• Volume 61, Issue 3

September 2003,   pages  483-631

• On the invariance properties of the Klein-Gordon equation with external electromagnetic field

Here we attempt to find the nature of the external electromagnetic field such that the KG equation with external electromagnetic field is invariant. Lie’s extended group method is applied to obtain the class of external electromagnetic field which admits the invariance of the KG equation. Though, the field potential only explicitly appears in the equation, the constraints for the invariance are only on the electromagnetic field.

• A charged spherically symmetric solution

We find a solution of the Einstein-Maxwell system of field equations for a class of accelerating, expanding and shearing spherically symmetric metrics. This solution depends on a particularansatz for the line element. The radial behaviour of the solution is fully specified while the temporal behaviour is given in terms of a quadrature. By setting the charge contribution to zero we regain an (uncharged) perfect fluid solution found previously with the equation of statep = μ + constant, which is a generalisation of a stiff equation of state. Our class of charged shearing solutions is characterised geometrically by a conformal Killing vector.

• Non-static plane symmetric cosmological model in Wesson’s theory

The problem of non-static plane symmetric perfect fluid distribution in Wesson’s [1] scale invariant theory of gravitation with a time-dependent gauge function is investigated. The false vacuum model of the universe is constructed and some physical properties of the model are discussed.

Theγ-ray yields from inelastically excited 2+ and 4+ levels of144,146,148,150Nd nuclei using16O beam at near barrier energies in coincidence with the back-scattered projectiles were measured. The 2+ and 4+ level cross-sections were deduced from the measuredγ-ray yields and fitted to the DWBA calculations to obtain the reduced transition matrix elementsM(E4: 0+ → 4+). The deducedM(E4) values for148Nd and150Nd nuclei, 0.16(0.05) and 0.22(0.12) eb2, respectively are consistent with theoretical predictions.

• A relativistic mean-field study of magic numbers in light nuclei from neutron to proton drip-lines

In an axially deformed relativistic mean-field calculation of single-particle energy spectra ofN = 8 (Li-Mg) andN = 14,16 (C-Mg) isotonic chain and the one- and two-neutron separation energies of various isotopes of Li-Mg, new magic numbers are found to exist atN = 6 andN = 16 and/orN = 14, which are in addition to theN = 8 andN = 20 magic numbers. In neutron-rich nuclei, the shell gap atN = 6 is larger than atN = 8 and a large gap is observed forN = 16 or 14 for the neutron-rich andN = 14 for proton-rich nuclei. Large shell gaps are also found to exist atN = 14 and 16 orN = 16 alone for nuclei near theβ-stability line. The above results are independent of the parameter sets TM2, NL3 and NL-SH used here. Similarly, new large shell gaps are predicted atZ = 616 and/or 14 for protons.

• Fusion of light exotic nuclei at near-barrier energies: Effect of inelastic excitation

The effect of inelastic excitation of exotic light projectiles (proton-as well as neutron-rich)17F and11Be on fusion with heavy target has been studied at near-barrier energies. The calculations have been performed in the coupled channels approach where, in addition to the normal coupling of the ground state of the projectile to the continuum, inelastic excitation of the projectile to the bound excited state and its coupling to the continuum have also been taken into consideration. The inclusion of these additional couplings has been found to have significant effect on the fusion excitation function of neutron-rich11Be on208Pb whereas the effect has been observed to be nominal for the case of proton-rich17F on the same target. The pronounced effect of the channel coupling on the fusion process in the case of11Be is attributed to its well-developed halo structure.

• Anomalous scattering factors of some rare earth elements evaluated using photon interaction cross-sections

The real and imaginary parts,f’(E) and”(E) of the dispersion corrections to the forward Rayleigh scattering amplitude (also called anomalous scattering factors) for the elements La, Ce, Pr, Nd, Sm, Gd, Dy, Ho and Er, have been determined by a numerical evaluation of the dispersion integral that relates them through the optical theorem to the photoeffect cross-sections. The photoeffect cross-sections are derived from the total attenuation cross-section data set experimentally determined using high resolution high purity germanium detector in a narrow beam good geometry set-up for these elements in the photon energy range 5 to 1332 keV and reported earlier by the authors. Below 5 keV, Scofield’s photoeffect cross-sections compiled in XCOM program have been interpolated and used. Simple formulae forf” in terms of atomic number and energy have also been obtained. The data cover the energy region from 6 to 85 keV and atomic numberZ from 57–68. The results obtained are found to agree fairly well with the other available data.

• Dynamical properties of a two-level system with arbitrary nonlinearities

We investigate some aspects of a generalized JC-model which include arbitrary forms of non-linearities of both the field and the intensity-dependent atom-field coupling. We obtain an exactly analytic solution of the model, by means of which we identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained.

• Phase conjugation of gap solitons: A numerical study

We study the effect of a nearby phase-conjugate mirror (PCM) on the gap soliton of a Kerr non-linear periodic structure. We show that phase conjugation of the gap soliton (in the sense of replication of the amplitude profile in the reverse direction) is possible under the condition of PCM reflectivity approaching unity. This is in contrast with the results for linear structures, where the wave profiles can be conjugated for arbitrary values of the PCM reflectivity. The sensitivity of the conjugation of the gap solitons to PCM reflectivity is ascribed to the fine balance of non-linearity with dispersion, necessary for their existence.

• Field theoretic calculation of energy cascade rates in non-helical magnetohydrodynamic turbulence

Energy cascade rates and Kolmogorov’s constant for non-helical steady magnetohydrodynamic turbulence have been calculated by solving the flux equations to the first order in perturbation. For zero cross helicity and space dimensiond = 3, magnetic energy cascades from large length-scales to small length-scales (forward cascade). In addition, there are energy fluxes from large-scale magnetic field to small-scale velocity field, large-scale velocity field to small-scale magnetic field, and large-scale velocity field to large-scale magnetic field. Kolmogorov’s constant for magnetohydrodynamics is approximately equal to that for fluid turbulence (≈ 1.6) for Alfvén ratio 05 ≤rA ≤ ∞. For higher space-dimensions, the energy fluxes are qualitatively similar, and Kolmogorov’s constant varies asd1/3. For the normalized cross helicity σc →1, the cascade rates are proportional to (1 − σc)/(1 + σc , and the Kolmogorov’s constants vary significantly with σcc.

• Three-dimensional wake potential in a streaming dusty plasma

The oscillatory wake potential for a slowly moving or static test dust particulate in a finite temperature, collisionless and unmagnetized dusty plasma with a continuous flow of ions and dust particles has been studied. The collective resonant interaction of the moving test particle with the low-frequency and low-phase-velocity dust-acoustic mode is the origin of the periodic attractive force between the like polarity particulates along and perpendicular to the streaming ions and dust grains resulting into dust-Coulomb crystal formation. This wake potential can explain the three-dimensional dust-Coulomb crystal formation in the laboratory conditions.

• Quantum treatment of the Anderson-Hasegawa model in the presence of superexchange

We revisit the Anderson-Hasegawa double-exchange model and critically examine its exact solution when the core spins are treated quantum mechanically. We show that the quantum effects, in the presence of an additional superexchange interaction between the core spins, yield a term, the significance of which has been hitherto ignored. The importance of this term is further assessed by numerically exact computation for a four-spin system.

• Surface critical magnetic field Hc3(T) of a bulk superconductor MgB2 using two-band Ginzburg-Landau theory

Two-band Ginzburg-Landau (TB G–L) equations for a bulk MgB2 were solved analytically to determine the temperature dependence of surface critical magnetic fieldHc3 (T). It is shown thatHc3 (T) has the same temperature dependence with Hc2 (T), similar to the case of a single-band superconductor,Hc3 (T) = 166Hc2 (T). We use an elimination procedure for the decoupling of G–L equations of two-band superconductivity, which eases the calculations. It is expected that the temperature dependence forHc3 (T) gives positive curvature nearTc.

• Magnetic behaviour of nano-particles of Fe2.9Zn0.1O4

DC magnetization measurements are reported in the temperature range 20–100 K on a poly-disperse nano-particle sample of the spinel ferrite Fe2.9Zn0.1O4 with a log-normal size distribution of median diameter 43.6 Å and standard deviation 0.58. Outside a core of ordered spins, moments in surface layer are disordered. Results also show some similarities with conventional spin glasses. Blocking temperature exhibits a near linear variation with two-third power of the applied magnetic field and magnetizationM evolves nearly linearly with logarithm of timet. Magnetic anisotropy has been estimated by analysing theM-logt curve. Anisotropy values show a large increase over that of bulk particle samples. Major contribution to this enhancement comes from the disordered surface spins.

• Surface plasma waves over bismuth-vacuum interface

A surface plasma wave (SPW) over bismuth-vacuum interface has a signature of mass anisotropy of free electrons. For SPW propagation along the trigonal axis there is no birefringence. The frequency cutoff of SPW$$\omega _{cutoff} = \omega _p /\sqrt {2(\varepsilon _L + \varepsilon )}$$ lies in the far infrared region and can be accessed using free electron laser. The damping rate of waves at low temperatures is low. The surface plasma wave may be excited by an electron beam of current ∼100 mA propagating parallel to the interface in its close proximity.

• # Pramana – Journal of Physics

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Posted on July 25, 2019