We discuss questions pertaining to the definition of ‘momentum’, ‘momentum space’, ‘phase space’ and ‘Wigner distributions’; for finite dimensional quantum systems. For such systems, where traditional concepts of ‘momenta’ established for continuum situations offer little help, we propose a physically reasonable and mathematically tangible definition and use it for the purpose of setting up Wigner distributions in a purely algebraic manner. It is found that the point of view adopted here is limited to odd dimensional systems only. The mathematical reasons which force this situation are examined in detail

We briefly outline the two popular approaches on radiative corrections to neutrino masses and mixing angles, and then carry out a detailed numerical analysis for a consistency check between them in MSSM. We find that the two approaches are nearly consistent with a discrepancy factor of 4.2% with running vacuum expectation value (VEV) (13% for scale-independent VEV) in mass eigenvalues at low-energy scale but the predictions on mixing angles are almost consistent. We check the stability of the three types of neutrino models, i.e., hierarchical, inverted hierarchical and degenerate models, under radiative corrections, using both approaches, and find consistent conclusions. The neutrino mass models which are found to be stable under radiative corrections in MSSM are the normal hierarchical model and the inverted hierarchical model with opposite CP parity. We also carry out numerical analysis on some important conjectures related to radiative corrections in the MSSM, viz., radiative magnification of solar and atmospheric mixings in the case of nearly degenerate model having same CP parity (MPR conjecture) and radiative generation of solar mass scale in exactly two-fold degenerate model with opposite CP parity and non-zero U_e3 (JM conjecture). We observe certain exceptions to these conjectures. We find a new result that both solar mass scale and U_e3 can be generated through radiative corrections at low energy scale. Finally the effect of scaledependent vacuum expectation value in neutrino mass renormalisation is discussed

In this paper we briefly outline the quadrature method for estimating uncertainties in a function which depends on several variables, and apply it to estimate the numerical uncertainties in QCD-QED rescaling factors. We employ here the one-loop order in QED and three-loop order in QCD evolution equations of the fermion mass renormalisation. Our present calculation is found to be new and also reliable when compared to the earlier values employed by various authors

A relativistic analysis of p +⁴⁰Ca elastic scattering with different nuclear ground state target densities at 135 to 200 MeV is presented in this paper. It is found that the IGO densities are more consistent in reproducing the data over the energy range considered here. The reproduction of spin-rotation-function data with the simultaneous fitting of differential cross-section and analyzing power, and the appearance of wine-bottle-bottom shaped Re U_eff(r) in the transition energy region, sensitively depends on the input nuclear ground state densities and are not solely the relativistic characteristic signatures. We also found that the wine-bottle-bottom shaped Re U_eff (r) is preferred by the spin observables in the transition energy region (i.e. 181 MeV to 200 MeV)

Following a fully self-consistent cranked Hartree-Fock-Bogoliubov (CHFB) approach with a pairing+quadrupole+hexadecapole model interaction Hamiltonian the structure of the yrast states of^76,78Kr nuclei is studied up to angular momentumJ = 24. Evolution of the shape with spin, and rotation alignment of proton as well as neutron 0g_9/2 orbitals is investigated along with the inter and intra-nucleus variations of theg factors as a function ofJ. We find that the shape of⁷⁸Kr remains prolate all through up toJ = 24, whereas⁷⁶Kr becomes triaxial beyondJ = 12

Pulse shape discrimination (PSD) with totally depleted transmission type Si surface barrier detector in reverse mount has been investigated to identify fission fragments in the presence of elastic background in heavy ion-induced fission reactions by both numerical simulation and experimental studies. The PSD method is compared with the other conventional methods adopted to identify fission fragments with solid-state detectors such as ΔE–E telescope and single thin ΔE detector and the data for the¹⁰B +²³²Th fission reaction are presented. Results demonstrate the usefulness of a single transmission-type surface barrier detector for the identification of fission fragments and projectiles like heavy ions

High-frequency deflection (HFD) technique with a delayed coincidence single photon counting arrangement is an efficient technique for radiative lifetime measurement. An apparatus for measurement of the radiative lifetime of atoms and molecules has been developed in our laboratory and measurements have been performed with great success in a large number of atoms and ions. The present version of the apparatus is described in this paper together with a brief description of the basic features and performance

Parametric study of optical emission from two successive laser pulses produced chromium and magnesium plasma is presented. The line emission from chromium and magnesium plasma showed an increase by more than six times for double laser pulse excitation than for single-pulse excitation. An optimum increase in emission intensity was noted for inter-pulse delay of ∼2–3 μs for all the elements. The experimental observations were qualitatively explained on the basis of absorption of second laser pulse in the pre-formed (by first laser) coronal plasma by inverse Bremsstrahlung process, which were found responsible for the excitation of more ions and atoms in the plasma. This process starts as the plasma scale length becomes greater than the laser wavelength. This study further indicated the suitability of this technique in the field of elemental analysis

The static structure factors of liquid alkali metals have been modelled at temperatures close to their melting points and a few higher temperatures using the reverse Monte Carlo (RMC) method. The positions of 5000 atoms in a box, with full periodicity, were altered until the experimental diffraction data of the structure factor agrees with the associated model structure factor within the errors. The model generated is then analysed.

The position of the first peak of the pair distribution function g(r) does not show any significant temperature dependence and the mean bond lengths can be approximated within an interval of 3.6–5.3 Å, 4.5–6.6 Å, 4.8–6.7 Å and 5.1–7.3 Å for Na, K, Rb and Cs respectively. The cosine bond distributions show similar trend with the flattening up of the first peak with increase in temperature. In addition, the coordination numbers of these liquid metals are high due to the presence of non-covalent bonding between them. On the average, we surmise that the coordination number decreases with increase in temperature

Dynamic and static light scattering experiments have been performed at various molar ratios (γ) of water to AOT and temperatures on water-in-oil (W/O) microemulsions dispersed in n-heptane, n-octane, and n-nonane. Size and shape fluctuations of microemulsion droplets are determined with very high precision because polydispersity influences the characteristic features of scattering data as well as the hydrodynamic radius withγ. Self-consistent interpretation of dynamic and static light scattering data using optical properties and packing consideration on the basis of the layered sphere model are obtained. The estimated extent of polydispersity index of 17% is found, whereas the polydispersity is independent of the alkane types. The geometrical parameters, e.g., hydrodynamic radius, area per head group of the surfactant molecule and thickness of the surfactant layer of microemulsion droplets are also estimated and compared in three different n-alkane types. The best interpretation of the temperature dependence of data has shown a transition from spherical droplets to ellipsoid aggregates with increasing temperature. Axial ratio increases with increase of temperature and the longer the alkane the larger is the axial ratio. The parameters describing the polydispersity and shape change are in agreement with theoretical and experimental results found in the literature

A new type of discrete VLF emissions recorded at the low-latitude ground station Varanasi (geomag. lat. 14°55′ N, geomag. long. 154°E;L = 1.07) during the strong magnetic activity on 29–30 April 1990 have been reported. A generation mechanism for various temporal and spectral features of discrete VLF emissions recorded at Varanasi is presented on the basis of cyclotron resonance interaction between whistler mode wave and energetic electrons ejected by substorm electric fields. An attempt is also made to determine parallel energy and wave growth relevant to the generation process of discrete VLF emissions. Finally, our results are discussed with other published works

We report the use of low dielectric constant materials to form two-dimensional microwave band-gap structures for achieving high gap-to-midgap ratio. The variable parameters chosen are the lattice spacing and the geometric structure. The selected geometries are square and triangular and the materials chosen are PTFE (ε = 2.1), PVC (ε = 2.38) and glass (ε = 5.5). Using the plane-wave expansion method, proper lattice spacing is selected for each structure and material. The observed experimental results are analyzed with the help of the theoretical prediction

Some biological complexes containing iron are investigated experimentally at room temperature using the Mössbauer resonance. The complexes show quadrupole doublet and Kramer’s degeneracy is found to exist. The electric field gradient, difference ins-electron densities and quadrupole coupling constant have been calculated in each case. These parameters are used to obtain information on the surroundings of the Mössbauer atom

In the present work we have reported the unique effects of P₂O₅-doped PLZT ceramics with composition (Pb_0.92La_0.08)(Zr_0.65Ti_0.35)O₃ +x wt% of P₂O₅ (wherex = 1, 3 and 5) prepared chemically by co-precipitation method. X-ray diffraction studies suggest that the prepared compound was very fine (10–25 nm), homogeneous and of rhombohedral symmetry. The apparent density of samples decreased with the P⁵⁺ additions. Studies of dielectric constant and dielectric loss as a function of frequency (10–1000 kHz) and temperature suggest that the compound undergoes diffuse type of phase transition without any sign of relaxor behaviour. With increasingx, dielectric constant was found to decrease appreciably, whereas Curie temperature (T_C) was found to increase

Statement of Kaur and Mahajan [1] about the definition of Δ used by Chandra [2] is not correct. Even if we take Δ = μω_e²r_e²/2D_e, the relation between Δ and G(=8ω_ex_e/B_e) is obtained as Δ = 4.21452856G, provided the vibrational energy of a diatomic molecule is expressed in terms of limited Dunham coefficients, Y₁₀, Y₂₀, Y₀₁ and Y₁₁. This relation is still different from that of Kaur and Mahajan [3]