucleation of regions with a degree of long-range orderη<1, which ends at a temperature close to 1080°C with the polymorphic transformationα2 phase→β solid solution.