Table of contents

See ibid., vol.5, L19-20. The usefulness of Pradhan's approximation is shown for some other examples.

The authors dispute the claim of McDowell and Richards (abstr. A.2906 of 1972) that the discontinuity of the coulomb T matrix is well-behaved on-shell.

Three recent approximations for transition amplitudes for transitions between highly excited states induced by external time-dependent fields are shown to be related. Slight errors in two of the approximations are corrected.

Experimental results are presented which show that the highest principal quantum number observed in an absorption series, when observed using a flash light source, is set by line broadening by ions and electrons produced by photoionization within the absorption cell.

Translational energy spectra of H^- ions arising from single and double collision double charge transfer of 4 keV protons on H₂ at small scattering angle have been measured. Comparison of the energy losses corresponding to the observed peaks with the expected values shows that the Franck-Condon principle is obeyed in such collisional transitions.

The unitarity of the scattering matrix has long been used as a numerical check on impact parameter calculations. The invariance of the system under time-reversal provides a further numerical check, and the explicit condition imposed on the scattering matrix by time-reversal invariance in the linear trajectory approximation is derived.

Ab initio self-consistent field calculations of potential energy curves for the ground and first excited states of HF⁺ have been performed. The excited A² Sigma ⁺ state is found to be bound, in agreement with the most recent experimental results. Qualitative arguments suggesting that the Hartree-Fock potential curves dissociate to the correct atomic limits are borne out by the calculations. A previous suggestion that interaction of the ground state X² Pi with an excited state significantly affects the shape of the curve is not supported. Calculations have also been made of the perturbations between the lowest states due to spin-orbit interactions.

A calculation of the energy and various expectation values of the 1¹S, 2^1.3S and 2^1.3P states of helium using perturbation theory is described. The method is based on zero order wavefunctions generated by the frozen core Hartree-Fock approximation. To fourth order in the energy and second order in the wavefunctions excellent agreement with the calculations of Pekeris is obtained.

An alternative variational principle for the phase function method is presented which can be extended to include many channel scattering and exchange effects. The connection between this approach and the Hulthen-Kohn method is discussed.

A theory of resonant dissociative attachment of electrons to hot diatomic gases is presented. The molecule state is approximated by a harmonic well and the negative ion, resonant, state by a line of constant slope and the rate of decay of the resonance is assumed independent of internuclear separation. The transition matrix elements that arise in the course of the calculation are evaluated using different approximations. The results of these approximations are compared with exact results obtained entirely numerically. The theory is used to interpret the experimental results of Fit et al for oxygen and thereby deduce some of the properties of the system O₂+e.

The Z^-1 expansion of the total energy of an ion with N electrons has by now been worked out are fully for systems with from 2 to 10 electrons, up to third order. This paper is concerned with the behaviour of the energy coefficients epsilon _n(N) in the Z^-1 expansion. The principal results are as follows: to establish epsilon _n(N) approximately Nⁿ⁺¹3/ for sufficiently large N, by appeal to the Thomas-Fermi theory of positive ions; to obtain the first two terms in epsilon ₀(N) exactly in such an asymptotic expansion; to give approximate forms for large N for epsilon ₁(N) and epsilon ₂(N); to point out that the total energy E(Z,N) can be plotted, as Z becomes large, in a universal form by considering E(Z,N)/Z⁷3/ against N/Z. It is emphasized that the Thomas-Fermi theory of the binding energies of neutral atoms is giving an approximate summation to all orders in Z^-1 of the Z^-1 expansion. The relation of the present theory to the result of Foldy that atomic binding energies in the range Z=2 to 90 are approximately proportional to Z¹²5/ is also discussed.

The mean excitation energies I and I', appropriate to stopping and straggling respectively, have been calculated for atomic He, Ne, Ar, Kr, Xe and Rn. In cases where comparison is available, the agreement with experiment is satisfactory. Excitation energies are also presented for individual subshells of the atoms concerned. Their relationship with subshell excitation energies arising from a conventional inner-shell correction formalism is discussed.

An analytical scattering amplitude for charge exchange processes is derived by means of a quantum three body theory for rearrangement collisions. This expression is the rigorous first order term of a perturbation series and should be useful in the intermediate and high energy range, say E>25 keV. It is equivalent to the continuum distorted wave approximation introduced by Cheshire by means of an impact parameter method.

The cross sections for the process Na⁺+Li to or from Na+Li⁺ are calculated in the range 100 eV-12 keV using a perturbed stationary state formulation and found to agree with experiment to the extent of reproducing detailed structure. A simple interpretation is advanced of the observed quasi-oscillatory structure.

A method is presented for obtaining exact scattering phase shifts using an integral equation formulation. It is similar to recent work by Reinhardt and Szabo but differs in that in the integral equation used, no inherent singularities have to be avoided. The method has been applied to both the exponential and screened coulomb potentials, and has proved to be complementary to the method of numerically integrating the radial equation-this Fredholm integral method converges more quickly for non-zero angular momentum and/or high impact energies. It is, however, applicable to all angular momenta and at all energies, including the zero-energy limit. The main drawback is that knowledge of the second born off-shell matrix elements for the potential is required.

Values of some excitation cross sections of the alkali metals, lithium, sodium and potassium are presented, which have been calculated by using a simple regional trial function in a variational principle for the R matrix. A comparison is given, where possible, between the results of these calculations and other theoretical, and experimental values. The agreement between the calculations presented and the best available comparison data is found to be surprisingly good suggesting that the other cross sections which are presented and for which no such comparison is possible, may be quite accurate also.

The Li^- free-free scaled absorption coefficient is calculated at the infrared threshold using the phase shifts for the elastic scattering of electrons by neutral lithium atoms. Contributions to the cross section for different values of the angular momentum of the free electron are investigated.

The sensitivity of the length, velocity and acceleration formulae, for photoionization of two electron systems to inaccuracies in the bound and continuum wave- functions is discussed for high energy photons. Analytic formulae are derived for the high energy behaviour of the nonrelativistic continuous oscillator strength for He, Li⁺ Be²⁺, B³⁺, C⁴⁺, N⁵⁺, O⁶⁺, F⁷⁺, Ne⁸⁺ and Mg¹⁰⁺, which, together with the recent calculations of Bell and Kingston (see Abstr. A75756 of 1971) enable accurate photoionization cross sections to be evaluated at all photon energies.

The authors have investigated the excitation of hydrogen atoms by alpha particle impact and by proton impact from the ground state to the 3s and 3p levels in the energy range 30 to 2000keV using the method of distortion. A comparison of their results with the corresponding results obtained by the first and second born and the approximation of Cheshire and Sullivan (1967) shows that the effect of distortion is to reduce the cross sections and that this effect is greater on 1s to 3s transition than on 1s to 3p transition.

A model problem with close coupling is considered. It is shown that even at energies approximately 200-1000eV the 2s-2p coupling can account for 20% change of the cross section for excitation of the 2p state.

Equations for approximate wavefunctions describing the scattering of charged particles by atoms are often obtained by using a truncated eigenfunction (or close coupling) expansion. It is shown how allowance can be made for the states omitted in the expansion, by the introduction of suitable second order potentials. The potentials are evaluated in a closure approximation and depend on an effective energy parameter which can be chosen so that the correct long range interaction is obtained in the incident channel. An impact parameter version of the method is introduced and the relationship with the Glauber approximation is discussed.

For Pt. I see Ibid Vol.5 No.3 p537. The method of Paper I is applied to collisions of electrons and protons with atomic hydrogen. One-channel and two-channel approximations are used and results are presented for elastic scattering and 1s-2s, 1s-2p and 1s-3p excitation.

The impact parameter method is formulated for general atom-atom collisions, taking full account of the electron spin. A full discussion of reflection symmetry in the scattering plane is given and a useful relation resulting from time-reversal invariance is derived. The validity of the impact parameter method is then investigated for the near resonant charge exchange process H⁺+Xe to H+Xe⁺(²P₁2/). Good agreement with experiment is obtained.

The orbital energy against internuclear separation curves 'correlation diagrams' for the symmetric Ne-Ne and the asymmetric Ne-Ar systems have been determined using an ab initio Hartree-Fock molecular orbital method. On the basis of these findings the usefulness of the electron- promotion mechanism, proposed by Fano and Lichten (1965) in accounting for inner-shell vacancy formation resulting from heavy ion-atom collisions is evaluated. The mechanism is considered to be of most value in explaining the findings related to the formation of L shell vacancies. In some asymmetric systems where there is evidence for the production of K shell vacancies it has been shown that the electron-promotion mechanism is not applicable. Other experimental results are interpreted as providing direct evidence that the adiabatic approximation is not strictly valid for these collision processes. The findings suggest that more detailed calculations using a modification of direct scattering theory are required.

The electron-promotion model of Fano and Lichten (1965) has been applied to the calculation of the cross section for production of K shell vacancies in symmetric ion-atom collisions. The promotion is assumed to occur via rotational coupling between the 2p sigma and 2p pi molecular orbitals. Certain statistical factors which govern the probability of a vacancy occurring initially in the 2p pi molecular orbital have been derived. A peak in the vacancy production probability at small impact parameters is predicted and is shown to correspond to deflection through 90 degrees . Good agreement with experiment is obtained when the method is applied to the Ne⁺-Ne system and an approximate scaling law is suggested by which the cross section for K shell vacancy production in other symmetric collisions may be deduced.

Cross sections for the rotational excitation of H₂, N₂ and O₂ by the impact of slow positrons are calculated in the distorted wave approximation. The effects of long range and short range interaction are investigated. It is found that the inclusion of the short range interaction affects the cross sections appreciably.

For Pt. I. see Ibid. Vol.5 No.3 p 589. The dependence upon molecular concentration of the equilibrium distribution and annihilation rates of slow positrons in the mixtures of rare gases with N₂ and CO has been investigated theoretically. The equilibrium annihilation rate is found to approach a constant value as the concentration of the molecule is increased.

The annihilation decay rates of positrons in He, Ne, Ar has been calculated as a function of temperature. This is done by solving the Boltzmann diffusion equation by an iterative procedure. The annihilation decay rate decreases with the increase of temperature. In the case of He and Ne, this dependence is weak, but in Ar, there are appreciable variations. A comparison is made between the theoretical and experimental results and the agreement is reasonable.

For Pt II see abstr. A75744 of 1971. The cross sections for the direct excitation of the 2¹S and 2¹P states of helium by electron impact are evaluated in a first order approximation in which the interaction between the incident electron and target nucleus is represented by a coulomb wave final state in the T matrix. The results obtained for the differential cross sections are much greater than those of the Born approximation for large scattering angles, and the present results are in much better agreement with experiment. The present calculation predicts inelastic differential cross sections which have the asymptotic energy dependence of E^-3 for all nonzero angles of scattering. The total cross sections converge to the Born values at high energy.

The ratios of the inelastic electron scattering cross sections for the n=2 levels of helium to the corresponding elastic scattering cross sections have been measured in a crossed beam apparatus over the 30 degrees to 150 degrees range for incident energies of 82 and 200 eV. In both cases, at angles greater than 40 degrees the ratio of the sum of the inelastic cross sections to the elastic cross section was constant at a few percent in qualitative agreement with a similar experiment in atomic hydrogen by Williams. The four n=2 states were observed to have markedly different angular dependencies at 82eV incident energies. Only the ¹S and ¹P states were important at 200eV; the ratio ¹S/¹P was very nearly 2 at all angles larger than 60 degrees . Within experimental error, over the range of variables studied, the observed cross sections agreed with those predicted by the first born approximation only for ¹P at angles less than 45 degrees at 82eV incident energy and for ¹S and ¹P at 30 degrees and 200eV incident energy.

Cross sections for electron loss from metastable hydrogen in collisions with argon, molecular hydrogen, nitrogen, and oxygen have been measured in the energy range 2-60 keV. The results are compared with recent experimental work of Gilbody et al. and with theoretical predictions based on the semiempirical classical impulse approximation of Bates and Walker and, in the case of hydrogen, with born approximation calculations of Bell and Kingston. While a satisfactory agreement between theory and the present experiment is found, measured cross sections are significantly larger that those of Gilbody et al. (see abstr. A23337 of 1971).

Drift velocities have been measured at 77K and 293K for electrons in neon in the range 1.6*10^-3<E+or-N(Td)<2 (1 townsend (Td)=10^-17 V cm²). It was found that the drift velocities were very sensitive to the presence of traces of molecular gases, especially N₂. Results of high accuracy required very high purity neon and, in particular, a knowledge of the N₂ impurity levels to better than 1 ppm. These data were used to determine the momentum transfer cross section for electrons in neon in the energy range 0.04<or= epsilon (eV)<or=6.0 Error limits of +or-1% are claimed for the drift velocity and +or-3% for the cross section.

Electron densities and drift velocities have been measured in the positive column of a He-Cd laser discharge under conditions appropriate to laser oscillation at 4416 AA and 3250 AA. In a pure helium discharge the electron drift velocity is proportional to the E/p value of the discharge, and drift velocities measured (3-12 * 10⁶ cm s^-1 for E/p values in the range 4-16 volt cm^-1 Torr^-1) are in agreement with those of earlier investigators for low current densities. The behaviour of drift velocity with E/p can be explained in terms of a momentum transfer cross section for electrons with helium which is inversely proportional to electron velocity. The associated electron collision frequency at unit pressure is 2*10⁹ s^-1Torr^-1. At constant discharge current and helium frequency at unit pressure is 2*10⁹ s^-1Torr^-1. At constant discharge current and helium pressure the presence of a small partial pressure of cadmium in the discharge increases the electron density (by about 40% to 2.5*10¹²cm^-3 under conditions appropriate to lasing) and decreases the electron drift velocity and E/p value.

Using a theta-pinch plasma at temperatures between 2 and 3*10⁶ K and densities of 1 to 8*10¹⁶ cm^-3, measurements have been made on the satellite lines which appear on the long-wavelength side of the helium-like resonance lines of oxygen VII and nitrogen VI. These satellites are due to emission from doubly excited or inner-shell excited lithium-like ions. The relative intensity of the satellites to the resonance lines were measured as a function of time. The intensities are shown to fit well to a quantitative theory which has been developed to account for the emission. This indicates that the dominant populating mechanism is by dielectronic recombination, which would be the only mechanism in a steady state plasma. However, the transient nature of the theta-pinch leads to an additional mechanism which contributes in the early phase of the plasma, i.e. the inner-shell excitation of lithium-like ions.

The radiative lifetime of ¹S₀ metastable level of atomic oxygen has been measured in the laboratory by recording the time dependence of the decay of intensity of the 5577 AA forbidden line during the afterglow to a pulsed discharge in inert gas-oxygen mixtures. The effects of metastable atom diffusion to the walls of the vessel, radiative decay and collisional deactivation were separated by correlating the decay constants measured over a wide pressure range.

The generalized oscillator strength of the transition r¹S to 4¹P in zinc has been measured at 150 eV incident electron kinetic energy and over an angular range 1.5 degrees to 11 degrees . These measurements have been placed on an absolute scale by normalizing to the optical oscillator strength. Absolute generalized oscillator strengths for other lines in the spectrum have been obtained by normalizing to the resonance line. The reduced matrix elements (4¹S//r²//5¹S) and (4¹S//r^-2//6¹S) were found to be 6.1 au+or-+or-15% and 2.5 au+or-30% respectively), and the electric quadrupole transition probabilities A_nO(4¹S to 4¹D) and A_nO(4¹S to 5¹D) calculated to be 2287s^-1+or-10% and 760 s^-1+or-20% respectively.

An explanation based on Deodhar's hypothesis (1962) is given for the origin of Coster's low frequency satellite L_{gamma 10} for the first time. This hypothesis is also used to account for the origins of the high-frequency satellites L_{beta i'}, L_{beta i"} amd L_{gamma 2',3} equally well. The assignment proposed by Kapoor et al (see abstr. A10764 of 1970) for the emission of the high frequency satellite L_{gamma i} for some rare earths of the type 4f is now shown to be valid for all the elements Z=41-83 for which this satellite has been reported in the literature. The close agreement between theory and experiment observed in this investigation supports the claim for the validity of Deodhar's hypothesis. Finally, it is pointed out that perhaps X-ray satellites arise to some extent in a way almost similar to X-ray diagram lines.

Relative integrated intensities for the 40 bands of the (B to X) system of lanthanum oxide have been measured by the technique of photographic photometry. A Morse model is employed to compute the Franck-Condon factors and the r-centroids. The variation of the electronic transition moment R_e(r) with the internuclear separation r is found to be R/sub /e(r)=const*exp(1.98r) in the range 1.643AA<r<1.995AA. Smoothed relative band strengths are derived for the 27 bands. Effective vibrational temperature of the source is determined.