Table of contents

The results of new high resolution studies of the ¹ Sigma _u⁺ states of N₂, both Rydberg and non-Rydberg, are summarized and a table of rotational constants and other data is presented. The b' ¹ Sigma _u⁺ state has been studied from v=1 to v=28. The irregularities in the lower vibrational levels and their interpretation as being due to a homogeneous interaction with the first ¹ Sigma _u⁺ Rydberg state c'₄ (i.e. n=4 of (3 sigma _g)np sigma _u) are further documented. At higher levels an even stronger interaction, in this case with the next ¹ Sigma _u⁺ Rydberg state c₅' (n=5) is shown to be occurring.

For pt. II see abstr. A67674 of 1970. Calculations of the 1s-2s and 1s-2p excitation cross sections in e^--H scattering are reported which agree qualitatively with experiment over an energy range from close to the ionization threshold to 54.4 eV.

The reactions which pump the upper laser levels of the He-Cd and He- Zn lasers are investigated by means of a study of excitation during thermal energy charge transfer and Penning reactions in a flowing afterglow of helium. Measurements of emission line intensities from the reaction products enables relative cross sections to be estimated for population of excited states of CdII and ZnII.

The probability of exciting the 2s state of hydrogen in an exchange collision between a proton and a hydrogen atom has been measured by Bayfield. Calculations are carried out which give some evidence on the mechanism responsible for the experimental observations.

Complete two- and three-electron electrostatic effective interactions were included in the energy level calculations of the 3d^N4p configurations of third and fourth iron group spectra. The inclusion of these interactions greatly improved the fit between calculated and observed energy levels. Reliable and consistent values were obtained for the various interaction parameters.

A general formula has been established for the expansion of the product of two normalized associated Legendre polynomials centred on the nuclei a and b. This formula has been utilized for the calculation of two-centre integrals with Slater-type orbitals. For the two-centre Coulomb, hybrid and one-electron integrals (overlap integrals and nuclear attraction integrals) with an arbitrary combination of quantum numbers, analytical formulae have been obtained in a closed form; new auxiliary functions have been introduced, determined by polynomials according to the parameters of Slater atomic orbitals, by means of which all these integrals are expressed in the form of a linear combination. Useful recurrence relations have also been established for these auxiliary functions.

The integral integral f(r) mod r-R mod ^-1 mod r-R' mod ^-1 dr is reduced to a form suitable for numerical computation. The reduction does not depend on the form of the f(r) and consequently the method works equally well for Gaussian and Slater orbitals.

It is shown that Pade approximants can be obtained directly from the Fredholm expansion for scattering phase shifts. The accuracies of various Pade and Fredholm approximants taken up to the third order in the strength of the interaction potential are assessed by evaluating the S-wave phase shifts for the elastic scattering of particles by square-well and exponential potentials. The second-order Pade and Fredholm approximants are found to be quite accurate and both superior to the second Born approximation, while taken to third order they generally yield very accurate values for the phase shifts.

The semi-empirical method of Cushion (1963) for the calculation of vibrational matrix elements for diatomic molecules is improved upon by the employment of more sophisticated potential functions. Comparison with available experimental data shows that the method can provide oscillator strengths for Delta v=1 and Delta v=2 transitions to an accuracy of better than 5% and 50%, respectively.

The continuous oscillator strength df/d epsilon for photoionization of atomic helium is evaluated in the dipole length and velocity formulations using a 50-parameter correlated ground-state wave function together with both Hartree-Fock and polarized-orbitals free-state representations. The results are compared with those obtained from 6-parameter and 20- parameter correlated ground-state wave functions. It is found that if we take a particular free-state representation and calculate df/d epsilon using increasingly more accurate ground-state wave functions then the dipole velocity results tend much more rapidly to a constant value than do those obtained from the dipole length formula. However, if one chooses a particular ground-state wave function and compare the two continuous oscillator strengths calculated with the Hartree-Fock and polarized-orbital free-state representations, then, at low photon energies, there is much better agreement between the two dipole length values than there is between the dipole velocity results.

An impact-parameter treatment is used to obtain cross sections for reactions such as Na ²P₁2/+He to Na²P₃2/+He. The coupled equations with and without rotational coupling are numerically solved. The reaction between this work and the Landau Zener formula is discussed. It is shown that rotational coupling cannot be neglected even at low velocities. The effect of repulsive exchange interaction is shown to be much more important, at temperatures exceeding 400 K, than Van der Waals interaction for Na-He collisions. At 400 K, the cross sections are 78 AA² for Na-He, 68 AA² for Na-Ne and 62 AA² for Na-Ar.

Semi-theoretical potential energy curves for the x¹ Sigma and x³ Sigma states of the diatomic alkalis Na₂, K₂, Rb₂, Cs₂ and RbCs are presented and compared with other estimates. Using these potential-energy functions calculations of the total elastic and spin-change cross sections have been made. The cross sections are compared with experimental data and with the results of other theoretical calculations.

Physical considerations based on the fact that colliding atoms or molecules are deformed during their collision are used to separate the low-energy repulsive part of the pair potential into single-molecule properties. A prescription for deriving combining rules for two-parameter potentials is obtained and is then applied to the Lennard-Jones 12-6 potential. The predicted characteristic energies for unlike pairs are markedly better than those obtained from existing combining rules and are usually within 10% of the observed values.

Collisions between H⁺ ions and H(1s) atoms are studied theoretically, allowance being made for the fact that the relative motion of the nuclei is not rectilinear. A simple physical argument is given for supposing that if the encounter is sufficiently close and fast and if the axis of quantization is taken to be parallel to the final direction of the velocity of relative motion vector then the probability of excitation to the 2p_+or-1 state around either nucleus is ¹/₂ sin² Theta where Theta is the scattering angle in the centre of mass system. This prediction is verified by computations in which the electronic motion is treated by the perturbed stationary state method (in a 4-state approximation) and the motion of the nuclei is treated semi-classically with a forced common turning point. Other aspects of H⁺-H(1s) collisions are covered by the computations. The results are in accord with the results of the full quantal investigation recently carried out by Knudson and Thorson (abstr. A30138 of 1970). Special attention is given to the case of 6 degrees scattering. Satisfactory agreement with the measurements of Lockwood and Everhart (abstr. A3715 of 1962) is achieved.

Cross sections for symmetrical resonance and asymmetrical resonance charge transfer occurring between protons and hydrogen atoms in the second quantum level have been calculated in the quantal two-state and eight-state approximations using the impact parameter formulation. Momentum transfer has been taken into account by the method suggested by Cheshire (1967). As one goes from the quantal two-state approximation to the eight-state approximation, there is a considerable change in the results, especially at low energies of impact. The cross sections obtained by the quantal eight state approximation and those obtained by Bates and Reid (1969) using a classical approximation are in remarkably close accord.

Excitation cross sections for the processes He(1¹S)+B to He(N¹L)+B( Sigma ) for N=2, 3, 4, 5 and L=S, P, D, and for target atoms B of helium, neon, argon and krypton are calculated over the incident energy range 1.0 keV-6.4 MeV, in the first Born approximation with the added approximation of closure used to describe excitation of the target. Scaled cross sections are also calculated for neon, argon and krypton target atoms over the incident energy range 1.60 keV-400.0 keV by use of velocity-dependent scaling factors determined from electron-loss data for the collision of hydrogen atoms. At this time the tentative nature of such an application of the scaling factors must be emphasized.

The effect of substitution by weakly perturbing substituents on the breathing frequencies, nu ₂ and nu ₆, of benzene have been studied semi-empirically. The magnitudes of these frequencies in polysubstituted benzenes are given by the relation nu ₂(subs)= nu ₂(benz)-( Sigma _ma_m+ mod Sigma _mb_mexp(im pi ) mod ²) and nu _u(subs)= nu ₆(benz)-( Sigma _mc_m- mod Sigma _mb_mexp(im pi ) mod ²) for the symmetric and the trigonal one respectively, where a_m, b_m and c_m are the characteristics of the substituent at position m of the ring. The ratio of intensities of respective vibronic bands in the longest wavelength electronic spectra of polysubstituted benzenes is I_u'/I_g'=(0.01) mod Sigma _mb_m exp(im pi ) mod ².

For pt. I see abstr. A43263 of 1968. A previously published theory describing the vibrational relaxation of a system of anharmonic oscillator diatomic molecules has been extended to cover situations in which a continuously changing translational temperature is imposed on the gas. With this extension, the theory is applicable to the results of recent experiments in which vibrational relaxation has been studied in expanding gas flows, several of which have indicated anomalously fast rates of de-excitation in N₂ and CO. Calculations including the effects of rapidly falling translational temperature have been performed for CO. It has been found that near-resonant vibration-vibration exchanges continuously distort the vibrational distribution function in response to the changing translational temperature. This distortion does not contribute to the vibrational de-excitation of the gas, since the vibrational exchange processes do not remove vibrational quanta from the molecules. However, in an expanding flow it causes a continuous reduction in the vibrational 'temperature' of the 1 to 0 transition and can therefore give the appearance of a rapid rate of de- excitation. An empirical expression for the apparent rate of de-excitation is given in an appendix.

The effect of irradiation from an incandescent light source on the average current of a discharge in argon (the Joshi effect) was studied for pressures of 0.7 to 10 torr using a cylindrical glass vessel (length 1.2 cm, diameter 5.3 cm) and applying an a.c. voltage (of frequency 20-500 Hz) to external electrodes. The first current pulse group in each half cycle was found to consist of a steady wide low pulse which appears at a constant phase angle and a flickering narrow high pulse erratic in phase angle. Irradiation with a 200 W lamp placed 30 cm from the vessel reduces the amplitude of the second pulse considerably. By increasing the applied voltage beyond threshold the relative change in average current Delta I/I was found to increase continuously whereas other workers have always observed a decrease in Delta I/I with rising V.

The transport of electrons through gases in the regime of elastic and inelastic collisions is discussed and it is shown how the equation for the energy distribution derived by Smit follows more simply from consideration of the velocity diagram. The present analysis was applied to helium, neon and helium-neon mixtures where numerical integration techniques were employed to calculate electron energy distribution functions and transport coefficients in the range 3<or=E/p₀<or=40 V cm^-1 torr^-1. The present results are compared with previous theoretical calculations and experimental measurements of electron transport coefficients and it is shown that approximations involved in some previous calculations can lead to significant errors.

Theoretical wavelengths and oscillator strengths have been calculated in the single configuration Hartree-Fock approximation for 3p³⁴S-3p²(³P)3d ⁴P transitions in Ar IV-Fe XII within the L-S coupling approximation. Comparison is made with experimental and theoretical results, whenever available.

Polarization effects in stimulated Raman and stimulated Rayleigh scattering and self focusing are investigated from the viewpoint of the scattering of polarized photons by molecules. Both stimulated vibrational Raman scattering in liquids and stimulated rotational Raman scattering in gases are considered, and it is demonstrated that the polarization changes and relative power thresholds for different laser polarizations should be somewhat different to those predicted in other theories. For example, the ellipticity eta ⁰ of the stimulated rotational Raman photons in the forward direction from Delta J=+or-2 transitions in gaseous symmetric top molecules is given in terms of the initial ellipticity eta ¹ by sin 2 eta ⁰= -⁵/₇ sin 2 eta ¹, whereas conventional theories predict that eta ⁰ and eta ¹ are equal in magnitude and opposite in sign. Furthermore it is shown that deviations from this relation could provide a measure of the degree of optical orientation of the molecules.