Table of contents

The Painlevé property for nonlinear diffusion equations is investigated. The results are compared with other approaches for testing the integrability of nonlinear field equations.

A class of exact solutions for a time-dependent uniform density sphere is given. The model is non-regular since there exists an interior surface where the pressure is infinite. However, it is shown that this surface is always hidden by trapped surfaces. The equation for the zero pressure boundary of the fluid sphere is investigated, and it is found that this equation always has just one solution when integration constants are properly chosen. The pressure gradient is shown to be negative, and all models possesses the strange property that the circumference is not an increasing function of diameter. We also find that for contracting models the pressure is a decreasing function of time for the interior layers close to the singular surface. Two kinds of matter "velocities" are investigated, and it is found that just one of these is a decreasing function of radial coordinate.

The systematic appearance of limit cycles, homoclinic and heteroclinic orbits in the Lorenze model has been mapped in the r-b parameter plane at σ = 10. New structures in the model are thereby revealed.

We present a study of the Bose-Einstein interference effect for pions of equal charge and similar momentum vectors in inclusive antiproton-proton reactions at 9.1 GeV/c. The results are used to provide an estimate of the space-time dimensions of the region emitting the pions. We obtain an average radius R = 1.3 ± 0.1 fm and a time of emission cτ = 0.9 ± 0.2 fm. The parameter λ, a measure of the fraction of interfering like-charge pions, is found to be λ = 0.8 ± 0.1. No large deviation from a spherical shape of the pion source is observed. We emphasize the importance of establishing a non-interfering background.

B (E3) values in the trans-lead region lie in a region of about 1-50 Weisskopf units. Of particular interest are those cases which with a relatively small scattering are grouped around effective B (E3) values of 22 and 35 W.u. The former cases are due to fast single particle transitions of the type πi_13/2 → πf_7/2 or νj_15/2 → νg_9/2 Where the initial states are mixed with the final state plus the 3^- octupole excitation of the core of ²⁰⁸Pb. Transitions with very high B (E3) values are likely to be associated with mixed configurations both in the initial and final states allowing fast proton as well as neutron transitions. The proton transitions are taken care of by the valence protons and the neutron transitions by core deexcitations. The quantitative relation between different groups of B (E3) values are illustrated by analyzing the E3 decay of the core excited 16⁺ and 39/2^- isomeric states ²¹⁰Po and ²¹¹At, respectively.

A model consisting of protons filling the shells 1g_9/2 and 2p_1/2 is least-squares fitted to 63 low-lying energy levels in N = 50 isotones from ⁸⁹Y to ⁹⁶Pd. The single-particle energies and two-particle interaction matrix elements are treated as free parameters. A root-mean-square deviation of 64 keV is obtained for the levels included in the fit. Binding energies and excitation spectra for all the N = 50 nuclei between ⁸⁸Sr and ¹⁰⁰Sn are calculated with the resulting effective interaction.

Lifetimes of 28 different rotational levels of the PH⁺A² Δ state υ' = 0, 1) have been measured using the High Frequency Deflection technique. Rotational levels above the dissociation limit of the ground state showed influences of predissociations. CASSCF calculations of the electronic transition moment of the A² Δ – X² Π transition made possible the determination of the lifetimes toward predissociation. CASSCF + CI calculations of the A² Δ, X² Π, ²Σ^-, and ⁴Π state potential energy curves were performed. These curves were combined with experimental Rydberg-Klein-Dunham potential energy curves in a scaling procedure in order to obtain accurate potential energy curves which were used in a model calculation of the predissociation rates. These model calculations showed that a second order interaction between the A² Δ state and the ²Σ^- state via an excited ²Π state is the most plausible mechanism for the observed predissociation.

Calculated oscillator strengths are listed for 2s² 2p⁵ - 2s 2p⁶, 2s² 2p⁵ - 2s² 2p⁴ns, 2s² 2p⁵ - 2s² 2p⁴nd and for 2s² 2p⁴nl - 2s² 2p⁴n'l' (l = s, p; l' = p, d; n, n' = 3, 4) transitions of Mg IV.

They have been computed with the aid of a HXR computer program, initially developed by Cowan [18], including configuration interaction and some relativistic effects. Ab initio values of Slater radial energy integrals have been adjusted by a non-linear least-square optimization routine, using the available experimental energy levels.

We investigate light-induced bound-free transitions in the presence of radiative recombination in models of continuum resonances for which the only singularities of the coupling function are a finite number of simple poles in the complex plane. Using elementary complex analysis, finding the time-dependent solution to the ensuing set of integro-differential equations is reduced to a study of sets of linear algebraic equations and roots of a polynomial. As an example we treat bound-free Rabi flopping for a Lorentzian resonance. We suggest that the extremely restrictive conditions for observing coherent transients, a narrow resonance and a large dipole moment matrix element, may be met in two-electron excitation of an atom.

The first-order semiclassical approximation method with hyperbolic projectile trajectories, velocity symmetrization, relativistic electronic wavefunctions and target recoil amplitudes is used for systematic studies of K-shell Coulomb ionization. The first-order description is modified by the use of a binding correction. In the low projectile velocity region studied the theoretical cross sections are largely consistent with weighted averaged measurements. Two sets of empirical reference cross sections are considered, the first being found to contain an additional superfluous target dependence, the second improved set showing considerably increased agreement with the present SCA results. The inadequacy of the ECPSSR model for the very low projectile energy region is demonstrated. The implications for the construction of model independent empirical scaled cross sections are discussed.

The B²Σ-X²Σ band system of gaseous barium hydride in the wave length region 8900-11200 Å has been examined in absorption using a King furnace. The spectrum has been obtained by means of Fourier transform spectroscopy. Seven bands have been rotationally analyzed. Term values and molecular constants of the B²Σ and X²Σ states have been determined by standard least-squares analysis. The following molecular constants have been derived (cm^-1):

The core-excited quartet and doublet spectra of B III, produced by foil excitation of fast B⁺-ion beams, have been studied in the wavelength region 300-6300 Å. A large number of new transitions have been observed, for the first time allowing a detailed test ot theoretically predicted core-excited B III ⁴L- and ²L-term schemes. For a number of quartet states, the line assignments are supported by lifetime measurements. All the assigned, core-excited spectral lines are in excellent agreement with theoretical predictions by Chung et al. These predictions have been extended to include quartet states with L > 2.

We report four new observations of transitions within the core-excited doublet system of Li I. Absolute term energies for eight doublet states in the system have been determined at an accuracy better than 10 cm^-1. The energy scale was established from the recent experimental term energy of the 1s2s2p⁴P⁰ state of Mannervik and Cederquist combined with the wavelength for the laser-induced intercombination transition 1s2s2p⁴P⁰ – 1s2p²²P recently observed by Willison et al. In this context also isotope shift and mass polarization had to be considered. The present experimental absolute term energies are compared with recent theoretical and experimental results.

The Kadomtsev-Pogutse fluid model of anomalous transport has been extended to take account of non-linear effects. The results are relevant to both tokamaks and pinches, although the specific application in this paper is to ALCATOR. As a result of the interactions between parallel and perpendicular energy transport, the small-scale magnetic fluctuations lead to an expression for the anomalous electron thermal diffusivity. It is found for fluctuation levels typical of high m, n modes, that the perpendicular thermal diffusivity generally increases with radius, the values being consistent with experiment.

The magnetic part of the energy in Ni is separated from the total thermal energy and used for a study of the ferromagnetic and paramagnetic states.

We have observed non-ohmic behavior in the resistivity of VO_x for very small electric fields. In an attempt to explain these results several models are considered. We suggest that the sharpening of the transition to the insulating state with applied electric field is due to a reduction of the length of time during which regions of the sample fluctuate into the insulating state.

In this paper we present calculations which elucidate the effect of Fermi surface distortions (introduced by a pair of Bragg planes) as well as the effect of matrix elements on the wave vector dependent electronic susceptibility χ(q). Calculations of the anisotropic χ(q) are also reported.