Classification of Three-Dimensional Integrable Scalar Discrete Equations

We classify all integrable three-dimensional scalar discrete affine linear equations Q ₃ = 0 on an elementary cubic cell of the lattice . An equation Q ₃ = 0 is called integrable if it may be consistently imposed on all three-dimensional elementary faces of the lattice . Under the natural requirement of invariance of the equation under the action of the complete group of symmetries of the cube we prove that the only non-trivial (non-linearizable) integrable equation from this class is the well-known dBKP-system. SPT acknowledges partial financial support from a grant of Siberian Federal University (NM-project No 45.2007) and the RFBR grant 06-01-00814.     

Semiempirical molecular orbital calculations for four-, six- and eight-atom systems

The geometry, bond order, binding energy, ionisation potential, dipole moment and net charges have been calculated for cis-N₂O₂, trans-N₂O₂, N₂O₄, BF₃, CH₃, NH₃, BH₃ and B₂H₆ systems using semiempirical molecular orbital methodsindo and the results compared with available experimental,ab initio andmindo/3 data.     

Adiabatic time-dependent Hartree-Fock theory with the consistency condition

Adiabatic time-dependent Hartree-Fock (atdhf) theory, including the authors’ work in this field, has been summarised. In response to the criticism of Yamamuraet al the role of curvature in preventing the choice ofpure rpa mode as the solution near the static Hartree-Fock minimum has been discussed.     

The Hamiltonian constraint in the teleparallel equivalent of general relativity

In the teleparallel equivalent of general relativity the integral form of the Hamiltonian constraint contains explicitly theadm energy in the case of asymptotically flat space-times. We show that such expression of the constraint leads to a natural and straightforward construction of a Schrödinger equation for time-dependent physical states. The quantized Hamiltonian constraint is thus written as an energy eigenvalue equation. We further analyse the constraint equations in the case of a space-time endowed with a spherically symmetric geometry. We find the general functional form of the time-dependent solutions of the quantized Hamiltonian and vector constraints.     

Electron energy loss spectroscopy (eels) of organic molecules in vapour phase: Design and fabrication of an indigenouseel spectrometer

An indigenous electron energy loss spectrometer has been designed and fabricated for the study of free molecules. The spectrometer enables the recording of low-resolution electronic spectra of molecules in the vapour phase with ready access to the vacuum ultraviolet region. Electron energy loss spectra of aliphatic alcohols and carbonyl compounds as well as of benzene derivatives have been recorded with the indigenous spectrometer and the electronic transitions in these molecules discussed. Contribution No. 274 from the Solid State and Structural Chemistry Unit, dedicated to Dr. Raja Ramanna on his 60th birthday.     

The application ofclean to crystallographic problems

It is suggested that the radio astronomical technique of image reconstruction calledclean could be profitably used in crystallography to improve sharpened Patterson maps andE-maps. The method is here generalized to handle the symmetries which arise in crystallographic maps. Simulations on model one and two dimensional structure are presented to illustrate the power of the method.     

Off-diagonal long-range order and currents in weakly coupled superconductors

Within the framework of quasi equilibrium approximation, Josephson’s expression for current in a weakly coupled superconducting system is derived without the use of any specific microscopic model. It is based only on the existence of the off-diagonal long-range order in the two-particle reduced density matrix. Allowing for deviations from the quasi equilibrium approximation, generalised Josephson equations are obtained which include ohmic terms. The effect of relaxation and thermal fluctuations is examined in detail to emphasise the physical origin of various terms in the expression for current.     

Exact energy eigenvalues by summation of thejwkb series

For the potentialV(x)=V ₀ tan² x, the corrections to the lowest orderjwkb (Bohr-Sommerfeld) energy quantization rule are non-zero. These higher order corrections are explicitly computed using the formalism of Dunham. The resultingjwkb series for the energy eigenvalues is summable, and yields the exact bound state spectrum.     

Angular distribution in ternary fission

The angular distribution of long-range alpha particles emitted in keV-neutron induced fission of²³⁵U has been measured using a technique which employs only a particle telescope to derive the angular information. The neutron energy region investigated is 100 keV-1 MeV. The angular distribution oflras has been found to be peaked perpendicular to the neutron-direction with a substantial amount of anisotropy near 200 keV.     

deSitter space-time and rotation

A metric containing a parameterb is presented. It represents two distinct families of space-times, the Taub-nut family and the deSitter family, according asb=1 andb=4 respectively. The metric of the deSitter family of space-times contains a further parameterm. Whenm=0, the space-time is the usual homogeneous and isotropic deSitter space-time. But ifm≠0, the metric represents a space-time which is homogeneous but not isotropic satisfyingR _ik =Λg _ik . In this space-time, the 4-velocity of an observer at rest will have non-zero twist. The metric withb=4,m≠0 is interpreted as a metric representing a “rotating deSitter space-time”.     

Some theoretical studies on concurrent events in photoelectron spectroscopy

Concurrent events in photoelecron spectroscopy such as photoionisation, shake-up and shake-off transitions are studied using atomic wavefunctions recently developed by one of the authors and the concept of the Slater transition state. Various transition energies and intensities are calculated to test the efficiency of the wave-functions and the applicability of the transition state method to these processes. It is concluded that the method is reliable enough to be useful in the assignment of these transitions in the experimental spectrum.     

Recoil corrections to magnetic moments of charmed baryons in themit bag model

Recoil corrections to magnetic moments of charmed baryons are studied in themit bag model. It is noticed that such corrections which improve the octet baryon magnetic moments have considerably significant contributions to charmed baryon’s moments also.     

Approximate angular momentum projection from an intrinsic random phase approximation Hartree-Fock state

An approximation procedure is described to calculate the projected energies from an intrinsicrpa hf wave function. The method of moments is used to find the relevant parameters. A model calculation is carried out for illustrative purposes.     

Change of confinement scale in nuclei and the EMC effect

We study a model in which the confinement scale of quarks in a nucleus of massA changes asA ^1/3. This explains theA dependence of structure functions (emc effect) as seen in muon, electron and antineutrino deep inelastic scattering from nuclear targets. We also investigate a prediction of this model—anA dependence of theqcd scale parameter A.     

Electrical and photoelectrical studies of plasma polymerized acrylonitrile

The electrical and photoelectrical properties of plasma polymerized acrylonitrile (PAN) are reported. The polymer films were studied in silver-PAN-silver systems. Electrical conductivity at room temperature was of the order of 10⁻¹¹ ohm⁻¹ cm⁻¹. The space charge limited current (SCLC) studies at room temperature and thermally stimulated current studies (TSC) over a temperature range of 290–500°K led to a clear understanding of carrier concentration, carrier mobility, trapping levels and activation energies. Photoelectric measurements were used to draw a band picture in plasma depositedPAN.     

Ga0.47 In0.53 As—The material for high-speed devices

Electron transport properties of Ga_0.47In_0.53As are reviewed. The available physical constants of the material and results on electron mobility in bulk materials, 2deg systems and under hot-electron conditions are presented. Applications of the material in the construction offet’s and photo-conductive detectors are briefly discussed.     

EXAFS study of intermetallics of the type RGe2 (R=La,Ce, Pr,Nd, Sm,Gd, Tb,Dy, Ho,Er and Y) Part I: Determination of Ge-Ge distances

A study of theEXAFS associated with theK x-ray absorption discontinuity of germanium in pure germanium and in the rare-earth germanides RGe₂ (where R=La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er and Y) has been carried out. The Ge-Ge distances have been obtained in these compounds. Considering the phase to the RGe₂ system, the bond lengths in these compounds have been determined. The values obtained by us for the RGe₂ compounds (R=La, Ce, Pr, Nd, Sm, Gd, Dy and Y) agree with those obtained earlier by crystallographic methods. The bond lengths for the compounds TbGe₂, HoGe₂ and ErGe₂ are also being reported.     

On the mass spectroscopy of charmed multiquark hadrons

The possible existence of charmed multiquark hadrons are investigated using phenomenologicalmit bag model and the SU(4) flavour symmetry. The masses of 6q, 9q and 15q systems having the same quantum numbers as the physically interesting ordinary nuclei, hypernuclei and supernuclei are estimated. We find that several new states with distinct signatures are predicted.     

Study ofl-tryptophan corepressor binding to mutatedE. coli tryptophan repressor proteins by optically detected triplet-state magnetic resonance

Phosphorescence and optically detected magnetic resonance (ODMR) measurements have been carried out on the tryptophan (Trp) residues ofEscherichia coli Trp repressor protein (W Rep) and its two single Trp-containing mutants, W19F and W99F. The enhanced resolution afforded by the W19F and W99F mutants allowed us to characterize the triplet state of boundl-Trp corepressor using phosphorescence wavelengt-selected ORMR spectroscopy. We find that at 77 K the 0,0 band peak wavelength ofl-Trp is shifted from 405.5 nm in the aqueous solvent to ca. 410 nm when bound to the corepressor binding site. This red shift of the phosphorescence along with a corresponding increase in the zero-field splittingE value and narrowing of the ODMR linewidth characterize a binding site that is less polar, as well as more polarizable and homogeneous, than the aqueous solvent. This conclusion is in agreement with the X-ray crystallographic structure of the holorepressor protein that places the indole chromophore of the bound corepressor in a cleft in which it is sandwiched by the side chains of arginines 54 and 84.