Showing papers in "Journal of Physics B in 1981"

Calculation of the average properties of atoms in molecules

Abstract: An algorithm for calculating atomic properties, based on the topological theory of molecular structure, is described and applied For any given molecular system atoms are rigorously defined in terms of the topological properties of the system's charge distribution rho (x) in three-dimensional space The essential feature of this distribution is that its only local maxima, the attractors of the associated gradient vector field grad rho (x), occur at the positions of the nuclei The region of space occupied by an atom, the atomic basin, is the space traversed by all gradient paths of grad rho (x) which terminate at its nucleus This property is used to construct a coordinate transformation which maps each atomic basin onto three-dimensional space The Jacobian J, of this transformation depends solely on the second derivatives of rho (x) The determinant of J is obtained by solving a first-order differential equation governed by grad2 rho (x) Any atomic property may then be calculated by an integration of an associated single-particle density over the basin of the atom Numerical integrations of some atomic properties of diatomic and polyatomic molecules are reported

Experimental study of the ionisation of atomic hydrogen by fast H+ and He2+ ions

Abstract: Cross sections for the ionisation of ground state hydrogen atoms by 38-1500 keV H+ and 125-2200 keV He2+ ions have been determined using a crossed-beam technique. Collision products produced in the intersection of the primary ion beam with a highly dissociated thermal energy beam of hydrogen are identified by time-of-flight spectroscopy and counted using a coincidence technique. Cross sections sigma (H+) for proton impact, which involve much smaller uncertainties and cover a wider energy range than previous measurements, now permit an accurate assessment of the validity of the various theoretical predictions. Cross sections sigma (He2+) for He2+ impact, the first such measurements, are also compared with theory and measured cross section ratios sigma (He2+)/ sigma (H+) are considered in terms of the Z2 scaling predicted by the Born approximation.

Oscillator strengths and collisional damping parameters for lines of neutral calcium

Abstract: Relative oscillator strengths for 37 lines of neutral calcium have been measured to an accuracy of +or-5% using the absorption method. The oscillator strengths are placed on an absolute scale by reference to recent lifetime measurements. All lines have lower energy levels in the range 2.5 to 3.0 eV above the ground level and the set of lines includes most of those important for the determination of the calcium abundance in late-type stars. In addition the same equipment has been used to study collisional broadening by helium of 17 lines chosen from among those with newly measured oscillator strengths. These measurements provide interesting insight into the dependence of the collisional damping parameter on total angular momentum within a spectral multiplet and on the configuration of the upper level.

Centrifugal distortion constants for diatomic molecules: an improved computational method

Abstract: The perturbation theory approach to calculating centrifugal distortion constants is reformulated to eliminate summations over excited vibrational states. In the usual formulation of Rayleigh-Schrodinger perturbation theory, these summations appear when the solution of an inhomogeneous differential equation is expressed as a sum over the eigenfunctions of the unperturbed Hamiltonian. In the present method, this differential equation is solved numerically, eliminating the summations and giving an exact solution using much less computer time than in the original perturbation theory method. The centrifugal distortion constants are then calculated by a straightforward numerical integration. The effects of continuum levels are included exactly, so that the results remain valid for vibrational levels near dissociation. Numerical tests are performed for realistic potential curves, and the method is shown to give accurate results.

Possible rearrangement processes in L-shell ionisation of atoms by heavy ions

Abstract: The authors investigate the possibility of collision-induced transitions of a vacancy between the L subshells of atoms, when the vacancy is created by direct ionisation at heavy-ion impact. A simple model with a two-step mechanism for the production and rearrangement of a vacancy is presented. The success of this model indicates that intra-shell excitations (de-excitations) during the collision are probably responsible for the previously observed large discrepancies between the theory and experiment in the L-shell ionisation of gold by carbon, nitrogen and oxygen ions.

The elastic scattering of electrons from inert gases. III. Argon

Abstract: The R-matrix calculations of O'Malley et al are simplified and extended to the intermediate impact energy range in which the He ground-state wavefunction is coupled with a 'P pseudo-state to include the full static dipole polarisability. Phaseshifts, differen- tial, integrated and momentum transfer cross sections for electrons elastically scattered from helium are reported for the impact energy range of 5 to 200 eV. At low energies the present calculation essentially reproduces the results of O'Malley et a1 for 5 E G 16.5 eV. At intermediate energies good agreement between the present calculations and the most recent measurements is observed.

Selective electron capture into highly stripped Ne and N target atoms after heavy-ion impact

Abstract: Auger electron and X-ray spectra from Ne and N gas targets excited with 1.4 MeV amu-1 Ar12+, Kr15+, Xe24+, and Pb36+ ions are measured, varying the target pressure and mixing other gases into the target volume. A dramatic change of line intensities from outer-shell configurations having a KL two-electron core and a third electron in the n=4, 5, 6 shell is observed, depending on the target pressure and systematically on the target ionisation potential. This effect is explained by highly selective electron capture from neutral target atoms or molecules into outer-shell orbitals of slowly (Er<10 eV) recoiling and highly stripped target atoms with metastable core states. It turns out that selective electron capture is a dominant mechanism for the population of H-, He- and Li-like states of low atomic number (Zt

Electron-atom scattering at intermediate energies

Abstract: Over the last few years there has been much interest, both theoretically and experimentally, in electron-atom scattering at intermediate energies. The theoretical work has been driven mainly by the many applications in astronomy, laser physics and plasma physics which require accurate data for their interpretation and by experimental advances which provide an important stimulus to theory. The increasing availabililty of more powerful computers has enabled the development of more sophisticated theoretical methods to study electron scattering in the intermediate energy regime, which faces particular difficulties owing to the infinite number of open channels which occur in this energy region. In order to obtain accurate results in the intermediate energy region, the theoretical approaches used must be able, in some way, to allow for loss of flux into these highly excited states and continuum states of the target atom or ion. Recent theoretical approaches which have been proposed include extensions of low-energy methods, the use of optical potentials and extensions of the Born approximation by the inclusion of higher-order terms.

Milne's differential equation and numerical solutions of the Schrodinger equation. I. Bound-state energies for single- and double-minimum potentials

Abstract: Milne's approach to the numerical solution of the Schrodinger equation via a non-linear differential equation an the quantisation of a quantum action is investigated in detail. An accurate and efficient computational method is presented which allows a rapid second-order convergence onto a desired eigenenergy En. Numerical sample calculations demonstrate the efficiency of the method, which has special advantages for accurate calculations of high quantum states. The present method can be easily extended to the calculation of quasi-bound levels at resonance (complex-values) energies.

Crossed beam measurement of absolute cross sections: an alternative method and its application to the electron impact ionisation of He+

Abstract: A new experimental method is reported for the crossed beam measurement of absolute cross sections. It essentially consists in sweeping one of the beams across the other in a linear 'see-saw' motion. The method is applied to one case of electron-ion collisions. A description is given of an electron gun designed to realise a linear and distortionless motion of a ribbon electron beam. Measurements are reported regarding the electron impact ionisation of He+ in the energy range 55-74 eV.

Absorption of additional photons in the multiphoton ionisation continuum of xenon at 1064, 532 and 440 nm

Abstract: The energy spectrum of electrons produced by multiphoton ionisation of xenon atoms has been measured, using a new type of electron energy analyser with an acceptance angle of 2 pi sr. Absorption of additional photons above the minimum number required for ionisation has been observed in the non-resonant as well as in the resonant multiphoton ionisation process. In the resonant proces the AC Stark shift is used to link wavelength detuning to the light intensity, in order to find the probability of extra photon absorption as a function of light intensity.

Electron impact ionisation of Li-like and Be-like ions

Abstract: Electron impact ionisation cross sections for positive ions in the Li and Be isoelectronic sequences are calculated in the Coulomb-Born exchange and distorted-wave exchange approximations - using close-coupling wavefunctions to represent the initial and final states of the target system. The corresponding ionisation rate coefficients are also computed as a function of temperature. The results obtained are compared with experiments, with the infinite-Z method of Golden and Sampson (1979) and with the Lotz semiempirical formula. For C, N, O and Ne ions the mutual agreement is better than 25% and in some cases is of the order of a few per cent. For Fe23+ and Fe22+ the Lotz formula gives rates up to 40% higher than the Coulomb-Borm at high temperatures (>108K), indicating that the formula probably gives an inaccurate estimate of the high-energy behaviour of the cross section for these ions.

The two-body problem in the presence of a homogeneous magnetic field

Abstract: For arbitrary gauge the authors derive the generalised momentum operator for an N-body system with a momentum-independent and translationally invariant interaction in a homogeneous magnetic field. When they specialise to neutral two-body systems the separation of the centre-of-mass and relative coordinates can be carried out explicitly. In order to reveal the global properties of the energy spectrum, the classification, quantum numbers, degeneracy, etc, are discussed for the non-interacting case and for a harmonic interaction. The hydrogen atom is chosen for studying in detail the physically important case of a Coulomb interaction. The essential results of this first consistent treatment of the hydrogen atom in strong magnetic fields as a genuine two-body problem are (i) the non-trivial reaction of the collective motion of the system transverse to the magnetic field on the internal state, and (ii) the non-negligible' effects of the finite proton mass on the energy spectrum for B>or approximately=1011 G, which is at variance with the customary, widely held, view.

Time-dependent theory of non-Hermitian Schrödinger equation: application to multiphoton-induced ionisation decay of atoms

Abstract: A rigorous and practical time-dependent formulation of quantum decay processes is obtained by converting the Hermitian Schrodinger problem into an equivalent non-Hermitian Schrodinger equation. The properties of the original Hermitian and the reduced non-Hermitian Hamiltonians are compared and the non-Hermitian formulation is shown to be consistent with the theorem of Fock and Krylov for the description of truly decaying states. A self-consistent non-unitary algorithm is developed and used to obtain expressions for the time-dependent transition amplitudes of interest; they automatically preserve the total probability in the sum space at all future times tau >0. The formalism is coded for application to the important problem of ionisation decay of a ground-state hydrogen atom coupled to a strong radiation field with a sub-threshold photon frequency. The first quantitative information on the time dependence of two- and three-photon (resonant and non-resonant) ionisation of the hydrogen atom is obtained.

Calculation of vibrational excitation of N2 by electron impact at 5-50 eV using extended-basis-set Hartree-Fock wavefunctions

Abstract: The cross sections 0 to 0, 0 to 1 and 1 to 2 for vibrational excitation of N2 by electron impact at 5, 10, 20, 30 and 50 eV are calculated in a static-exchange-polarisation model. The calculations are based on the Hartree-Fock target wavefunctions of Cade, Sales and Wahl (1966) for the static potential and for the Hara (1967) free-electron-gas exchange potential. Target charge polarisation is included by the effective polarisation potential of Morrison and Collins (1978), scaled as a function of internuclear distance by the polarisabilities. The calculated cross sections are well converged with respect to channels. The results show clearly both the low-energy Pi g resonance and the intermediate-energy Sigma u resonance.

Electron-photon coincidences with polarised electrons

Abstract: The authors present a theory of electron-photon coincidence experiments with polarised electrons, taking spin-orbit coupling effects during the excitation into account. The influence of the initial polarisation vector on the angular distribution and polarisation of the emitted photons is discussed in detail. As an explicit example the excitation process 1S0 to 3P1 in mercury is considered. Finally, the results are specialised to experiments where the scattered electrons are not observed. Using symmetry arguments and deriving additional selection rules they relate the degree of light polarisation to the initial polarisation. Two experimental results are presented.

Population of N2(A 3Σu+) metastable states in a pure nitrogen glow discharge

Abstract: The concentration of the nitrogen metastable molecule N2(A 3 Sigma u+) is determined in a pure nitrogen glow discharge as a function of the pressure (from 0.1 to 2 Torr) and of the discharge current (up to 30 mA cm-2) using the optical absorption of the first positive system bands. The absorption maximum is of the order of 2% corresponding to a N2(A 3 Sigma u+, nu =0) concentration of about 1.4*1012 cm-3. Measurements of the concentration of nitrogen atoms, the electronic field are also reported. A kinetic model indicates that the N2(A) molecules are created by electronic excitation from ground-state molecules and lost mainly by diffusion to the walls and collisions with N(4S) atoms.

Charge exchange with multiply charged ions at low energies: application to the N3+/H and C4+/H systems

Abstract: The cross sections for charge exchange in N3/H and C4+/H collisions are computed using a molecular treatment for energies in the range 0.01 to 100 eV. The potential surfaces of all molecular states which interact via avoided crossings, either directly or indirectly, with the entry channel have been calculated using a model potential method. Radial-coupling matrix elements between all interacting states of the same symmetry have been determined with precision. These are subsequently used in a fully quantum mechanical treatment of the collision dynamics. Explicit introduction of translation factors is avoided by imposing the boundary conditions on a sphere of finite radius R0. In the interaction region, the scattering equations take the simple PSS form with the radial-coupling matrix elements computed with respect to the origin of electronic coordinates at the centre of mass of the nuclei. With any other choice of origin, the PSS equations must be modified accordingly. The influence of rotational coupling is investigated for the C4+/H system. It is found to be unimportant.

A comparison of the absorption spectra of the fluorobenzenes and benzene in the region 4.5-9.5 eV

Abstract: The gas-phase extinction-coefficient spectra of ten fluorosubstituted benzenes are presented and compared with benzene in the region 4.5-9.5 eV. The three singlet-singlet transitions analogous to the B2u from A1g, B1u from A1g and E1u from A1g transitions of benzene are presented and discussed. The appearance of the elusive 1E2g state is reported in 1,3,5-TFBz and two tetrafluorobenzenes, while in monofluorobenzene and o-DFBz the 3s and 4s members of the 1E1g Rydberg state are detected. From this work the authors conclude that they have the following order for benzene: 1B2u<1B1u<3s(1E1g)<1E1u

K-shell excitation of HF and F2 studied by electron energy-loss spectroscopy

Abstract: The fluorine K-shell (1s) excitation spectra of HF and F2 have been studied by small-angle inelastic scattering of 2.5 keV electrons. The F2 spectrum exhibits a dramatic 1s to sigma * shape resonance 14.5 eV below the F 1s ionisation threshold which is qualitatively different from the 1s to sigma * transitions observed in all other first-row diatomics. An empirical correlation between experimental term values for both sigma * and pi * K-shell shape resonances and the sum of the atomic numbers of the heavy atoms in a series of first-row molecules is demonstrated and tested with respect to the energy of the 1s to sigma * transition in F2. The sigma * and pi * energies of a variety of molecules have been predicted using this relationship. In contrast to F2, the HF spectrum is more atom-like, exhibiting a moderately intense 1s to sigma * transition followed by the np Rydberg series. The equivalent-core analogy is applied to the HF and F2 results to predict excitation and ionisation energies of NeH and NeF.

Spectral line broadening due to the interaction between very excited atoms: 'the dense Rydberg gas'

Abstract: The authors report the first observation of spectral line perturbations, due to van der Waals coupling between very excited atoms, in a sample where the average interatomic distance is about 15 times the Rydberg atom radius. Broadenings of the order of intervals between adjacent lines reveal Rydberg-Rydberg couplings no longer negligible compared with the atomic binding energy. The authors analyse the excitation mechanism of this 'dense Rydberg gas' by laser light non-resonant for the unperturbed atoms.

Total cross sections for electron excitation transitions between the 11S, 23S, 21S, 23P and 21P states of atomic helium

Abstract: The five-state R-matrix calculations of Berrington et al. (1975) on the excitation of helium by electrons have been revised and extended to higher electron impact energies. Inelastic scattering cross sections are presented for all transitions between the 11S, 23S, 21S, 23P and 21P states of helium, and elastic cross sections are presented for the n=2 states.

Energy and angular dependence of H-(D-) ions produced by dissociative electron attachment to H2O(D2O)

Abstract: Energy and angular distributions of H-(D-) ions formed by dissociative attachment in H2O(D2O) have been observed for the processes situated in the region of 6.5, 8.6 and 11.8 eV. The angular behaviour would indicate that the symmetries of the resonant states responsible for these processes are 2B1, 2A1 and 2B2, respectively. The energy distributions of the H-(D-) ions for all three processes show that most of the dissociation energy is in the form of translation and furthermore the distributions for each process and isotope are similar. This similarity would indicate that the potential surfaces and the autodetachment widths of the H2O- states are also about the same which would support the proposals and calculations of Jungen, Vogt and Staemmler (1979) who predict that these three states are formed by two electrons in 3sa1 orbitals bound to an H2O+ core with a vacancy in the 1b1, 3a1 and 1b2 orbitals, respectively.

Local against non-local complex potential in resonant electron-molecule scattering

Abstract: Resonant scattering of electrons from molecules is discussed in the context of both a non-local complex potential and a local complex potential (boomerang model). Vibrational excitation cross sections are computed for an exactly solvable model and compared with those calculated within the boomerang approach. The range of applicability of the local complex potential approach is analysed in detail. A semi-local approximation to the cross sections is introduced which is only slightly different from the boomerang approximation, but leads to improved results.

Effective collision frequency of electrons in noble gases

Abstract: The electron-neutral collision frequency in the noble gases has been calculated using recent numerical results for momentum transfer cross sections by assuming a Maxwellian distribution of electron velocities. In all these gases, except for argon, good agreement is obtained with most previously published experimental and theoretical data. Mean free path, mobilities and diffusion coefficients are also calculated from the resulting effective collision frequencies. The empirical formulae are presented for an electron temperature dependence of the electron-neutral collision frequency for all noble gases up to Te

On the interpretation of low-energy electron-HCl scattering phenomena

Abstract: A general non-adiabatic theory of near-threshold resonant electron-molecule scattering in the presence of a long-range direct scattering potential is developed. As a special case, resonant s-wave scattering in the presence of a dipole potential is worked out in detail. An exactly solvable dynamical model for electron-HCl scattering is proposed and is shown to reproduce the essential features of the vibrational excitation functions of HCl measured by Rohr and Linder (1976). Particular emphasis is given to the analysis of the analytic properties of the S matrix and related quantities in the fixed-nuclei approximation. The passage of a resonance through threshold is shown to be a non-trivial phenomenon for polar molecules. The authors propose a re-interpretation of the HCl- potential energy curves obtained by the stabilisation method.

Merged electron-ion beam experiments. IV. Dissociative recombination for the methane group CH+,...,CH5+

Abstract: The dissociative recombination of the methane-derived group, CH+,...,CH5+, has been measured over the centre-of-mass energy interval 0.03 to 2 eV. Assuming a Maxwellian distribution of the electron velocities, the derived rate coefficients for CH+,...,CH5+ at 100K are, respectively, 5, 8.7, 12, 12.8 and 12.8*10-7 cm3 s-1. The recombination cross section for the diatomic ion CH+ is large. This has far reaching consequences for the theories of molecular formation in interstellar clouds. The cross sections for the polyatomics CH2+,...,CH5+ are also large and roughly equal in magnitude. Like CH+ they exhibit a close to E-1 energy dependence below 0.1 eV. For CH3+, CH4+ and CH5+ the slope of the cross sections increases above 0.1 eV.

Electron scattering from Ne II using the relativistic R-matrix method

Abstract: The R-matrix method for electron scattering from atoms and ions using the Dirac Hamiltonian has been programmed and a test case of electron scattering from Ne II is considered. The agreement for the total cross section between the relativistic calculation and previous non-relativistic calculations is excellent. The relativistic calculation enables cross sections for transitions between fine-structure levels to be obtained.

Analytic theory of resonances, virtual states and bound states ion electron-molecule scattering and related processes

Abstract: Using the formalism of discrete state-continuum interaction as introduced, for example, by Feshbach and Fano, formally exact operator expressions are derived for the cross sections of resonant electron scattering, dissociative attachment and related processes. Concentrating on the fixed-nuclei limit, a rigorous description of resonances, virtual states and bound states and their connection at threshold is developed. In principle the approach is to impose the threshold law on the decay width of the resonance and to take proper account of the energy-dependent level shift. The analytic structure of the fixed-nuclei S matrix for electron scattering is obtained by analytic continuation into the complex momentum and energy planes. At energies sufficiently close to threshold the results are of universal validity, depending only on angular momentum and the leading multipole moments of the molecular charge distribution. The approach is exemplified for s-wave and p-wave scattering by short-range potentials, where it reproduces the well-known results of general analytic S-matrix theory. New results are then obtained for the behaviour of resonances and bound states of polar molecules close to threshold.

Theoretical study of low-energy electron and positron scattering on Be, Mg and Ca

Abstract: Static exchange and static exchange plus polarisation calculations are carried out for elastic electron and positron scattering with Be, Mg and Ca. All three atoms are found to have a low-lying 2P resonance in the electron scattering case. Magnesium and calcium are also predicted to have higher lying 2D shape resonances near 2.0 and 0.7 eV, respectively. The 2D resonance in Mg is very weak and broad ( Gamma >3.0 eV) while that in Ca is much more pronounced and is much narrower ( Gamma approximately 0.6 eV). These findings are in agreement with recent experiments. In addition a very broad feature appears in e--Be d-wave scattering near 5 eV. While maxima occur in the p-wave cross sections for positron scattering, these do not appear to be due to resonances. However, evidence is provided for exceptionally broad resonances in d-wave positron scattering and for a virtual (or antibound) state in s-wave scattering.