Table of contents

We consider the problem of finding the energy levels and wave functions of discrete-spectrum states for a class of Hamiltonians connected with root systems of the Lie algebras and in the limit case describing quantum systems of N interacting particles on a straight line in the Morse potential. It is shown that this problem may be reduced to an algebraic problem. Exact expressions are obtained for the dependence of energy levels on parameters of the interaction potential.

From the inverse scattering problem of the Heisenberg Spin chain, we have deduced the Square eigen function expansion of the variation of the non-linear Spin variables. The situation is different from the usual A.K.N.S. problem as the linear problem is not an eigenvalue problem in literal sense, and this also makes, the formulation of the equation for square eigen function difficult. So we have considered the corresponding equivalent matrix Schrödinger problem, and proved the orthogonality of square eigen-functions after having expressed the variation of the scattering data in terms of the field variables and square eigen-functions.

The ²⁷Al(α, n)³⁰P reaction has an astrophysical interest in connection with the syntheses of elements in the solar system and in stars during explosive carbon burning. A good knowledge of the energy dependence of the cross section for this reaction is therefore of importance. In the present work the yield from a thick ²⁷Al-target was measured for α-particles in the energy range 3.04 to 3.66 MeV corresponding to stellar temperatures between 2.08 and 2.75 × 10⁹ K. The observed neutron yield curve was used to determine nucleosynthesis reaction rates, N_A⟨σν⟩.

The wavelengths of three transitions in Fe XXIV and one transition in Fe XXIII of the type n = 4 to 2 have been accurately measured in solar flare spectra. The measured wavelengths are compared with previous measurements and with ab initio and semi-empirical calculations that include screening parameters in the nonrelativistic, relativistic, and radiative terms.

Low pressure broadening and shift of four spectral lines of argon, 591.2, 687.1, 693.7 and 737.2 nm have been investigated. The values of the pressure broadening and shift coefficients for argon-argon, argon-neon and argon-helium interactions in the glow discharge are determined. For all lines in the pure argon a red shift and in the argon-helium mixture a blue shift has been found. In the argon-neon mixture the shifts of these lines are small and have different signs.

Calculations of energies and transition probabilities are reported for forbidden lines in the ground configurations of the germanium (4p²) and arsenic (4p³) isoelectronic sequences up to silver (Z = 47). Configuration interaction and relativistic effects were included in the framework of the HXR and HFR self-consistent-field methods. Transition probabilities have been obtained in intermediate coupling using parameter values for the 4p² and 4p³ configurations obtained either by fitting or by extra-(inter)polation when experimental energy levels are missing. Except for Ge I and As I, transition probabilities are reported for the first time for all these ions.

A note concerning transition probabilities for Fe XII is also appended.

Using the second order polarization propagator method we have calculated the band oscillator strengths of the "forbidden" Lyman-Birge-Hopfield band system, a¹Π_g ← X¹Σ_g⁺, of N₂ and the radiative lifetime τ(v') of the a¹Π_g state for 0 ⩽ v' ⩽ 4. We find that τ(0) = 58.6 μsec and τ(4) = 68.2 μs. About 95 per cent of the intensity are magnetic dipole contributions and only about 5 per cent come from the electric quadrupole radiation.

Two close-lying ¹Π-¹Σ⁺ systems of the isotopic molecules ¹²⁰Sn¹⁶O and ¹²⁰Sn¹⁸O in the region 1790-1920 Å have been obtained by the flash-absorption technique. Five bands belonging to the ν' = 0 progression of each system have been rotationally analyzed and molecular constants for the two upper states are given.

A theoretical and experimental investigation is presented for the process of atomic K-shell excitation for GeV particles with special emphasis on the influence from the polarization of the surrounding target medium. It is shown that the transition radiation emitted upon entrance into the target compensates partly the reduction due to the density effect. In this way inner-shell excitation yields are obtained which depend on penetrated depth into the target, e.g., with the net result that polarization effects may be neglected for thin samples. A simple relation is constructed which explains all existing experimental data. The large spread in γ values (1-10⁴) for a GeV secondary beam has been exploited to measure the above relativistic effects in one single experiment. Here the simple model has proven to stand all tests including variation of target thickness, comparison of X-ray yields from the front and back sides of the target, and inclusion of a stack of foils to produce extra transition radiation upstream with respect to the target.

By separating all atmospheric perturbations into high- and low-frequency modes, we deduce new simplified equations for acoustic gravity waves.

The dynamical behaviour of two coupled oscillators depend on two parameters: The frequency ratio and the amount of the non linearities. Experimental results, obtained on free Rayleigh-Bénard convection, are reported; at nearly constant R_a value, a complex dynamical behaviour with the rotation number is evidenced near the onset of chaos. Regimes with weak or more developed chaos are observed in the vicinity of phase-locked states as it was first pointed out by numerical studies.

Steady state analysis is carried out for plasma between coaxial cylinders in presence of an externally applied uniform axial magnetic field under the assumption of quasi-neutrality of electric charge and neglect of sheaths at the walls. The radial distributions of plasma density and electric potential are given as functions of the ratio of inner and outer radii of the two cylinders. For any given value of this ratio and gap size, an equivalent radius of a cylindrical plasma is given that has the same temperature and electric field for the same gas under the same physical conditions as the coaxial plasma. The equivalent radius may be used to determine the temperature and axial electric field of a cylindrical plasma of the same gas under the same physical conditions are known from theory or experiments.

A recent experiment for determining the weak structure factor |F₃₀₁| of Zn is shown, in principle, to contain sufficient information for also fixing its sign. It is an example of a generally applicable method when this determination is carried out in conjunction with well-indexed Renninger rotation diagrams for finding azimuthal angular regions relatively free of multiple beam interactions.

Optical absorption spectra of VO²⁺ and Cu²⁺ ions in rubidium Zinc sulphate hexahydrate single crystals are investigated both at the laboratory and liquid nitrogen temperatures. The optical absorption spectrum of VO²⁺ is characteristic of tetragonal symmetry, whereas that of the Cu²⁺ is characteristic of rhombic symmetry. EPR spectra of polycrystalline samples of these substances are also recorded and analysed. By correlating the optical absorption and EPR studies, molecular orbital coefficients and orbital reduction parameters are calculated.

In an earlier report the van der Waals interaction between an atom and a metal surface was calculated taking into account the finite extension of the atom. This was found to make the atom to response less well to density fluctuations of short wavelengths. Since those fluctuations are more important close to the surface, the ordinary divergent expression for the van der Waals potential, when the atom-metal separation goes to zero, was replaced by another which gave finite values of the interaction even at distances very close to the surface. The previous treatment is extended in this paper to include also the inability of the metal itself to respond to short wavelength density fluctuations. As can be expected, the improved metal response affects the physisorption potential close to the surface. Oure results are conveniently parameterized for a number of atom/metal configurations in order to make them of easy use in many other applications.

Mössbauer investigations of three meteorites of the type SNC-achondrites are reported. The results are compared with Mössbauer spectra of other meteorites, and selected terrestrial and lunar rocks. Through the oxidation state of iron in the pyroxenes and magnetic oxides studied, the work confirms that the mantle of the Earth is highly oxidized compared with the mantle of asteroidal bodies and lunar basalts. The investigations show that at least one of the SNC meteorites (Nakhla) comes from a highly oxidized parent body, believed to be the planet Mars. Based on the results obtained, a somewhat general conclusion about the oxidation state of iron in planetary bodies is proposed.

Comparative measurements indicate that the phase velocity of low frequency waves in the ionospheric E-region is often lower than the drift speed of the electrons that drive the waves unstable. In order to understand these results, the linear instability theory is modified to conform with zero growth rate even above threshold. The result is that the waves travel at the ion-acoustic velocity with an amplitude stabilized at the observed level, and also that the electron gas is substantially heated by the wave.

Erratum for Physica Scripta32, 248 (1985)