Table of contents

An error is pointed out in the expression given many years ago for the differential cross section for ionization by electron impact of the 2p(m=+or-1) states of a hydrogenic atom, calculated using Born's Approximation.

An analytic solution is presented for the problem of construction of a nonspherically symmetric separable potential from scattering data. The input data employed consists of the forward and backward values of the scattering amplitude for all the directions of incidence and at all the energies. The authors' result is a generalization of the solution given by Gourdin and Martin for the spherically symmetric case. Possible applications of effective interactions so determined are briefly discussed.

Inelastic e-H differential cross sections are evaluated using previously derived theory. The results compare well with the angular and energy distributions of the Coulomb projected Born approximation confirming the discrepancy with the Born. The ambiguities in the absolute value of the differential cross section which were found for elastic scattering are still evident for the inelastic case.

The process of recombination of positive and negative hydrogen ions is considered at low energies. The exchange interaction in (H⁺, H^-) system at the relevant pseudo-crossing points is found asymptotically exactly. In the cross section calculations of the process account was taken for the exponential character of this interaction and non-divergency of the potential energy curves at infinity.

The author draws attention to the fact that the recent results of Lloyd et al. (see ibid., vol. 5, 1712 (1972)) were incorrectly compared with those of Kupriyanov (1966) and that they can be more suitably compared with those of Dorrestein (1942) and of Hotop and Niehaus (1968).

A new coincidence technique has been used to study the polarization of radiation from atoms excited by electron impact. The measured polarizations are as predicted theoretically, in contrast with results obtained by the older 'threshold polarization' technique. The present coincidence technique can be extended to study details of excitation mechanisms.

For pt. I see ibid., vol. 5, L196 (1972). An analytic formula for rapid calculation of rates of N-photon electron detachment of negative ions is obtained. Two-photon (ruby) detachment rates of I^-, Br^- and F^- are estimated and compared with the corresponding perturbative estimates (and an experimental measurement). The conditions of validity and the usefulness of the formula is discussed. The estimated three-photon (ruby) rate in Cl^- is also given.

The K X-ray spectrum from a 30 MeV chlorine ion beam was measured as it was stopped in aluminium. The spectrum exhibits six lines located approximately half way between the K_{alpha 1,2} and K_{beta 1,3} lines of chlorine. These lines can be interpreted as K_alpha transitions with various 2p shell vacancies and with the M shell electrons partially stripped.

For pt. I See Abstr. A930 of 1971. It is shown how the integral integral f(r)Y_LM( theta , phi ) mod r-R mod ^-1 mod r-R' mod ^-1dr can be reduced to a single integral on the interval (0, 1) which is amenable to numerical computation. The analysis does not depend on the functional form of f(r). Integrals involving products of spherical harmonics are also discussed, in particular the case where the integrand contains a product of two spherical harmonics.

The problems connected with extracting useful information from the local perturbations which are often observed in the spectra of diatomic molecules is briefly discussed. The interest is in particular focused on the cases for which the perturbing state cannot be observed through transitions to other states. It is shown that the most important parameters of the unobserved perturbing state can be evaluated from an exact numerical diagonalization of the appropriate secular matrix combined with a least squares fitting procedure. The usefulness of the method is exemplified for the case of OH⁺ which has strong perturbations in the A³ Pi , v=1 sublevels. The Lambda doubling parameters of the A³ Pi , v=1 sublevels (A³ Pi -x³ Sigma ^- interaction) are recalculated and brought into agreement with those of the unperturbed A³ Pi , v=0 levels.

Asymptotic expansions in the internuclear separation R^-n of the dipole transition moments Q(R)=( psi (r mod R) mod r mod psi '(r mod R)) involving the electronic Born-Oppenheimer states of H₂⁺ are presented. The four leading terms of all non-zero dipole transition moments involving the 20 states correlating to a proton and a hydrogen atom with principal quantum number n=1, 2, and 3 are given. Numerical calculations indicate the expansions are useful beyond R=10a₀ for transitions involving only the n=1 states. The useful range decreases with increasing n, as expected. The coefficients of the charge transfer transitions can be related to the permanent dipole and polarizability of the hydrogen atom in the field of a proton. A perturbative approach due to Coulson, usable for larger systems, was found to give the same asymptotic coefficients.

A calculation of optical dipole transition oscillator strengths between the 1 ¹S, 2 ^1,3S, 2 ^1,3P, 3 ^1,3S, 3 ^1,3P and 3 ^1,3D states of helium using perturbation theory is described. The method is based on zero order wavefunctions generated by the frozen core Hartree-Fock approximation. The results to second order are in excellent agreement with the values calculated by Pekeris and co-workers.

The wavefunction for electron collisions with an N-electron atom is expanded in the form Psi = Sigma _i Theta _i+ Sigma _j Phi _jc_j where Theta _i is an antisymmetrized product of an atomic eigenfunction times an orbital function theta _i for the colliding electron; theta _i contains a radial function F_i; Phi _j has the form of a bound state function for the (N+1)-electron problem. The condition is imposed that (P_gamma mod F_i)=0 if l_gamma =l_i, where P_gamma is an atomic radial function and where l_gamma and l_i are orbital angular momenta associated with P_gamma and F_i; this condition does not imply a restriction on Psi so long as a suitable set of states Phi _j is included. The variational principle is discussed and two approximations are described: (i) The distorted wave (DW) approximation is valid when the coupling is not too strong. Particular attention is paid to the normalization of the DW functions F_i. The coefficients c_j are determined using the variational principle. (ii) The variational principle is used to obtain a set of coupled integro-differential (ID) equations for the determination of the functions F_i and the coefficients c_j.

A theory is developed of the process e+H(n_pl_p) to e+H(n_ql_q) making exact allowance for the long-range dipole interactions. It is predicted that at threshold the cross section Q(n to n+1) approximately n⁶(n<or=33) and n⁵(n>33) while at sufficiently high energies the more familiar law Q(n to n+1) approximately n⁴1n n is recovered. The threshold behaviour has some effect on thermal reaction rates for n<or approximately=20.

For pt III see abstr. A70819 of 1972. The theory of scattering of low energy electrons by closed shell polyatomic molecules is developed. Coupled inhomogeneous differential equations are obtained describing the motion of the scattered electron in the fixed nuclei approximation. The symmetry group of the molecule is used to reduce these equations to their simplest form and expressions for the total, differential and momentum transfer cross sections are obtained. A transformation to the laboratory frame is then derived and this is used to obtain expressions for the rotational excitation cross sections in terms of the S matrix calculated in the fixed molecular frame. Special emphasis is given in this paper to the C_2v and O_h symmetry groups and the equations describing electron scattering by water molecules are discussed in some detail.

The S state elastic scattering resonances below the n=2 level of the electron-hydrogen system are investigated numerically in the 1s-2s-2p close-coupling framework. The assumption that the 2s and 2p levels of hydrogen are degenerate is dropped. Of the infinite sequence of resonances which is obtained when complete degeneracy is assumed, it is found that only five singlet and four triplet resonances remain in the presence of a 2s-2p splitting of 3.22*10^-7 Ryd, the approximate experimental value in hydrogen. More generally, there is a splitting which will cause any given resonance to vanish, that is, to be pushed above the hydrogen 2p level; these critical splittings are determined. In terms of the critical splittings, it is found that all shifts in resonances due to an arbitrary 2s-2p splitting fall on a single universal curve. As a result, a simple recursion relation among resonances in the presence of an arbitrary splitting can be obtained.

Cross sections for the excitation of the 2³P and 3³P states of helium from the ground state by electron impact are calculated using Ochkur approximation. Results are compared with various theoretical cross sections and experimental data.

The problem of an atom interacting simultaneously with the quantized modes of the vacuum electromagnetic field and with a classical time dependent field is investigated utilizing the general theory of damping devised by Heitler. Spectral lineshapes are obtained as a function of the variables of the classical field and are studied in detail for the case of spontaneous emission from coupled levels of dissimilar lifetimes. In the limit that the time dependent coupling vanishes, the resulting spectral line is the same as that derived by Weisskopf and Wigner.

The theory of photoionization measurements for a general atomic system is developed in terms of a density matrix which determines the ejected electron and residual ion polarizations as a function of the target atom and incident photon polarization states. Expressions are derived which relate the photoelectron angular distribution and spin polarization parameters to the reduced matrix elements for the photoelectric transition. These expressions incorporate the fine structure of the atomic levels and the complete interaction between the residual ion and the ejected electron. The polarization of the residual ions which are formed in excited states is treated in terms of the subsequently emitted decay radiation.

Differential cross sections for the photoelectric transitions He(2¹S₀,2³S₁)+h(cross) omega to He⁺(1s,2s,2p,3s,3p,3d)+e^- have been calculated for incident photon energies above the n=2 threshold using Hylleraas bound state wavefunctions and close coupling final state wavefunctions. Particular attention has been given to the angular distribution of the photoelectrons ejected in the transitions to the excited states of the residual He⁺ ion. When the partial cross sections are transformed to a representation which diagonalizes the long range r^-2 interactions coupling degenerate final state channels, it is found that some linear combination of the degenerate channels is preferentially excited over a range of incident photon energies from the threshold to several times the threshold value. At higher energies the calculated ( sigma _2s+ sigma _2p)/ sigma _1s and ( sigma _3s+ sigma _3p+ sigma _3d)/ sigma _1s ratios approach the asymptotic values predicted by the theory of Kabir and Salpeter.

The photoionization cross sections of H^- and He(1¹S₀) have been calculated for incident photon energies above the n=2 threshold using Hylleraas bound state wavefunctions and close-coupling final state wavefunctions. At low energies it is found that excitation to the 2p state of the residual atom or ion is more probable than excitation to the 2s state, a result which is in disagreement with calculations which do not include the effects of close-coupling between the final states. An analysis indicates that the relative distribution between the n=2 states is determined mainly by the long-range 2s-2p dipole coupling. This is revealed by the dominance of a particular partial cross section in a representation which diagonalizes the long range r^-2 interactions coupling the degenerate n=2 states. Finally, the angular distribution of the ejected electrons is calculated in the case of H^-.

The photoionization absorption coefficients of helium, neon and argon have been measured by single beam photometry in the 60-230 eV photon energy range using a synchrotron radiation source and channel electron multiplier photodetection. The accuracy of most of the data is +or-3% rising to +or-5% for a few cases in helium. Agreement with theory is typically better than 20% for photon energies up to 150 eV with greater discrepancies at higher energies especially for helium and argon.

The generalized oscillator strengths of the transitions 4¹S-4¹P in zinc and 5¹S-5¹P in cadmium have been studied at 255 eV incident electron kinetic energy over an angular range 3 degrees to 20 degrees . The data have been placed on an absolute scale by normalizing to the optical oscillator strength. The first non-zero minima were observed at ( Delta P)²=1.0 au and 0.8 au, for zinc and cadmium, respectively. The positions of the second maxima were found to be ( Delta P)²=1.5 au and 1.7 au, for zinc and cadmium, respectively. Comparison is made with theoretical calculations.

The broadening and shift of the calcium resonance line, lambda 4227 angstroms, have been measured with high accuracy when the line is formed in absorption under pressures of He, Ne, Ar, Kr, and Xe up to one atmosphere. He and Ne cause symmetrical broadening over the entire pressure range in agreement with the predictions of the 'impact theory'. The onset of asymmetrical broadening indicating breakdown of the 'impact approximation', is noticed at pressures of Ar, Kr, and Xe close to one atmosphere. The peculiar way in which broadening and shift change with perturbing gas is discussed in terms of 6-12 and 6-8-12 interatomic potentials.

Measurements of O₂⁺ recombination rates at translational temperatures between 600K and 2500K, obtained using the shock tube technique, are presented. They follow a T^-0.63 dependence, with alpha having a value 1.14*10^-7 cm³s^-1 at 625K. It is concluded that ground vibrational state recombination was observed and this is discussed with reference to the GVS model of dissociative recombination.

For pt. I see ibid., vol. 5, no. 9, 1773 (1972). Measurements of N₂⁺ recombination rates at translational temperatures between 700 K and 2700 K, obtained using the shock tube technique, are presented. They follow a T^-0.37 dependence and extrapolate to a value of 1.78*10^-7 cm³s^-1 at 300 K. It is concluded that ground vibrational state recombination was observed and the results are compared with other measurements reported.

A new type of potential function is derived from the atomic Hartree-Fock self- consistent potential which has almost identical occupied orbitals, but an adjustable set of unoccupied bound orbitals. Comparisons are made between the properties of this potential and the Hartree-Fock potential for trivalent praesodymium. It is shown that the use of the new potential introduces considerable simplifications into atomic configuration interaction calculations.