Table of contents

Kohn's variational method is used to calculate the positron-helium scattering length and low energy S-wave phase shifts for a quite realistic Hylleraas type of helium function containing an electron-electron correlation term. The zero energy wavefunction is used to calculate the value of the annihilation rate parameter Z_eff. All the results are significantly different from those for Drachman's helium model B, but are in better agreement with the available experimental data.

A comparison has been made of the experimental electron emission cross sections from autoionizing states of helium for electrons, H⁺, H₂⁺, and He incident at the same velocity of relative motion on helium in the backward ejection angles. While emission cross sections from the singlet states, (2s²) ¹S, (2p²) ¹D, and (2s2p)¹P, have broad maxima in 100-200 eV region for electron impact, the maxima for the other projectile impacts appear in the energy region corresponding to much slower velocities. The emission cross section from the (2s2p) ³P state excited by electrons is of quite different features as compared with those by the other projectiles.

Electron-photon scattering in presence of a background potential is considered for arbitrary intensities of laser radiations. Cross sectional expressions are derived which automatically include the effect of the background on the electron states. If the electron states are approximated by plane waves, they are shown to reproduce the results given by previous authors. An explicit result for the total elastic cross section in the combined laser pulse Coulomb field, is given. A simple upperbound is obtained for the corresponding bremsstrahlung (inverse bremsstrahlung) cross sections.

For any diatomic molecule three different virial theorems can be formulated. The most general one is independent of the problem and the representation. The other two stemmed out of adiabatic representation. The first of them is the well known electronic Slater's virial theorem. In this paper the virial theorem has been derived from the Born-Oppenheimer type coupled nuclear equations.

It is shown that by measuring the ratio of the total two-photon ionization rate for circularly polarized light to that for linearly polarized, one can obtain the ratio of the nP to epsilon S and nP to epsilon D bound-free radial matrix elements. Also discussed is the case of three-photon ionization in which the ratio of the nD to epsilon P and nD to epsilon F bound-free radial matrix elements can be obtained.

Excitation of the 4³S and 4³D states of helium in He(2³S)-He(1¹S) collisions has been studied in the energy range 20-100 keV. Cross sections for the excitation of the He(1¹S) target and He(2³S) projectile to these levels have been separately determined and shown to considerably exceed corresponding cross sections for excitation in He(1¹S)-He(1¹S) collisions.

The total ionization cross section of Ar atoms by metastable He atoms was measured in the relative velocity range of 1 to 4*10⁵ cm s^-1 by an atomic beam time of flight method, and is compared with the existing theoretical results.

Inelastic differential scattering cross sections have been measured in the laboratory energy range of 200 to 350 eV using a time of flight technique. Energy losses are observed corresponding to excitation of each of the channels He(1s²)+He(1s2l) and He(1s2l)+He(1s2l). The results confirm the initial step in the recently proposed ionization mechanism of two electron excitation followed by autoionization as the particles dissociate.

A charge-exchange optical pumping experiment to study collisions between Cs atoms and Cs⁺ ions in a He buffer gas is reported. Cs⁺ ions are polarized by charge-exchange collisions with optically pumped Cs atoms. From measurements of the line-widths of the Cs⁺ ion resonance and electron spin resonance, the charge- exchange cross section sigma _ce(Cs⁺-Cs) and electron spin-exchange cross section sigma _se(e-Cs)are found to be sigma _ce(Cs*-Cs)=(4.5+or-0.5)*10^-14 cm² and sigma _se(e-Cs)=(2.6+or-0.4)*10^-14 cm² respectively.

The ejected electron spectrum of Cd vapour has been observed at 90 degrees to the direction of the incident electron beam. Spectra obtained at incident energies between 15 and 40 eV show multiplet structure not observed at higher energies, nor in ultraviolet absorption studies. A number of the multiplets have been assigned based on the calculation of Wilson (1968).

The production of CO₂⁺(B² Sigma _u⁺( nu '=0) to x² Pi _g) fluorescence radiation by extreme ultraviolet excitation of CO₂ was experimentally investigated in the 650-685AA region using synchrotron radiation. The cross section for the production of fluorescence radiation was found to exhibit structural features corresponding to the Tanaka-Jursa-LeBlanc bands, indicating that the upper states associated with these bands interact with the CO₂⁺(B² Sigma _u⁺)+e^- continua, producing the ion in this excited state by autoionization.

X-ray spectra from Ar-Ar collisions at various energies are used in conjunction with theoretical (Hartree-Fock) calculations to obtain relative probabilities of states of excitation of the Ar atoms. These in turn are used to obtain semi-empirical mean fluorescence yield values. The fluorescence yields thus obtained are compared with those obtained from total auger and X-ray measurements. Large discrepancies are found and reasons for them are discussed.

Corrections to the interaction integrals of 4f electrons, which are due to the interaction of configurations for which two f electrons are excited, are calculated with a pair function approach. Using first-order pair functions of this kind, second order and third order ladder diagrams are evaluated. The third order diagrams are quite small. This indicates a satisfactory convergence of the theory and means that an exact pair treatment is not necessary to deal with correlation effects among the f electrons. It is found that the second order results obtained in the Hartee-Slater potential introduced by Lindgren (1971) agree quite closely with Hartree-Fock results. Since the pair equation can more easily be solved in a local potential, the Hartree-Slater potential is probably a better starting point of perturbative calculations for the rare earth elements.

A new computational method for the evaluation of dispersion coefficients between atoms is described. Results are given for the two-body coefficients through R^-10 for a representative selection of one and two-electron atoms, the uncoupled Hartree approximation being employed in the latter case, and also the leading non-additive three-body terms are calculated for triplets of hydrogen and helium. Particular refined computations are described for atomic hydrogen, values of 6.499 026 705 and 21.642 464 54 au being obtained for the dipole-dipole and triple-dipole coefficients respectively.

The trial function suggested recently by Power and Somorjai (1972) has been tested by the calculation of upper and lower energy bounds for the ground states of He and Li⁺. Upper bounds have also been computed for the next seven singlet, and the first seven triplet, states of both species.

Relativistic Hartree-Fock results for one-electron energy eigenvalues and (rⁿ), Slater integrals, ionization energies and hyperfine interaction integrals in a number of rate earth atoms and ions are presented. The magnitude of relativistic and exchange contributions in each case is discussed by comparison with relativistic Hartree-Fock-Slater, relativistic Hartee and non-relativistic Hartree-Fock calculations. Inclusion of relativity and a full treatment of exchange are shown to be essential if detailed agreement with experiment is required. However, because the atomic ground states are usually near the LS coupling limit, the authors calculations for single jj coupling configurations are not adequate for quantitatively treating properties which involve the 4f electrons directly.

A 'combined' analytic theory of classical excitation of hydrogenic atoms and ions by charged particles is presented: it is valid for all energy transfers at sufficiently high incident particle velocity. The theory reduces to the binary encounter or classical impulse approximation and to an adiabatic dipole perturbation theory in their respective ranges of validity. The combined theory agrees reasonably well with published Monte Carlo trajectory calculations. It is confirmed that adiabatic effects are a major defect of binary encounter theory. The energy transfer distribution for fixed impact parameter is studied.

A local linear response method for static atomic polarizabilities and shielding factors is presented, and a new numerical method for solving the pertinent first order perturbation equations is employed. Applications to atoms with a singlet ground state and Z<or=36 are made. Satisfactory agreement with best available results is obtained with Slater's exchange potential having alpha =1, for all atoms.

A general analytical result has been obtained for multiphoton ionization of hydrogen from metastable 2S state. Numerical results are given for the ratio of cross sections of ionization by linearly polarized and circularly polarized light for N=2,3,4 (where N is the number of photons absorbed). In all these cases the cross section for linearly polarized light dominates over the cross section for circularly polarized light.

The continuous oscillator strengths for photoionization of the 2¹S and 2³S states of helium are evaluated in the dipole length and velocity formulations for transitions which leave the He⁺ ion in a 1s, 2s or 2p state. The calculations are performed with two sets of wavefunctions: Calculation A uses frozen core Hartree-Fock bound and free state functions; Calculation B uses a 56-parameter bound state representation with frozen core Hartree-Fock free state functions. Where possible the results are compared with the more accurate values of Jacobs and Burke.

It is shown that it is possible to derive from first principles a form for a local, central, complex potential that fits elastic electron scattering on hydrogen at various energies with two free parameters. The energy-dependence of the parameters is discussed. Understanding of the optical model based on hydrogen enables the authors to use published Hartree-Fock calculations to construct a potential that gives excellent fits to argon at several energies with no free parameters. In all cases, the total reaction cross section, obtained from independent experimental information, is used to determine the strength of the imaginary part of the potential.

Electron-hydrogen atom inelastic collisions were studied as a three-body classical interaction process. The approach employed in this work differs from the previous study of the same problem of Abrines et al. (1966) in that (i) a different classical model of the undisturbed ground state hydrogen atom was employed and (ii) a systematic investigation of the cross sections was performed in place of a Monte-Carlo method. The basic feature of the model atom employed in the present work is its zero angular momentum due to the assumption of the radial motion of the atomic electron ('free-fall' trajectory). The results are compared with experiment, yielding better agreement at low energies than that obtained by Abrines et al. Some comparisons of the three-body results with the binary-encounter approximation are also given.

The eikonal approximation has been used to investigate the elastic scattering of electrons by hydrogen and helium atoms. The results for the differential cross sections for both the systems are compared with the experimental findings and also with the corresponding results obtained by other theoretical workers.

The energy and angular distributions of electrons ejected from autoionization states in neon have been observed by electron impact. The energies of the primary electrons are 50-1000 eV. The resonance peaks due to electrons ejected from the inner-shell excited states (2s2p⁶ns)¹S, have been clearly observed over the wide range of incident energy and ejection angle, whereas the peaks due to (2s2p⁶np)¹P state become evident as the impact energy is decreased below approximately 100 eV. The resonance peak due to the doubly excited states e.g., (2p⁴3snp)¹P, have not been evident. The line shapes of the resonance peaks are almost symmetric.

The close coupling approximation is applied to positron helium scattering with allowance for virtual positronium formation. The results are found to depend markedly on the choice of the target wavefunction. It is suggested that this is due to the violation of the bound principle for the close coupling approximation when inexact target functions are used.

A variational form of the continuum distorted wave approximation is used to provide further evidence that the second Born term dominates in the high energy limit of proton-hydrogen forward charge transfer.

Cross sections for the electronic excitation of the (ns,mp)¹P states (for n,m=2,3,4) from the ground state are calculated using the Born approximation and multi-parameter Hylleraas-type wavefunctions. The influence of the interelectron coordinate r₁₂ is discussed.

Collisional excitation by free electrons of transitions in various ions of the type 2s²2p^q-2s2p^q+1, determines the strength of many semi-forbidden lines observed in quasars. Collision strengths for the transitions N⁺ and O²⁺ 2s²2p²³P-2s2p³⁵S⁰, and N²⁺ 2s²2p ²P⁰-2s2p²⁴P are calculated from solutions of coupled integro-differential equations. In all cases allowance is made for configuration interaction between 2s²2p^q and 2p^q+2, and all 2s2p^q+1 channels are included.

The Wilets and Gallaher (1966) formulation for H⁺-H collisions has been generalized to the heavy ion-atomic hydrogen collision. The resulting coupled differential equations have been solved and a corresponding computer program has been constructed to extract numerical results. Four-state calculations have been carried out for the specific example of He²⁺-H collisions using both eigenfunction and pseudo-state expansion bases. Charge transfer, excitation and ionization cross sections as well as 2p polarization fractions are presented and compared with other theoretical calculations and experimental measurements where these are available. The computations encompass the range of He²⁺ energies from 6.3 keV-4 MeV. It has been found that: the neglect of rotational coupling effects underestimate charge transfer cross sections at impact energies of the He²⁺ ion less than about 15 keV; at high velocities of encounter the charge transfer cross section to the He⁺(1s) state predominates over that to the He⁺(2s) or He⁺(2p) state and is confined to a small range of impact parameters; excitation cross sections are sensitive to the choice of pseudostates. It is further shown that an eigenfunction expansion basis is unlikely to reproduce the 1.2 degrees total charge transfer probability experiment of Keever and Everhart (1966) in a calculation employing a four-state approximation.

The rotational excitation cross sections for e^--N₂ scattering for incident electron energies from 0.2 to 10.0 eV are calculated. Initial rotational levels up to 20 are considered.

A general formula is given for the cross section for the (e,2e) reaction on molecules in terms of a multicentre model for the SCF orbitals. Rotations and vibrations are taken into account. For the cases of homonuclear diatomic molecules and methane it is shown how symmetries reduce the computational labour to the point where it is possible to use the reaction as a simple test of the details of the SCF orbitals. The details of a calculation for H₂ involving rotational excitations are given.

It is shown that the model potential techniques used for systems with closed-shell cores can be extended to open-shell cores without difficulty. The method is applied to calculate potential energy curves for the molecules HeH⁺ and He₂⁺. The results are in good agreement with ab initio calculations. Some interesting long-range curve crossings in HeH⁺ are discussed.

An empirical scheme of parametrization of the CNDO is presented which satisfies the invariance requirements of the method. Calculation of single bond and orbital energies are presented for a number of symmetric triatomic molecules.

The Bloch-Siegert shift displayed by a spin 1/2 particle system is measured in a double resonance experiment on the ground state of an optically oriented ¹⁹⁹Hg vapour. The displacement of the nuclear magnetic resonance peaks corresponding to the one and three quantum transitions are studied as a function of the radiofrequency field intensity. Similarly, the displacement of the component of the vapour polarization which is modulated at twice the RF field frequency is observed. The experimental results are compared with the existing theoretical approaches to the Bloch-Siegert effect, and a good agreement is found with the semiclassical theory leading to the continued fraction solution.

For pt.III, see abstr. A46187 of 1973. The authors solve the problem of a doublet excited state under the influence of an arbitrarily strong RF field and optically pumped by a transverse beam. The solution is obtained as a continued fraction, which is easily evaluated on a computer. Haroche's resonances at even multiples of the radio frequency are investigated and their Bloch-Siegert shifts are determined. The lines are less power broadened than the multi-photon resonances earlier investigated, and they are hence more exactly measurable. In the perturbation limit the authors regain results derived by Haroche and Cohen-Tannoudji from a quantum theory. Detection at either the DC component or any of the oscillating components is discussed. For the Hanle effect the authors find a generalization of the Cohen-Tannoudji dressed g-factor. The experimental results for a rotating RF field are discussed, and experiments using a linearly oscillating field performed by Tsukada, Yabuzaki and Ogawa are compared with the theory. Good agreement is found.

For pt.III, see abstr. A64132 of 1972. Cross sections for the dissociative ionization of H₂⁺ by electron impact have been measured for interaction energies below 940 eV. A source was used which produced H₂⁺ ions under clearly defined conditions. The cross section attained a maximum value of 0.2 pi a₀² at 103 eV which is in fairly good agreement with classical predictions by Alsmiller (1962) and Mathur et al. (1970). A Bethe plot of the results rolls over in a way which suggests that the Bethe approximation will only be valid for this reaction for energies of at least several hundred eV.

A crossed beam experiment has been performed to measure the function for 1S-2S excitation of He⁺ ions by electron impact. Absolute cross sections for direct excitations to the 2S state were deduced by fitting the measurements to Born's approximation at high energies after allowance had been made for the contribution from cascade. Just above threshold the cross section was 1.28*10^-2 pi a₀², which agrees closely with the previous measurement by Dance et al. (1966), but it is less than half the threshold cross section predicted by the close-coupling calculation of Burke et al. (1964). There is, however, much better agreement with the recent distorted wave polarized orbital calculation by McDowell et al. (1973). The present measurement was free from any evidence of error due to space charge interactions between the colliding beams and it was possible to examine structure in the excitation function associated with the formation of autoionizing states of helium.

By using an electron impact spectrometer with a greatly improved energy resolution it has been possible to study the appearance of H₂^- resonances in the energy range 11.0 to 12.25 eV in reactions which lead to specific rotational-vibrational states of the final H₂ molecule. Rotational excitations having Delta J=-2 (i.e. 2 to 0, 3 to 1), Delta J=0 (i.e. 0 to 0, 1 to 1,2 to 2, etc), Delta J=+2 (i.e. 1 to 3,3 to 5), and Delta J=+4 (i.e. 1 to 5), accompanied by vibrational excitations Delta v=0, 1, 2, 4, 6 and 8 have been studied. Two series of resonances (series a and c) have been seen, and their symmetry classifications have been established as ² Sigma _g⁺ and ² Pi _u respectively.

The total atomic cross sections are determined in carbon, aluminium, copper, tin and lead at gamma ray energies of 84, 129, 145.41, 279.12, 322, 411.8 and 661.6 keV by a new method reported by the authors earlier. The values of bound electron incoherent scattering cross sections sigma _b are extracted from the total atomic cross sections by subtracting the theoretical sum of photoelectric and Rayleigh scattering cross sections. The sigma _b values are compared with the corresponding values of sigma _KN, sigma _TF and sigma _HF calculated on the basis of Klein-Nishina (KN) formula, Thomas-Fermi (TF) model and Hartree-Fock (HF) model respectively. The discrepancy between sigma _b and sigma _KN worsens as the photon energy decreases and the atomic number increases, thereby indicating the increasing importance of the binding energy effects. Discrepancies with sigma _TF and sigma _HF show similar behaviour. These are attributed to limitations inherent in the TF and HF models.

The cross section for C-K X-ray production in the bombardment of graphite by copper ions is reported and found to be much larger than the C-K cross section in carbon ion bombardment of copper. The difference is ascribed to C-K production by recoiling carbon atoms, and a calculation of this contribution to the cross section according to the expression of Taulbjerg and Sigmund (1972) gives reasonable agreement with the data.

For pt.II, see abstr. A23320 of 1971. A non-relativistic Hartree-Fock self-consistent-field procedure with spin-orbit interaction corrections has been used to investigate the effect of multiple ionization in the valence shell of the krypton atom on M and N shell binding energies and on the transition energies of M shell de-excitation processes. The study of the non-radiative relaxation mechanisms includes intra-shell Coster-Kronig and super-Coster-Kronig transitions as well as normal inter-shell Auger transitions. The predicted energies for Auger transitions have been compared with the experimental spectra available from electron impact studies. In general, with the exception of M-N₁N₁ discrepancies are discussed.

Employing a 40 cm curved mica crystal spectrograph of the transmission type, the beta -region of the L emission spectrum of holmium 67 has been investigated. Two new quadrupole lines at lambda =1601.2 and 1593.7 (xu) corresponding respectively to the transitions L₃N₂ and L₃N₃ have been reported for the first time. Wavelength data of different workers on the already reported lines in this region have been given for the sake of comparison.

X-ray transitions from scandium due to proton, helium, and oxygen bombardment are reported. The oxygen +Sc spectrum displays the largest number of satellites including three hypersatellite transitions and in the He+Sc spectrum double electron transitions were observed. Hartree-Fock-Slater calculated energies were used to assign the transitions.

The red degraded bands of the orange-red system of ⁶⁵Cu¹⁶O have been observed in emission under a dispersion of 0.6 AA mm^-1 and rotational analysis of both sub-bands of the (0,0) band has been made. The analysis indicates that the transition is ² Sigma ⁺-² Pi _(a).

Data about electronic band systems of the gaseous compounds of gold and various X elements of the carbon column (Si, Ge, Sn, Pb) observed in the red and near infrared parts of their thermal emission spectra and assigned to ² Sigma -² Pi transitions, are summarized, commented and completed in order to have a synthetic view of the subject. An observation of the second system of AuPb is reported. Arguments based both on a molecular orbital picture and on the evolution of the ² Pi splitting through the four molecules are in favour of a regular ² Pi ground-state, the unpaired electron being centred on the X atom.