Table of contents

It is shown that the non-negative expectation values of (r^k) in the Coulomb approximation, when only one Whittaker function in the integrand is expanded in an asymptotic series, is identical to the corresponding hydrogenic expressions evaluated at non-integral quantum numbers. A test for the validity of the hydrogenic normalization is suggested and generalization to the calculation of oscillator strengths is discussed.

The velocity distribution of H(n=3) atoms produced by electron impact on H₂ has been obtained indirectly from the study of anti-crossing signals on the H_alpha line of atomic hydrogen. Two distinct groups of velocities have been detected: slow atoms at 8 and 9 km s^-1 appear above a threshold at 17.2 eV, fast atoms with a continuous range of velocities between 30 and 40 km s^-1 above 27 eV.

The total cross sections for positrons in He, Ne, Ar and Kr have been measured in the energy range 2-400 eV, using a time-of-flight technique, and compared with those of other authors.

The 400 eV(e,2e) experiments of Weigold et al (1973) on argon are analysed in the off-shell impulse approximation using Hartree-Fock single particle wavefunctions. The theory fits the data excellently. It is sensitive to the model used for the single particle wavefunctions. Spectroscopic factors describing the probability of each of the observed excited states of the Ar II ion consisting of a 3s^-1 configuration are obtained from the analysis. They obey the appropriate sum rule, thus confirming the validity of the theory.

The angular dependence of resonance structure in elastic electron-mercury scattering is studied for electron energies from 4 to 5.5 eV. The results confirm the spectroscopic classification ²D_3/2 and ²D_5/2 to the resonances at 4.5 eV and 5.15 eV proposed by Fano and Cooper (1965).

Ab initio valence shell CI calculations of full potential curves for the quartet states of N₂⁺ show that several of these are bound and have lower energies and larger equilibrium distances than expected.

The authors present a fully quantum mechanical calculation of the higher order terms in the Bloch-Siegert shift. Contrary to Cheng and Stehle's (1971) QED calculation, the results are in complete agreement with those of semi-classical approaches, as can be expected in the RF domain.

The authors present an experimental check of the method used in the preceding note (see ibid., vol.6, l214, 1973) for calculating higher order radiative shifts of magnetic resonances. Although indirect, this check is conclusive as regards the validity of the method.

Analytical expressions are obtained for the Bloch-Siegert shift in magnetic resonance experiments using results derived previously by Shirley (1965) Series (1973) from semiclassical theory. These expressions together cover the whole range of the shift from 0 to 100%.

An emission spectrum of C⁸⁰Se is observed between 3950 and 4400 AA. The a³ Pi _1,0+ to x¹ Sigma ⁺ system is responsible for this emission. Carbon tetrachloride and traces of selenium vapour diluted in helium are sent to a Schuler type discharge. Both 0-0 sub-bands are analysed; their origins are situated at: 24396.6 and 24080.0 cm^-1. Some constants are determined: B'₀=0.544 (+or-5) cm^-1; B"₀=0.574(+or-5) cm^-1; r'₀=1.72 AA; r"₀=1.68 AA; Delta G_1/2(³ Pi _o) approximately=894 cm^-1; omega '_e(³ Pi _o)=910 (+or-5) cm^-1; T_e(³ Pi )=24470 cm^-1; A_v=0=326.₅ cm^-1.

Transitions which occur in collisions involving two heavy particles and a light particle may be treated in the impact parameter approximation. It is shown that in the limit that the heavy particles become infinitely massive, the Born expansion in the impact parameter treatment is exactly equivalent to the Born expansion in the correct wave treatment. This result has previously been proved for direct transitions and the present paper extends the proof to rearrangement transitions.

The authors show that the method used by Reinhardt et al (1972) to calculate the Fredholm determinant converges slowly. The dominant term in the error is evaluated and Reinhardt's success in calculating phase shifts is explained. An alternative way of using the Fredholm method is suggested which avoids the need for an extrapolation procedure.

The authors give the asymptotic expansion of the J=0 wavefunction for electron-hydrogen atom scattering which contains a leading term corresponding to an outgoing wave in any two-body channel. The coefficients in the expansion are found from a recurrence relation for the solution of which a computer program is written.

A simple variational calculation, suggested by work on hydrogen atom multipole polarizabilities, is applied to calculate second-order energy shifts E₂(l) for the 1s² configuration. The results for l>or=3 are better than some of those given by much more complicated calculations. Certain first-order expectation values are calculated exactly, and provide a sensitive check on the first-order perturbed wavefunction.

The solution of the first-order Hartree-Fock equations for the nsms ¹S states of helium-like ions for the case where the orbitals are constrained to be orthogonal is discussed. It is shown that the zero-order solutions discovered by Rebelo and Sharma (1972) uniquely determine the first-order solutions.

Hartree-Fock calculations are reported for individual terms of np⁵(n+1)p configurations in the Ne I (NwI, Na II, Mg III) and Ar I (Ar I, K II, Ca III) isoelectronic sequences with special emphasis on the ¹S term. For this term, the conventional restricted Hartree-Fock approach does not provide upper bounds to the energies, because of mixing with the np⁶¹S groundstate. Orthogonality to the groundstate has been introduced explicitly in the calculations. It is shown that, although this procedure provides upper bounds for the energies, the absolute errors are larger than in the conventional approach. Non-diagonal energy parameters are of importance in the calculations, especially for ¹S. For the ¹S term in Ne I, the epsilon _3p,2p parameter is larger than the diagonal epsilon _3p,2p parameter. This appears to be the first time such a case has been reported. The size of the non-diagonal energy parameters necessitated some modifications of the calculational procedure.

The semiclassical theory of uniform approximations to the cross section for small-angle scattering is investigated numerically for various potential models, including the familiar Lennard-Jones interatomic potential. Calculations of the differential cross section using the semiclassical formulae are compared with quantum mechanical calculations to investigate the accuracy and range of validity of the uniform approximations. It is demonstrated that such methods can predict very precisely the shape of the differential cross section over a surprisingly wide range of conditions.

The method of Huzinaga and Arnau (1970, 71) for improving virtual orbitals in the Hartree-Fock is discussed from different points of view. An application to the calculation of excitation energies and oscillator strengths (f values) for the helium atom is given. The calculated excitation energies are found to be accurate to within 2 to 3%. The agreement of the calculated f values with those obtained by more sophisticated methods is remarkable.

It is proven that the model transition probability sin2( tau x)sech²( tau y) for perturbed symmetric resonance, where tau is the collision time and x+iy is the complex adiabatic action difference integrated along a line joining the point of closest approach to a complex adiabatic degeneracy, is exact not only for (unperturbed) symmetric resonance but also for the Rosen-Zener and the Callaway-Bartling model potential problems. The theories of Stueckelberg (1932), Demkov (1964) and Nikitin (1968) are reconciled in that all provide good approximations to the new formula under various different restrictions. Further model potential problems are presented as illustrations of the efficacy of the model formula.

It is demonstrated numerically that detailed balance indeed is well satisfied in the multi-state impact parameter formulation of proton-hydrogen atom collisions. It is also demonstrated numerically that detailed balance is a much more sensitive test of computational accuracy than is the charge conservation test usually employed in such impact parameter calculations. It is suggested that detailed balance be used as a check on all impact parameter calculations. That even agreement with detailed balance may not be a sufficient test for accuracy of the results is pointed out.

The polarization of the resonance lines of ⁶Li, ⁷Li and Na, excited by electron impact, are calculated using the Glauber approximation. The present results are in good agreement with experimental values and with other theoretical calculations in the energy range from 2 eV to 5 eV.

A polarized orbital distorted wave model is used to calculate total and differential cross sections for 1s to ns(n=2,3,4,5) electron impact induced transitions in H and He⁺ from threshold to 20 Ryd. The total cross sections for the 1s to 2s transitions are in good agreement with experiment, but cannot in this model show resonances. The differential cross sections at energies above 100 eV agree closely with those of Geltman and Hidalgo (1971). The model reduces to the Born-Oppenheimer (z=0) or CBO I(z=0) when the polarization and static potentials are omitted.

Photoionization cross sections are expressed in terms of quantities which vary slowly as functions of energy, and known functions which may vary rapidly. The theory is applied to photoionization of Be, with inclusion of the Be⁺ 2s and 2p states. The slowly varying functions are computered at energies above the 2p threshold and extrapolated to the resonance region below the threshold. A parametric form is obtained for the calculation of resonance structures this is superior to the form obtained by Fano (1961) for the case in which the widths of the resonances are comparable with the separation of resonances in a Rydberg series.

The theory of multiphoton ionization for an atomic system of arbitrary complexity is developed using a density matrix formalism. An expression is obtained which determines the differential N-photon ionization cross section as a function of the polarization states of the target atom and the incident radiation. The parameters which characterize the photo-electron angular distribution are related to the general reduced matrix elements for the N-photon transition. Two-photon ionization of unpolarized atoms is treated as an illustration of the use of the theory. The dependence of the multiphoton ionization cross section on the polarization state of the incident radiation, which has been observed in two- and three-photon ionization of Cs, is accounted for by the theory. Finally, the photoelectron spin polarization produced by the multiphoton ionization of unpolarized atoms, like the analogous polarization resulting from single-photon ionization, is found to depend on the circular polarization of the incident radiation.

General formulae are derived for the rotational energy and fine structure of Hund's case (c) electronic states in diatomic molecules. The calculation is based on a perturbation approach in which the total electron Hamiltonian (including relativistic effects) is taken as the unperturbed Hamiltonian. The'small' Coriolis term -2BJJ_a (which lead to a case transition) then represents the only perturbation operator of interest. This enables the calculation of converge rapidly, with the consequent result that one obtains compact intermediate case (c)-case (e) energy formulae of high accuracy. Furthermore it is shown how the standard case (a)-case (b) formulae emerge as special cases of the general intermediate case (c)-case (e) expressions. The present treatment is confined to the following values of mod Omega mod : mod Omega mod =1/2, 3/2, 0, 1 and 2, which are believed to represent the states observable in practice.

For pt. I see ibid., vol. 6, 1479 (1973). A theoretical discussion of the rotational energy and fine structure of Hund's case (c) states in diatomic molecules was given in Pt. I. In this paper the theoretical results are applied to several electronic states of heavy diatomic molecules. The states chosen are the E_1/2 and F_1/2 states of YbH and YbD, and A² pi , B² Sigma and C² Sigma states of HgH and the x³ Sigma ^- ground states of AsF and SO. This variety of states exemplifies several aspects of the theory, which in particular for the ³ Sigma states gives a much more the traditional Hund's case (a)-(b) model.

An apparatus is described in which beams of electrons and H^- ions intersect at an angle of 10 degrees . This was used to make a large number of absolute measurements of the detachment cross section of H^- for energies between 12 and 22 eV, with an energy resolution of about 0.25 eV. The existence of a large structure in the detachment cross section reported by Walton et al. (1971) was confirmed and, in addition, a second resonance was revealed which had an apparent width of order 0.4 eV at an energy 17.1+or-0.35 eV above the ground state of H^-.

The band spectrum of SrI is excited in a high frequency discharge through a mixture of heated strontium metal and iodine vapour, from a ¹/₂ kW oscillator working at a frequency of 30-40 MHz. High resolution spectrograms of SrI in the region lambda 6500- lambda 7200 have shown the existence of two doublet systems consisting of a number of well marked sequences of bands degraded to shorter wavelengths. The double-headed bands are analysed and attributed to A² Pi -x² Sigma and B² Sigma -x² Sigma transitions analogous to the A-X abd B-X systems of SrF, SrCl and SrBr molecules. The vibrational constants of the ground states and excited states and doublet intervals of analogous states of the isoelectronic molecules have been compared. The vibrational quantum formulae which represent the inner P₁ and Q₂ heads of the alpha ² Pi -x² Sigma system and P₁ heads of the B² Sigma -x² Sigma system are given.

The operation of a nuclear spin maser oscillator with two independent resonant coils through which the active maser medium flows in succession is described. It is shown experimentally that the variation of the oscillation amplitude in the second coil as a function of particular parameters of the nuclear maser system is analogous to that obtained with a molecular beam maser operated with two cavities in series. A simple univelocity theory is presented which accounts for the gross features of the experimental results obtained with the two-coil nuclear maser. The influence of the velocity distribution of the nuclei is also investigated.

Neodymium glass laser pulses of up to 2 GW power, 10 ns duration and focused flux densities up to 2*10¹³ W cm^-2 have been used to form plasmas at temperatures up to 450 eV. Plane solid plastic targets with atoms of hydrogen, nitrogen, carbon, oxygen and fluorine were used. The relation between laser flux density and electron temperature was studied and found to be of the form temperature varies as (flux density)^x where x=0.40+or-0.05. Both the power law and absolute temperature are consistent with steady state hydrodynamical theories predicting x=⁴/₉. Temperatures were deduced from soft X-ray continuum emission using both relative and absolute intensities. The spatial features of the X-ray emission were observed with a pinhole camera. Grazing incidence XUV photographic spectra were used to identify the highest degree of ionization in the plasma. The results were correlated with steady state and transient ionization theories and with the measured electron temperature. Satisfactory agreement was found when self-absorption of resonance radiation was taken into account.

The processes which excite and de-excite levels of the zinc ion in a helium afterglow containing zinc vapour are studied using a flowing afterglow technique. It is shown that thermal energy charge transfer reactions between atomic helium ions and ground state zinc atoms result primarily in the excitation of the 6p²P and 5d²D levels of Zn II. The 6s²S levels receive their excitation via radiative cascade from the 6p²P levels. The 4f²F levels are excited by a two step process: charge transfer excitation into 4f²F. The collisional destruction rate of the 6p²P levels of Zn II is also measured. The observed collision processes are significant not only for the understanding of the He-Zn laser but also because of their implications for power output capabilities of charge transfer excited laser systems in general.

Intermediate coupling theory has been used along with the results from nonrelativistic Hartree-Fock calculations for average atomic configurations reported earlier to determine the energy characteristics of the multiplet structure associated with M-shell Auger and Coster-Kronig transition processes in the krypton atom. Detailed findings are presented for the neutral atom, while for the various multiply ionized states of the atom the relevant radial integrals are provided. These will enable the many multiplets of the possible radiationless de-excitation processes to be evaluated as required. For the M₄₅-N₁N₂₃ and M₄₅-N₂₃N₂₃ processes where the fine-structure is experimentally well resolved the predicted lines from an adiabatic model are within 1 to 3 eV of the observed peaks. For other processes the limited information available suggests that larger deviations may occur, especially when configurations involving holes in an s subshell are involved.

Stark broadened wavelength profiles of the hydrogen-like lines carbon VI (6-7) 3434, (7-8) 5290 AA and the quasi hydrogen-like lines carbon V (5-6) 2982, (6-7) 4945 AA have been recorded, with time resolution, in the high density plasma produced by the laser-irradiation of a polyethylene foil in vacuum. Stark theory of relevance to these new lines is reviewed. Half-widths are calculated for values of electron and ion density deduced from line intensities, and are compared with experiment. It is shown that the broadening is predominantly ion quasi-static, with C⁶⁺ and C⁵⁺ as the principal perturbing ions. The electron impact contribution to the broadening would be at least as great as the ion contribution if it were not for correlations in the perturbations of the upper and lower states. There is a factor of two difference between theory and experiment, which is about the maximum which can be explained in terms of errors in the experiment and in the formulation of the Stark theory.

The transient absorption time-profiles observed in the laser photolysis of benzenoid aromatic hydrocarbons are analysed in terms of the well established transition mechanisms for these molecules, and the theoretical and experimental traces are compared. The effects of fluorescence and ground state absorption on the time profile are considered, and the importance of fluorescence corrections is demonstrated for the case of 1,12 benzperylene.

The Lyman series has been observed for the hydrogen-like system of bare nitrogen (+7) plus an electron. The experimental resolution for these X-ray lines is about 2 eV.

Employing a high power, narrow band, frequency tunable dye laser, the 6s6p¹P₁⁰ level of Ba I has been selectively excited. The excited state absorption series 6s6p¹P₁⁰-6snd¹D₂ has been measured and extended from n=9 to n=41 and series perturbations by ¹D₂ levels have shown lines of the 6s6p¹P₁⁰-6s(n+1)s¹S₀ series. Terms of the auto-ionization series 6s6p¹P₁⁰-5dns¹D₂ have also been observed and assigned.

The hydrogen atom in a strong magnetic field is represented by means of sturmian functions, which offer a complete basis which is well adapted to describing the distortion induced by the field. Methods of computation of the eigenvalue spectrum using this basis are described, and a critical comparison made with results obtained by use of the incomplete basis of hydrogenic radial functions. A brief account is given of the techniques employed for dealing with the very large matrices appearing in the calculations.

It is shown that both for single and coupled spin systems in external magnetic time dependent fields, the quantum mechanical solution determines a unique solution for the classical motion of a single or a coupled system of rigid bodies with prescribed angular velocities proportional to the external field, the converse being also true.

The method is based on replacing the actual field B by an 'integrable' field, i.e. one for which the Schrodinger equation can be integrated. A simple criterion allows the best choice of field to be made for a given degree of approximation. Two examples are discussed: (1) the classic case of a small oscillating field transverse to a large steady field to an approximation beyond the rotating wave approximation, which reproduces, with certain modifications, the results of Bloch and Siegert valid for any j; (2) the field configuration of Pegg and Series (1970).

The introduction of a suitably moving coordinate system results in approximate equations of motion which lead in a direct manner to the Block-Siegert resonance shift, to 2nd or higher order, and to a simple visualization of multiple quantum transitions, including their correct quantitative treatment. The relation between the present method and that due to Shirley (1965), whose results are confirmed, is pointed out.

The continued fraction method which has been adapted to the longitudinal optical pumping by Stenholm (1972) is used in a phenomenological Bloch equation to study the saturation effect of the Haroche's resonances, caused by the transverse pumping. The present authors give calculations of the positions and shapes of the Haroche's resonances for large intensity RF field, which differ from earlier work for a weak RF field by Cohen-Tannoudji and Haroche (1967). It is shown that the variation of the width of the Hanle curve by the oscillating RF field, i.e. the modification of the atomic g factor, is closely connected with the behaviour of the Haroche's resonances.

The author attempts to show that, in contradiction with work by Chang and Stehle, the semiclassical description of RF resonance experiments is valid. The density matrix equation of motion is set up for a two-level atom interacting with a one-mode quantized field. The terms giving the semiclassical description are separated and the contributions arising from the rest are carefully evaluated. Corrections to the semiclassical treatment are found to be of order n₀^-2, where n₀ is the average number of RF photons. In practice such corrections are negligible.

Rotational analyses have been made of bands in the systems G² Pi -X² Pi , H² Pi -X, D² Sigma ^--X and C² Delta -X. Numerous perturbations indicate the presence of three further states, K, L, and M and reassignments have suppressed states A' and I. The variation with internuclear distance of spin-orbit coupling in the ² Pi -states is examined. All the states and constants of AsO are reassessed and the best available values are summarized.

Calculations of state functions in equilibrium plasmas produced behind shock-waves in potassium and caesium vapour are described and the results are presented graphically. For a given initial temperature T₁ of the saturated vapour and a given Mach number M of the incident shock, the temperature, density and degree of ionization behind both the incident and reflected shocks were calculated from the Rankine Hugoniot relations and the Saha equation over the range 3<or=M<or=16 and 580<or=T₁<or=700K for potassium and 520<or=T₁<or=640 K for caesium. The atomic energy levels and degeneracies were fed into the calculation to allow the partition function and the energy in the excited states to be evaluated. The levels were truncated by two different procedures and the effects are shown on the graphs.