Table of contents

The coupled integro-differential equations for electron collisions with an N-electron ion may be solved at energies which give bound states for the (N+1)-electron system. Results are obtained for the ¹P⁰ series in C²⁺, including the configurations 1s²2snp, 1s²2pn's, 1s²2pn"d and 1s²2s2p. The 1s, 2s and 2p radial functions are calculated for C³⁺ and the np, n's and n"d radial functions are solutions of the coupled integro-differential equations.

The interaction of an atom with two radiofrequency fields was recently examined theoretically by Allegrini and Arimondo (see abstr. A60907 of 1971) in terms of the dressed atom concept. This letter indicates how the same problem can be easily solved by the semi-classical approach of Pegg and Series (see abstr. A36273 of 1970).

One approach to the problem of calculating electron-atom or ion-atom cross sections at intermediate energies has been the use of the second born approximation. The complexity of the resulting calculations has led to the introduction of the simplified second born approximation (Holt and Moiseiwitsch, 1968). Evidence on the accuracy of this approximation is presented.

Recent calculations by Bray (see abstr. 1060 of 1971) describing the vibrational relaxation of anharmonic oscillators were presented in a format which is shown to be misleading when used to predict the behaviour of the vibrational 'temperature' between the lowest levels. These results are reinterpreted in terms of this low level 'temperature' and an approximate analytic expression is presented for use in expansion flows where collisional deactivation is unimportant. Good agreement is found between this expression and the numerical results.

For pt.I see ibid., vol.4, no.12, L129, 1971. Electric field induced anticrossing signals are used to measure the fine structure splittings S-D of n=4 in (⁴He)⁺. Extrapolation of the crossing position to zero electric field is carried out. The present results are (20145.3+or-7.8) MHz for the interval 4²S₁2/-4²D_3/2 and (27455.4+or-7.4) MHz for the interval 4²S_1/2-4²D_5/2 in agreement with Erickson's theoretical values of (20142.85+or-1.36) MHz and (27458.60+or-1.36) MHz respectively. The splitting 4²D_3/2-4²D_5/2 is derived from these intervals to be (7310.1+or-15.2) MHz compared with (7315.75+or-0.02) MHz from the theory. Combining 4²S_1/2-4²D_3/2 with 4²S_1/2-4²P_3/2, measured by Jacobs et al, provides a value for the Lamb shift 4²P_3/2-4²D_3/2 of Sigma =(34.4+or-9.0) MHz compared with the theoretical value of (37.19+or-1.36) MHz.

A pronounced feature is observed in the differential cross section of elastic electron-sodium scattering. Shape and energetic position (2.1 eV) show, that the structure is due to the opening of the inelastic 3²P-channel.

A family of diagonal hypervirial theorems is shown to be straightforwardly derivable for practically any reasonably well behaved bound state trial wavefunction and thus cannot be used as checks on the validity of the chosen wavefunction.

For pt. I see abstr. A11728 of 1971. In this paper the author has extended the work of Sharma and Bowtell (part I) to take into account the magnetic interaction in a relativistic Hartree-Fock treatment of the two electron atom. Also the results of calculations for the relativistic corrections to the ground state of the first 20 elements of the helium isoelectronic sequence, based wholly on the zero and first order energy parameters, are reported.

The necessary and sufficient conditions for a one-body reduced density matrix of rank 6 to be derivable from a three-body fermion wavefunction are presented. For this case it can be shown explicitly that the information content of the one-matrix is less than that of the wavefunction. The extension of these conditions to the cases of a three-body function of one-rank 7 and a four-body function of one-rank 8 are also discussed. The authors have obtained sufficient conditions for these two cases. Numerical studies reported in this paper lead us to believe that these conditions are the necessary and sufficient conditions.

The contributions of the non-spherical interaction terms, arising due to the anisotropy, shape factor, quadrupole moment and quadrupole induced dipole interaction, to the third virial coefficient C(T) of carbon dioxide gas have been calculated over a range of temperatures by using the method suggested by Alder and Pople. The results show the importance of such contributions to C(T). The agreement with the experimental C(T) data becomes much better by including such contributions and also that due to the non-additive interactions. The conclusions drawn for carbon dioxide are expected to hold all the polyatomic gases.

The variable phase method was used for the calculation of some properties of the H₂⁺ molecular hydrogen ion. It has been found that in the lowest ungerade static potential of the H₂⁺ molecule there exist 2 bound states. The scattering lengths for the lowest gerade and ungerade potentials are a_g=-30au, a_u=7.6*10²au. There is no appreciable change in these values due to the adiabatic corrections.

An analysis is made of the validity of Brillouin's theorem for atomic Hartree-Fock (HF) results. Consequences are derived for the use of the multiconfigurational HF method. Brillouin's theorems adapted to the unrestricted HF methods are recalled. As an application, the quality of HF results in hyperfine structure and isotope-shift problems is discussed. The computation of screening factors for field isotope shift is shown to be the most favourable case.

Configuration interaction wavefunctions for the 1s²2s²¹S, 1s²2s2p ³P and 1s²2s2p ¹P states are calculated for Be I, B II, C III, N IV, O V, F VI and Ne VII and are used to calculate oscillator strengths for the ¹S to ¹P transition.

A recently developed theory of electron scattering by complex atoms based upon the R matrix method, is used to calculate the elastic scattering of electrons by hydrogen and helium atoms. Phase shifts for e^--H scattering are obtained in the static approximation and also allowing for the atomic polarizability using the pseudo-state method. Phase shifts for e^--He scattering are obtained using both a Hartree-Fock and a correlated target wavefunction. A discussion is given of why a low energy e^--He resonance does not occur in the latter approximation and why probably one does not exist. Finally, the dependence of the phase shift on the number of basis states included in the expansion of the total wavefunction is discussed and a pseudo-potential method is introduced to obtain rapid convergence.

The frequency dependent polarizability is written as an expansion in terms of R-matrix states. It is shown that this allows the development of a unified treatment of atomic polarizabilities and photoionization cross sections. A general computer program has been written and this is used to calculate the polarizability of atomic oxygen for imaginary frequency.

The threshold excitation spectrum of helium is presented and discussed. From a series of trapped electron spectra for increasing well depths, the excitation functions of the four n=2 states of helium are obtained from threshold to above 22eV. The inelastic cross section to 23.5eV is observed and compared with total metastable production measurements.

A calculation is given for the collision frequency and the angular distribution of particles scattered from a well collimated atomic beam. It is assumed that their total number is small. Results are plotted for the flow from a supersonic nozzle with the Mach-number varying from 0 to 8.

The velocity distribution of caesium atoms issuing from a multi-channel glass capillary array has been studied and an energy-exchange process proposed to account for the modification to a Maxwellian distribution. The importance of knowing the exact distribution in the measurement of atomic beam total scattering cross sections is indicated by the calculation of the appropriate kinetic averaging factors.

Measurement of collisional-radiative recombination coefficients ( alpha ) in spark channels, for electron densities approximately 10¹⁶/cm³ and electron temperatures approximately 10⁴ K are described. alpha varied from about 10^-10 to 10^-11 cm³ s^-1 in accordance with the optically thin theoretical values of Bates et al.

Measurements are reported of transmission of energy monochromated electrons of energy 0.1-4eV through oxygen, nitrous oxide, nitric oxide, nitrogen dioxide, carbon dioxide, and benzene. Energy loss spectra are measured, and the zero angle scattering functions for excitation of different vibrational levels are reported. The functions show oscillatory structure due to temporary negative ion states. The function for O₂ is analysed in terms of the compound state theory, yielding O₂^-2 pi _g nuclear separation r_e=1.39AA in disagreement with the photodetachment value r_e=1.34+or-0.01AA (Celotta et al). The causes of this discrepancy are probably significant. The transmission functions for zero energy loss are treated by Fourier analysis, which yields the approximate vibrational energies of the temporary negative ion states of O₂^-, NO^-, NO₂^-, C₆H₆^-. It is possible that a second state of NO₂^- contributes the scattering at energies above 1.1eV.

For pt. I see abst. A63958 of 1971. The author analyses the linked diagram expansion for the polarization propagator, describing the atomic response to an external perturbation. In particular an application is made to the 5p⁶ shell in Xe and excitations into the 5p-nd ¹P channel discussed. These are described by an effective RPA expansion in which ladder diagrams, representing particle-hole interaction, are included. The expansion can be separated into two parts, one which describes absorption and one which describes virtual fluctuations or screening. The absorption part stems from the expansion 'on the energy shell' and forms a divergent series for the continuum threshold. The screening part forms a convergent series and can be expressed as an integral equation for a reaction matrix, describing 'off the energy shell' fluctuations. The author also discusses how to apply the theory to the case of many channels and presents a method for treating ground state correlations. The results for the dynamical response of the shell in terms of intuitively defined dielectric functions are discussed.

Existing theories of level crossing and modulation effects in the light scattered from optically thin vapours are restricted to cases where the light from different atoms is either completely incoherent (lateral scattering) or completely coherent (forward scattering). In the latter case the resonances are Doppler broadened equivalents of the well known Lorentzian forms predicted for lateral scattering. The more general case of partial coherence of the scattered light, which might be expected at small scattering angles, has not previously been considered. In this paper the degree of coherence of the scattered light has been formulated in terms of an autocorrelation function. For scattering from an ideal gas the autocorrelation function may be split into two terms representing complete incoherence and complete coherence. The predicted resonances for scattering into an arbitrary direction are mixtures of the Lorentzian and Doppler broadened forms, but the latter have a strong angular dependence that effectively restricted their observation to the small angular range associated with diffraction from the active volume of the vapour.

A spectrometer which has been used for studying the shapes of microwave spectral lines in gases is described. Radiation from a klystron was passed through a waveguide cell and detected with a crystal diode. The klystron frequency was modulated sinusoidally with a frequency of f/n, n being integral and in the range 1 to 5, and the detected output at frequency f was observed on an oscilloscope. In this way the first five harmonics of the modulation frequency were observed. The mean klystron frequency was swept slowly across the spectral line and the frequency separations between the various maxima and minima of the harmonic outputs were measured using frequency markers. The results were compared with those deduced from three theoretical lineshape models. Three cases were studied; the self broadened (J,K)=(6,6) line in the inversion spectrum of NH₃ the same line broadened by He; and the self broadened J=1 to 2 line in the rotational spectrum of COS. In all cases the lineshape was represented to within the experimental error by a Lorentz shape corrected for the Doppler contribution.