Table of contents

A form of the off-shell Coulomg T-matrix is presented for electron- hydrogen scattering which contains classical path sums. A correspondence identity results as the energy shell is approached.

New triplet transitions in AlF have been the subject of rotational analysis and some states which had formerly been assigned as singlets are now found to be case b triplet states with very small splittings. Perturbations in the first excited singlet state, A ¹ Pi , by a triplet state w ³ Sigma ⁺ enable the singlet and triplet stacks to be related. T_infinity for the first excited state, a ³ Pi _I, is 27254 cm^-1.

An improved method for the calculation of two-centre oscillator integrals is given for harmonic oscillators of equal frequencies. Formulae for a transition integral of arbitrary order are developed necessary for the calculation of optical transitions in colour centres.

Bands of gaseous LaS have been observed in thermal emission and in absorption, and the vibrational analysis of one system B² Sigma -X² Sigma ⁺ in the region 7000 to 8500 AA has been obtained, together with the rotational analysis of the 0-0 band. The bands possess four R and Four P branches, and the splittings can be interpreted in terms of (i) a large spin splitting gamma (N+1) in the upper state, (ii) a J independent case b_{beta s} nuclear magnetic hyperfine interaction in the ground state whose magnitude is within experimental error the same as in LaO.

Results of non-relativistic and relativistic calculations of cross sections for elastic electron scattering from mercury at energies from 0.25 to 8 eV, both with and without inclusion of exchange effects, are presented. It is shown that the large differences between relativistic and non-relativistic results noticed by other authors is due to neglect of exchange.

A model of an excited quantum system is considered. An exact solution is obtained for a non-stationary problem in which the interaction potential is an arbitrary function of time and coordinates. The obtained solution reduces in particular cases to well-known results for transition probabilities between highly excited levels of a quantum oscillator.

A perturbation theory has been developed for the relativistic Hartree-Fock equations for atoms with particular reference to the ground state of a helium-like atom. It is expected that the method developed here, in conjunction with the perturbation theory for the non-relativistic Hartree-Fock equations, will provide a powerful tool for the study of the extra-nuclear properties of heavy atoms.

The first-order extended Hartree-Fock (EHF) equations for the 2s²¹S and 2p²¹S states of two-electron atomic systems are solved exactly. The solutions are used to evaluate the second-order EHF energies exactly and the third-order EHF energies with great accuracy. The EHF equations of these states correctly take into account the zero-order mixing of the wave functions and are comparable in accuracy to the conventional HF equations for non-degenerate states. The results of this paper are compared with those of experiment and of other calculations.

Calculations are presented for the line strengths of transitions connecting the doubly excited singlet series of levels with the 2¹S state of helium. The calculated expectation values (E) and (r₁²) for the doubly excited and the 2¹S states are also given.

An approximation, based on regional trial functions, is used to calculate excitation cross sections between some optically connected states of hydrogen and of the alkalis, lithium, sodium and potassium. The cross sections obtained in this approximation, which is simpler than the Born-Oppenheimer approximation, are compared with other theoretical and with experimental results. On the basis of this comparison it is suggested that the wave functions, on which the calculation is based, may form an acceptable first approximation in a more detailed variational treatment.

The first Born approximation is used to calculate generalized oscillator strengths for the single ionization of atomic helium. Wave functions described by Bell and Kingston are employed to calculate both the length and velocity formulations of the Born matrix elements. Reasonable agreement is obtained with the available experimental data in the non-resonant energy loss region. Comparison of theory and experiment near the first ¹P⁰ resonance in helium indicates that it may be possible to derive the resonance parameters using only first Born calculations together with accurate experimental data for three energy loss values at any angle of scattering.

Quantal calculations are carried out on the rate at which the electronic transitions involved in He(2³S)+H(1²S) to He(1¹S)+H⁺+e occur. An impact parameter formulation is then employed to determine the rate coefficient for the process. At thermal temperatures the value obtained is 7.5(+or-20%)*10^-10 cm³s^-1.

Second quantization is used to derive the overlap integral between two harmonic-oscillator wave functions on different centres and with different force constants. The appropriate dipole moment and kinetic-energy integrals are also obtained.

A simple closed form is obtained for an approximation to the differential cross section for the elastic scattering of atoms by atoms, by an extension of the methods used by Massey and Mohr to calculate the total elastic cross section. Comparison is made with the accurate phase shift calculations of Bernstein, and with the experimental results of Hofstetter and Bernstein.

The spectra of ions in crystalline solids are generally described in terms of a phenomenological spin Hamiltonian. An important problem concerns the choice of operators making up this Hamiltonian. This problem is now commonly resolved by symmetry arguments, such as those described by Grant and Stradberg, and a spectrum is fitted with a truncated series of symmetry-derived parameters. It is noted that no consistent notation has been adopted for these parameters and to avoid further confusion a nomenclature, based on one in use for crystal- field operators, is suggested. Expressions are derived for a number of symmetry-allowed zero-field hyperfine operators which are of importance in the interpretation of ENDOR spectra, and possible relations between symmetry-derived parameters are briefly discussed.

The H⁺-H collision is investigated using the three-state molecular expansion, which takes account of the coupling between 2p sigma and the 2p pi states of the H₂⁺ quasi-molecule. Differential cross sections for direct elastic scattering, resonant charge exchange and direct and exchange excitation of H(2p) have been computed for a range of incident proton energies from 150 eV to 2.84 keV and for a range of scattering angles from 0 to 10 degrees (in laboratory system). The agreement with the experimental results is excellent. The nature of non-adiabatic effects in low energy H⁺-H collisions is discussed in detail.

A crossed beam method has been used to measure cross sections for H^-+e to H+2e for interaction energies between 12 and 1000 eV. For energies greater than 40 eV there is excellent agreement with measurements of Dance, Harrison and Rundel and when the energy exceeds 200 eV, the measurements confirm calculations by Inokuti and Kim based on Bethe's approximation. No evidence of structure was found in the detachment function.

An anomalously high saturation value for the decay constant of the 'alignment' is observed for coherence-narrowed 6¹S₀-6³P₁¹⁹⁸Hg fluorescent radiation scattered at right angles from the frontal region of the resonance cell. This is explained in terms of the radiation loss from the front face.

The pulse height per unit energy has been measured for two pure sodium iodide crystals for gamma-ray excitation in the energy region 30 keV to 1 MeV, at temperatures between 77 K and 200 K. By using a specially calibrated crystal, it has been possible to find the light output per unit energy in terms of photons per MeV. The purity of the crystals used has been investigated by recording their emission spectra, and the variation of scintillation efficiency with specific ionization of the incident radiation has been deduced from the gamma-ray response data.

The rotational analysis of two bands 1-1 and 1-2 of the D-X system of the SbO molecule has been performed. The transition has been identified as ² Pi ₁2/-² Pi ₁2/.

Term values of the He I-like spectrum of carbon, C V, are derived by using new measurements in the region below 300 AA and some previous observations at longer wavelengths. Ritz formulae and other relationships are established, permitting an arbitrary extension of the term system. The results are compared with available theoretical calculations of ionization energies. Part of the discussion includes He I and Li II.

The band spectrum of LuO was obtained in a d.c. arc and the blue system studied. Each band has been found to be double, and not single as previously reported. Consequently, a new interpretation of the electronic transition is given here. The dissociation parameters are also reported.

Using a 40 cm curved mica crystal spectrograph of the transmission (Cauchois) type, a detailed study of the L emission spectrum of cerium 58 has been made. Four new diagram lines at 1899.7 x.u., 1921.2 x.u., 2008.0 x.u. and 2162.6 x.u., corresponding, in that order, to the forbidden transition L_IO_I and the quadrupole transitions L_IN_IV,V, L_IIn_VI,VII and L_IIIN_VI,VII have been observed for the first time. The measurements of other dipole and quadrupole transitions have been made with a view to comparing them with those of earlier workers.