Table of contents

Lie Backlund type analysis is performed for the cylindrical KdV equation u_xxx + uu_x + u_t + δu/2t = 0 which explicitly contains the time variable "t". The point transformation is calculated and it is seen that the prolongations of the generators produce via the commutation of the (x, t) dependent generators. The generalised similarity solution is seen to satisfy Painle've II equation from which Backlund transformation of such solution has been constructed. Lastly it can be mentioned that consistent set of generators exists only for the δ = 1 corresponding to Nakamura's case γ = ½. The deduced Backlund transformation is helpful in generating rational solutions of CKDV.

We discuss how the strong-coupling lattice confinement mechanism, which is based on the polymer, or "surface", description of lattice gauge theory, may be extended to gauge theories in the weak-coupling regime.

We calculate the cross section of gluon bremsstrahlung in deep inelastic charged lepton-nucleon scattering, ln → lgX, including the effects of weak neutral currents. Results are given for the cross section in terms of target nucleon rest system variables and in terms of center of mass system variables.

The recent extension of the energy spectrum of ¹⁵⁶Gd to include up to five K^π = 0⁺, two K^π = 2⁺ and two K^π = 4⁺ rotational bands from an (n, γ) reaction study allows further tests of the validity of the dynamic pairing-plus-quadrupole model of nuclei. Eight of these rotational bands are obtained in the model, though the calculated energy scale is much expanded. Their decay characteristics are compared with experiment.

This report takes all the available good quality quantal calculations of excitation cross-sections by electron collision for lithium-like ions and intercompares them. There is a comparison also with the small amount of experimental data of 2s²S-2p²P cross-sections. On the basis of all of these data, a choice is made of the best cross-sections and these are integrated over Maxwellians to give excitation rate coefficients. In general data are available for up to seven transitions in five or six ions. When the results are compared along the iso-electronic sequence, trends are established which allow estimates to be made of the rate coefficients for these seven transitions for any lithium-like ion of nuclear charge greater than boron. The results are presented graphically and as simple formulae. The formulae reproduce the source data at various levels of accuracy from about ± 1% for individual ions to universal formulae of accuracy better than ± 15% in the relevant temperature ranges. The latter are contained on one page and represent an enormous condensation of the original source data without seriously compromising the authors' claimed accuracy.

Optical-emission spectra of core-excited Be I ⁵L and core-excited Be II ²L and ⁴L states have been studied by means of the beam-foil-excitation method. Multiconfigurational Hartree-Fock calculations have been performed for the optical transitions between the lower-lying Be I ⁵L states and between 1s2pnl (n = 2-4, l = 0-3) ²P⁰, ²P^e, ²D⁰, ²D^e, and ²F^e states in core-excited Be II ²L to facilitate the identifications. Some previously assigned core-excited Be II ⁴L transitions are shown to belong to either the core-excited Be I ⁵L or the core-excited Be II ²L spectrum. Additional identifications of core-excited Be II ²L transitions explain the main features of this spectrum. The identifications of Be II 1s2p4l⁴L states are discussed.

The differences between observed and theoretical values of level intervals within the n = 2 complex in ions isoelectronic with Li, Be, O and F have been studied as functions of Z. The theoretical values are based on the tables of Cheng, Kim and Desclaux. For spin-orbit intervals, σ (theor) is taken as their multiconfiguration Dirac-Fock value with Breit correction (MCDF + B), for other intervals within the same configuration the Z-independent correlation energy from Cheng, Froese Fischer and Kim is added, and for interconfiguration intervals a Lamb-shift correction is also included, obtained by transforming the values of Cheng et al. into a smooth function of Z. The difference σ (obs) - σ (theor) is then expressed by the formula A + B(Z - C)^-1 + a(Z - s)^x, where the first two terms account for the residual correlation energy and the last term comprises all additional relativistic and radiative corrections. In a few cases we had to use two such terms with opposite sign and exponents differing by 2 to 3 units. The constants A, B, C, a and x are adjusted to fit the observations within their error limits. As compared to a fitted polynomial, the present formula is much better suited for extrapolation and provides a sharper test of the experimental data, especially at the high-Z end of a sequence. It has revealed a number of incorrect line identifications in the Be sequence. The results of the analyses are summarized in tables of recommended level values and wavelengths, extending to Z = 36 and in some cases to Z = 42. The wavelengths obtained for the resonance lines in the Be, O and F sequences may become useful as wavelength standards.

This paper reports the relative population of the levels 3p, 3d, 4d, 5d, 4f, 5g, 6g, 6h, 7h, 7i, 8i and 8k in Na-like sulfur, S VI, after beam-foil excitation at an energy of 3 MeV.

For the first time the ANDC technique has been used to obtain the relative efficiency calibration of the detection system at discrete points in the wavelength interval 400-5000 Å, from the analyses of measured decay curves. The advantages and limitations of this method are discussed.

The populations obtained with this new technique are compared to previous measurements in multiply ionized atoms. The preferential population of the 3p and 3d levels observed in other Na-like ions is now accurately established. For the higher lying levels an almost constant population is observed.

A new method of the nonsingle-Lorentz spectra analysis is described. The method is founded on the mathematically correct regularization procedure permitting one to reconstruct the smoothed distribution function of Lorentzians, contributing to the spectrum, over their widths. Influence of the noise and background as well as the role of the spectral band and resolution finiteness was investigated by use of the computer simulation. To demonstrate the possibilities of the method, the distribution functions of the latexes, vesicles and 30 S subunits of E. coli ribosomes were reconstructed from scattered light spectra, measured by photon correlation spectroscopy. The regularization procedure proves to be the most reliable method for the polydispersity analysis.

Radiative electron rearrangement (RER) and hole-mixing effects in molecular ultra-soft X-ray spectra (USX) are theoretically analyzed at several levels of approximation and compared with X-ray photoelectron (XPS) transitions which result in the same residual ionic states. Numerical applications are carried out for the CO molecule with configuration interaction wavefunctions built on orbitals separately optimized for initial and final states. The USX spectra are more complex than the XPS spectrum in the energy ranges corresponding to RER and break-down of the MO-model due to interference from excited components of the initial state wavefunctions and due to non-orthogonality. This breaks the branching ratio rule that predicts equal satellite to parent ionic intensities for the XPS and the different core-sited USX spectra and does accordingly also limit the applicability of local selection rules for the hole-mixing in the USX spectrum.

Based on a previous study of echelle grating groove shapes, the groove edge defects of the master and its replicas were measured. It was found that the master and an even number of consecutive replicas have edge defects of several microns, whereas the first replica can be made almost without edge defects (< 0.1 μm). To eliminate the large groove edge defects of the master, the echelle gratings should be ruled in such a way that the included angle of the grooves is less than 90 deg. In this way the rough edges of the master are hidden in the steep corners of the replica's grooves, giving the replica the highest possible efficiency. Only replicas that are the mirror-images of the master should be used for spectroscopy.

Convective instability of a plasma slab (contained between two metal walls) subject to a longitudinal applied magnetic field is considered. The method of solution is akin to the variational method introduced by Chandrasekhar in 1961. It is found that the plasma is stable for wave-numbers less than a certain value k_c.

The electronic structure behaviour of Me₂O₃ oxides (Me = Ti, V, Cr) has been determined from XPS valence band and core level measurements. From Ti to Cr sesquioxide the relative intensity of the 3d band increases systematically which can be explained by the (atomic) photoelectric cross section and the number of 3d electrons. Simultaneously the 3d-2p band separation decreases indicating a more stronger band overlap equivalent an enhanced covalent bonding component. The different electrical properties among the corundum structure oxides are determined by the trigonal field splitted a_1g and e_g orbitals, their occupation and relative energy position at the Fermi level. The observations confirm the change from itinerant to more localized behaviour of d electrons caused by crystal structure parameter change (c/a ratio).

A new "Complex Calculation of Surface Segregation" (CCSS) method (presented elsewhere in greater detail) is first outlined and the factors of surface segregation are identified. The approximate description of these by subsequent structure model refinements is then discussed. It is shown by some considerations and by numerical results on the AgPd alloy as well, that such refinements lead to consequent diminutions of the surface free enthalpy. On this basis optimal values of calculational parameters, characteristic of surface conditions, may be calculated.

The infinite-range-Ising-spin-glass model is analysed using a new diagrammatic approach. The Sherrington-Kirkpatrick solution is regained in the paramagnetic region and the Bray-Moore soft mode is obtained in the spin-glass region. A possible order parameter characterizing the phase-transition at the Almeida-Thouless instability line is proposed.

We examine the effect of the core hole on several spectroscopies used to explore the conduction band of simple metals. We show that the static effect on the valence electrons is very strong and discuss under what circumstances this effect may be seen experimentally. In KLV Auger spectra a core hole is present in both initial and final states. Thus, there will be almost no dynamical effect, but the static effect must be accounted for in any quantitative calculation. We here present a full effective one-particle calculation for the KL₁ V and KL_2,3V spectra of sodium, that for the first time explain the "mystery" structure seen in experiment, by attributing this effect to the presence of a core hole. The agreement with experiment is gratifying although some discrepancy remains. For the main band of soft X-ray emission spectra the core hole is present in the initial state but not in the final state, yet the experimental spectra do not show the strong effect found in KLV. This is explained in terms of the Final State Rule, according to which rather accurate spectra can be obtained from a one-particle calculation provided final-state wave functions are used in the transition matrix elements. The dynamical switching of the core hole potential causes a singular behavior of the X-ray edge, which according to the Final State Rule can be accounted for by mutliplicative power-law factors. For the satellite emission band there is an additional core hole in both initial and final states, and, by the Final State Rule, the spectrum should show the static effect of precisely one core hole. This is confirmed by the good agreement between theory and experiment that we obtain for the L_2,3 SXE satellite spectrum of sodium. The Final State Rule is also used to explain the similar shapes of the main band and the satellite in the case of Li K emission, and for the interpretation of alloy spectra.

The EPR and optical absorption studies are reported for the nickel-bearing minerals, zaratite and takovite.

The optical absorption spectrum of zaratite at 300 K exhibits three intense bands and a weak band and also four other vibrational bands. The strong bands at 8195, 14 285 and 23 805 cm^-1 are assigned to ³T_2g(F), ³T_1g(F) and ³T_1g(P) and the weak band at 21 735 cm^-1 assigned to ¹T_2g(D) of Ni²⁺ in an octahedral symmetry. The crystal field parameters are evaluated to be Dq = 820, B = 899 cm^-1 and C = 4.1B. The four vibrational bands are attributed to water and hydroxyl stretching. The EPR spectrum of zaratite shows no transition due to Ni²⁺ but includes signals due to Mn²⁺, Fe³⁺ and Co²⁺. It is derived from the absorption studies that Ni²⁺ in zaratite is sited in an octahedral symmetry in a normal oxide/hydroxide structure.

The optical absorption spectrum of takovite at 300 K consists of three strong bands at 9100, 15 380 and 26 665 cm^-1 which could be assigned to the three spin-allowed transitions and two weak bands assigned to ¹E_g(D) and ¹T_2g(D) of Ni²⁺ in an octahedral symmetry. The two components at 8200 and 10 000 cm^-1 might be due to mild tetragonal distortion to split the octahedral band at 9100 cm^-1. The crystal field parameters which gave a good fit to the observed energies at Dq = 910, B = 940 cm^-1, C = 4.25 B. The EPR spectrum and the near infrared spectrum of takovite have close resemblance with those of zaratite. It is concluded that Ni²⁺ in takovite might be sited in a slightly tetragonally distorted octahedron in a normal oxide and or hydroxide structure.