Table of contents

We show here that the Hamiltonian (1.1) has n functionally independent integrals of motion in involution which are rational both in phase space variables and in parameters. Moreover these integrals are quadratic in momenta and the Hamilton-Jacobi equation of the system (1.1) is separable in generalized elliptic coordinates. A Lax representation for (1.1) and for higher flows is found. The system (1.1) constrained to an ellipsoid remains integrable.

We have made an analysis about the different class of soliton and soliton like exact solutions of nonlinear Schrodinger equation in three dimension through the help of a modified Lax pair suggested by Melnikoff. We show that it is possible to generate a new class of solutions which incorporates the usual soliton solutions as special cases. One important and distinctive feature of our calculation is that the input Kernels of the Gelfand-Levitan equation take into account of nontrivial, specified functional form of the boundary conditions of the two dimensional nonlinear field u(x, y) and v(x, y) in both cases of x and y → ∞.

Analytical conformity is established between the wave functions corresponding to different potentials and angular momenta. An approach suggested permits construction of a new series of potentials and pertinent solutions to the Schrödinger equation in a closed analytical form for variable values of energy and angular momentum along arbitrary straight lines in the ((l + 1/2)², E) plane.

The so-called non-Newtonian behaviour of solitons at small times is discussed in ϕ⁴ theory for time-dependent external forces F(t) ∼ tⁿ, n = 0, 1, 2,.... By the adiabatic approach, ϕ(x, t) ≈ exact kink + u(t), it is shown that (i) the field momentum P = - ∫_-∞^+∞ ϕ_xϕ_tdx satisfies Newton's law dP/dt ∼ F(t), and (ii) the acceleration of the kink in leading order of t is proportional to t⁰, t¹ or tⁿ⁺², depending on the initial conditions u(0) and u_t(0) for the motion of the vacuum. In consequence, for n ⩾ 2 the kink's acceleration is definitively different from the Newtonian acceleration (∼ tⁿ), whatever the initial conditions for the vacuum are. For F(t) = t² a numerical experiment is performed, showing good agreement with the adiabatic result, even for relativistic initial velocities. Expanding the perturbation function in the eigenfunctions to the linearized ϕ⁴ equation, one finds that in the two leading orders of t it does not depend on x while in the next two orders its x-dependence is given by a term proportional to the translation mode.

A search has been carried out for gamma production in 1487 inelastic interactions in π^--emulsion collisions at 340 GeV/c. Detailed examination of the inclusive gamma distribution has been made and the characteristics have been studied in terms of different production mechanisms. Inclusive π° spectrum has been extracted from the observed gamma spectrum. A critical hadronic temperature of about 148 ± 23 MeV/c has been deduced and its importance has been discussed in the context of quark-gluon plasma. Mean number of neutral produced particles has been found to be directly related to the mean number of charged particles obtained from different types of collisions.

Strong polarization effects are observed for inclusive hyperon production in hadronic collisions. Also quarks which are conventionally regarded as spectators turn out to be polarized, e.g. in the reaction K⁺p → X. Thus the "spectators" can take a more active part in the reaction. In this paper we study how measurements of hyperon polarization in the fragmentation of polarized protons can clarify the rôle of the spectator quarks, in particular whether it is possible for the spin of the spectators to flip during the interaction.

A method of projecting out the parts of the tensor- and spin-spin components of the nucleon-nucleon interaction that correspond to isospin 1 pseudoscalar and vector exchanges is given. From those potential components the isovector exchange current operators of main importance in magnetic electron scattering may be constructed. The resulting exchange current operators satisfy the continuity equation with the interaction potential. By using them in place of the usual single-meson exchange current operators consistency between the current operators and the wavefunctions used in evaluating matrix elements for nuclear electromagnetic reactions can be achieved. The utility of the results is illustrated for the case of backward electrodisintegration of deuterium and radiative np-capture.

Scattering lengths in the systems ⁴He, ⁶Li, ⁷Li, ¹²C, ¹⁶O, ¹⁷O, and ¹⁸O are derived from the measurements of the strong interaction atomic level shifts in the corresponding antiprotonic atoms. The Coulomb corrections to the scattering lengths are evaluated and it is found that they are large.

The Rb IV spectrum emitted from a sliding-spark discharge has been observed in the wavelength range 4500-290 Å. About 550 lines have been classified. From the observations 129 energy levels have been established in the 4s²4p⁴, 4s4p⁵, 4s²4p³5s, 6s, 5p, 4d and 5d configurations. The observed level structure has been interpreted by means of Hartree-Fock calculations and parametric fits including, in particular, Rydberg-series configuration interaction. The ionization energy of Rb³⁺ is estimated to be 421000 ± 2000 cm^-1.

Lifetime measurements are presented for the 1s2p³P_1,2 levels for He-like C V and N VI. From the measured lifetimes, transition probabilities are deduced for both allowed and spin-forbidden transitions. The values for the 1s²¹S₀ - 1s2p³P₁ transition rates, 0.29 × 10⁸ and 1.38 × 10⁸ s^-1 for C V and N VI respectively, are found to be in good agreement with theory.

New calculations of transition probabilities are presented for forbidden lines in the ground configuration of the phosphorus sequence from Ar to Ru. Relativistic contributions and configuration interaction effects were included in the framework of the HXR and HFR self-consistent-field methods. Energy levels and A values were computed in intermediate coupling with fitted or interpolated semi-empirical energy parameters. The variation in magnetic dipole and electric quadrupole oscillator strengths as a function of Z is extended beyond nickel to Z = 44.

The perturbation method for calculating atomic energies by power series in 1/Z and αZ has been extended to include parameters for screening and for expansion in the principal quantum number n. Numerical results are given and compared with observations for 1s nl and 1s²nl of the helium and lithium isoelectronic sequences.

The gallium spectrum emitted from a hollow cathode has been recorded in the region 500-9800 Å. 142 lines have been classified as transitions in Ga II. Energy levels have been derived from the observations, and perturbations within the n = 4 configuration complex are discussed. Besides the previously known mixing between 4s4d and 4p², it has been found that the structure of 4s4f is strongly affected by interaction with 4p4d. The ionization limit has been determined to 165 465.8 cm^-1.

The emission spectrum of krypton (injected into TFR tokamak plasmas) has been recorded photographically in the 15-300 Å spectral range by means of a 2 m grazing incidence spectrograph. Preliminary identification work, based on isoelectronic regularities from known spectra of other ions and ionization equilibrium calculations, has allowed 48 lines (belonging to the O I, F I, Na I, Mg I, Al I, Ar I and K I sequences) to be identified.

Average energies for the configurations 2p⁵ 3s, 3p and 3d in a number of neon-like ions from Al IV to Xe XLV have been calculated by means of the MCDF computer code of Grant et al. The results have been compared with observations and previous non-relativistic calculations. Fine-structure levels and 3s-3p and 3p-3d transition wavelengths have also been calculated with the MCDF code for Ti XIII and Fe XVII, both in the single-configuration approximation and in a multiconfiguration treatment including 2s 2p⁶nl. The configuration interaction was found to affect 2p⁵ 3p³S₁ most seriously. A separate optimization for the 3p¹S₀ state was needed, due to the particular radial dependence of this state. The calculated wavelengths show excellent agreement with the observations, and the MCDF calculations are well suited for wavelength predictions in neon-like n = 3 systems.

This paper presents advances in the use of high resolution x-ray spectroscopy for the measurements of tokamak plasmas and the study of atomic processes. The measurements refer to H- and He- like spectra of Ar (λ = 3.7 to 4.2 Å) obtained with a new crystal spectrometer at the Alcator C tokamak. With record count rates of up to 0.5 MHz, time resolved spectroscopy of individual plasma discharge was demonstrated at the 20 ms time scale. In particular, the time evolution of ion and electron temperatures, T_i(t) and T_e(t), was determined and occurrences of transient plasma phenomena were recorded in discharges with deuterium pellet injection. X-ray line emission was for the first time observed along different chords through the plasma so as to determine the radial dependence of the principal plasma parameters T_i(r) and T_e(r). These radial scan data are shown to be of interest for identifying manifestations of underlying atomic processes and ion transport effects. On the basis of the present results we assess the future use of x-ray spectroscopy diagnostics to obtain extended information on the temporal and spatial dependences of the main plasma parameters together with new information on transient phenomena as well as on the neutral content of tokamak plasmas.

The Bowen fluorescence mechanism was investigated by beam-foil spectroscopy because of the incompatible evaluations given by theory and experiment concerning its importance in exciting certain permitted oxygen lines in planetary nebulae. Since this excitation mechanism has already been studied by the beam-foil method of 0 III in detail, the present investigation examines the analogous transitions in other members of the isoelectronic sequence of carbon. In this manner, the disagreeing values for 0 III given by theory and experiment can be compared taking advantage of well-known quantum mechanical systematic trends along isoelectronic sequences. Specifically, the transitions in Ne V that correspond to the Bowen lines in 0 III were studied. For this purpose, the optical spectrum of beam-foil excited 2.5 MeV neon was measured between λ1700 Å and λ2400 Å. From the subsequent measurements, the systematic behavior of the oscillator strength for the two-electron transition 2s2p^{3 3}P⁰ - 2p3p³S was established for the carbon sequence. The graphic display of this trend confirms that the previous experimental f-values for 0 III are more consistent with the other members of the isoelectronic sequence than the ones given by theory. Consequently, we support the conclusion of the previous experimental investigators. The Bowen fluorescence mechanism by itself is sufficiently strong to explain the observed intense 0 III lines in planetary nebulae.

The emission spectra of CuS has been photographed at high resolution in the region 4 000 Å-5 000 Å. Three band systems have been rotationally analyzed for both isotopes, namely the E²Π_3/2 - X²Π_3/2, F(Ω = ½) - X²Π_1/2 and G²Π_3/2 - X²Π_3/2 systems. In order to reduce correlations between the molecular constants all lines of the analyzed bands (including lines of the A²Σ - X²Π_i system) were fitted together. Molecular constants of the states are given.

The study of chlorine absorption spectra in the vacuum ultraviolet by using a flash-pyrolysis system and a 2-m normal incidence spectrograph has produced new wavelength measurements and identifications of lines converging to the triplet P limits.

About 250 lines are identified and assigned to 30 series. The majority of the lines have been observed here for the first time. About 100 have been previously predicted, while 120 are newly observed, leading to 82 new even levels.

The analysis has been performed mainly through the method of quantum defect extrapolation.

The most intense, allowed lines are observed as transitions which involve both levels of the ground state with the same excited upper level. This has helped test and strengthens the correctness of assignments to series.

In this paper we wish to demonstrate the multi-element capability of Laser Enhanced Ionization (LEI) in flames by reporting the detection of 15 different elements. All the elements were excited by the fundamental or the first harmonic frequency-doubled light from one single dye in the laser system (Coumarin 47). Detection limits below the ppb region (parts-per-billion, ng/ml) were achieved for 13 elements (Al, Bi, Ca, Cd, Co, Cr, Fe, Ga, Li, Ni, Pb, Sr, Tl). The detection limits reported here are for several elements orders of magnitude superiour to those for existing comparable flame based spectroscopic methods. For 9 elements, the detection limits are found to be lower than any previously reported values for one-step LEI in flames.

A helical equilibrium equation with anisotropic pressure and mass flow is derived. A simple helical plasma model for high beta with highly anisotropic pressure (P_|| ≫ P_⊥) and small helicity is described. The effect of mass flow on a β-limitations which appears in this case is studied.

We consider the parametric excitation of lower-hybrid and ion-cyclotron waves in a plasma where the ion velocity distribution function is anisotropic. The threshold electric field is found to depend significantly on the ratio between the parallel and perpendicular ion temperatures.

Two different phase-space models of solitary electron holes are investigated and compared with results from computer simulations of an actual laboratory experiment, carried out in a strongly magnetized, cylindrical plasma column. In the two models, the velocity distribution of the electrons is described by a single waterbag distribution and a modified Maxwellian distribution, respectively. A comparison with the results obtained by a BGK scheme rather than the phase-space model method is also included.

A Ward identity is derived for the one-dimensional system with both electron-electron and electron-phonon forward scattering interactions. This identity is used to solve exactly the Dyson equations of the generalized effective interaction, phonon and electron Green functions for both T = 0 and T ≠ 0. The absence of both the quasi-fermion excitations and the jump in electron momentum distribution at the Fermi "surface" points out the failure of the Landau Fermi liquid theory for this system. The long-wavelength dielectric response function and the thermodynamic potential are also computed exactly.

An attempt is made to formulate the gate capacitance of MOS structures of ternary semiconductors having n-channel inversion layers under magnetic quantization without any approximations of weak or strong electric field limits. It is found, taking n-channel Hg_1-xCd_xTe as an example, that the gate capacitance exhibits spiky oscillations with the reciprocal magnetic field. It is further observed that the sharpness and the amplitudes of spikes increase with increasing magnetic field. Besides, the corresponding results for n-channel inversion layers on parabolic semiconductors are also obtained from the expressions derived.

The analysis of the large-scale structure of turbulence in a stratified atmosphere is important for the prediction and modelling of turbulence. The Monin-Obukhov similarity consideration is well suited for the modelling of small-scale turbulence. But the large-scale turbulence possesses new features and parameters, as connected with the appearance of a spectral gap in the stably stratified atmosphere, for the understanding of which an analytical investigation is needed. By a group-kinetic method, we derive the anisotropic form of the transfer function and its governing eddy viscosity. On this basis, we obtain the spectral laws k^-5/3, k^-1, k^-3 for the subranges of inertia, shear, and buoyancy, respectively. A gap connects the last two subranges by the variable anisotropy, as a result of the fall of the spectrum of the vertical velocity fluctuations. The variable anisotropy causes the deviations from the spectral laws k^-1 and k^-3. Our experiment supports our analytical prediction.