• Volume 78, Issue 5

May 2012,   pages  667-833

• The exact solutions for the interaction $V(r) = \alpha r^{2d−2} − \beta r^{d−2}$ by Nikiforov–Uvarov method

The exact solutions for the two- and 𝑁-dimensional Schrödinger equation have been rederived for the potential $V (r ) = \alpha r^{2d−2} − \beta r^{d−2}$ by Nikiforov–Uvarov method. Speciﬁc results are presented for (i) the hydrogen atom and (ii) an isotropic harmonic oscillator. The dimensionality of the problem is seen to enter into these relations in such a way that one can immediately verify the corresponding three-dimensional results. The local accidental degeneracies are also explained for the two- and 𝑁-dimensional problems.

• Equations of motion for a relativistic wave packet

The time derivative of the position of a relativistic wave packet is evaluated. It is found that it is equal to the mean value of the momentum of the wave packet divided by the mass of the particle. The equation derived represents a relativistic version of the second Ehrenfest theorem.

• Exact anisotropic sphere with polytropic equation of state

We study static spherically symmetric spacetime to describe compact objects with anisotropic matter distribution. We express the system of Einstein ﬁeld equations as a new system of differential equations using a coordinate transformation, and then write the system in another form with polytropic equation of state and obtain two classes of exact models. The models satisfy all major physical features expected in a realistic star. For polytropic index $n = 2$, we obtain expressions for mass and density which are comparable with the reported experimental observations.

• A rotating charged black hole solution in $f (R)$ gravity

In the context of $f (R)$ theories of gravity, we address the problem of ﬁnding a rotating charged black hole solution in the case of constant curvature. A new metric is obtained by solving the ﬁeld equations and we show that its behaviour is typical of a rotating charged source. In addition, we analyse the thermodynamics of the new black hole. The results ensure that the thermodynamical properties in $f (R)$ gravities are qualitatively similar to those of standard General Relativity.

• Pattern formation in arrays of chemical oscillators

We describe a simple model mimicking diffusively coupled chemical micro-oscillators. We characterize the rich variety of dynamical states emerging from the model under variation of time delay in coupling, coupling strength and boundary conditions. The spatiotemporal patterns obtained include clustering, mixed dynamics, inhomogeneous steady states and amplitude death. Further, under delay in coupling, the model yields transitions from phase to antiphase oscillations, reminiscent of that observed in experiments [M Toiya et al, J. Chem. Lett. 1, 1241 (2010)].

• Nucleation rate of the quark-gluon plasma droplet at ﬁnite quark chemical potential

The nucleation rate of quark-gluon plasma (QGP) droplet is computed at ﬁnite quark chemical potential. In the course of computing the nucleation rate, the ﬁnite size effects of the QGP droplet are taken into account. We consider the phenomenological ﬂow parameter of quarks and gluons, which is dependent on quark chemical potential and we calculate the nucleation rate of the QGP droplet with this parameter. While calculating the nucleation rate, we ﬁnd that for low values of quark phenomenological parameter $\gamma q$, nucleation rate is negligible and when $\gamma_q$ increases, nucleation rate increases signiﬁcantly.

• Two-particle momentum correlations in jets produced in $e^+ e^−$ annihilation at $\sqrt{s} = 60$ GeV

The goal of this analysis is to measure the two-particle momentum correlation in jets, in the reaction $e^+e^− \to$ hadrons, to study its dependence on jet energy, and compare the results with analytical predictions of the next-to-leading log approximation (NLLA), using data collected by the AMY detector at a centre of mass energy of 60 GeV. Results are obtained for charged particles and for events with $E_{c.m.} = 60$ GeV.

• Nucleon momentum distributions and elastic electron scattering form factors for some 1p-shell nuclei

The nucleon momentum distributions (NMD) and elastic electron scattering form factors of the ground state for 1p-shell nuclei with $Z = N$ (such as 6Li, 10B, 12C and 14N nuclei) have been calculated in the framework of the coherent density ﬂuctuation model (CDFM) and expressed in terms of the weight function $|f(x)|^2$. The weight function has been expressed in terms of nucleon density distribution (NDD) of the nuclei and determined from the theory and the experiment. The feature of the long-tail behaviour at high-momentum region of the NMDs has been obtained by both the theoretical and experimental weight functions. The experimental form factors $F(q)$ of all the considered nuclei are very well reproduced by the present calculations for all values of momentum transfer 𝑞. It is found that the contributions of the quadrupole form factors $F_{C2}(q)$ in 10B and 14N nuclei, which are described by the undeformed p-shell model, are essential for obtaining a remarkable agreement between the theoretical and experimental form factors.

• Effect of isospin-dependent cross-section on fragment production in the collision of charge asymmetric nuclei

To understand the role of isospin effects on fragmentation due to the collisions of charge asymmetric nuclei, we have performed a complete systematical study using isospin-dependent quantum molecular dynamics model. Here simulations have been carried out for ${}^{124}X_n + {}^{124}X_n$ ,where 𝑛 varies from 47 to 59 and for 40Y$_m$ + 40Y$_m$ , where 𝑚 varies from 14 to 23. Our study shows that isospin-dependent cross-section shows its inﬂuence on fragmentation in the collision of neutron-rich nuclei.

• A study of nanosized zinc oxide and its nanoﬂuid

The synthesis and characterization of nanosized zinc oxide and its nanoﬂuid in a polyvinyl alcohol (PVA) matrix have been done in the present investigation. Crystalline zinc oxide nanoparticles are synthesized using single-step chemical method while the nanoﬂuids are prepared by the dispersion of nanoparticles in PVA solution using an ultrasonicator. The prepared nanoparticles are characterized using X-ray diffraction, SEM–EDX and UV–visible spectrum. The particle size distribution measurement is carried out by acoustic particle sizer. The ultrasonic velocities are measured in the synthesized nanoﬂuid under different physical conditions using an ultrasonic interferometer. It is found that the degree of crystallinity of nanoparticles depends on the evaporation rate during its synthesis and ultrasonic velocity has non-linear relation with temperature for the present nanoﬂuid.

• Gravitational Jaynes–Cummings model beyond the rotating wave approximation

In this paper, the quantum properties of a two-level atom and the cavity-ﬁeld in the Jaynes–Cummings model with the gravity beyond the rotating wave approximation are investigated. For this purpose, by solving the Schrödinger equation in the interaction picture, the evolving state of the system is found by which the inﬂuence of the counter-rotating terms on the dynamical behaviour of atomic population inversion and the probability distribution of the cavity-ﬁeld as quantum properties is explored. The results in the atom–ﬁeld system beyond the rotating wave approximation with the gravity show that the quantum properties are not completely suppressed under certain conditions.

• Relativistic effects on the modulational instability of electron plasma waves in quantum plasma

Relativistic effects on the linear and nonlinear properties of electron plasma waves are investigated using the one-dimensional quantum hydrodynamic (QHD) model for a twocomponent electron–ion dense quantum plasma. Using standard perturbation technique, a nonlinear Schrödinger equation (NLSE) containing both relativistic and quantum effects has been derived. This equation has been used to discuss the modulational instability of the wave. Through numerical calculations it is shown that relativistic effects signiﬁcantly change the linear dispersion character of the wave. Unlike quantum effects, relativistic effects are shown to reduce the instability growth rate of electron plasma waves.

• Crystal growth, FTIR and thermal characterization of bis(ethyltriphenylphosphonium) tetrabromomanganate(II) dihydrate crystals

Single crystals of a novel compound, bis(ethyltriphenylphosphonium) tetrabromomanganate(II) dihydrate (BTP-Mn) were grown by solution growth-slow evaporation technique from aqueous solution of the compound at ambient temperature. The grown crystals were characterized by elemental analysis, powder X-ray diffraction, thermal analysis, nuclear magnetic resonance spectroscopy (NMR) and Fourier transform infra-red spectroscopy (FTIR) techniques. The chemical composition of the compound was revealed by elemental analysis and its crystallinity was conﬁrmed by powder X-ray diffraction. Thermal analysis conﬁrmed that the compound was stable up to 125°C. The various kinds of protons and carbons present in the compound were conﬁrmed by 1H NMR and 13C NMR technique respectively and the presence of phosphorous was conﬁrmed by ${}^{31}$P NMR spectrum in the compound. The modes of vibration of different molecular groups present in the compound were identiﬁed by FTIR spectral analysis. The second harmonic generation behaviour was tested by Nd:YAG laser source.

• The calculation of active Raman modes of 𝛼-quartz crystal via density functional theory based on B3LYP Hamiltonian in $6–311+$G(2d) basis set

We obtained an approximation of the force ﬁeld of 𝛼-quartz crystal using a new idea of applying density functional theory [J Purton, R Jones, C R A Catlow and M Leslie, Phys. Chem. Minerals 19, 392 (1993)]. Our calculations were based on B3LYP Hamiltonian [A N Lazarev and A P Mirgorodsky, Phys. Chem. Minerals 18, 231 (1991)] in $6−311+$G(2d) basis set for H\$_{16}Si7O6 cluster and included a unit cell of the lattice. The advantage of our method is the increase in the speed of calculations and the better adaption of simulation results with the experimental data.

• Design of self-correction coils in a superferric dipole magnet

Design of self-correction coils in a superferric dipole magnet is carried out. By adopting the self-correction coil (SCC) scheme, we can do online correction of unwanted ﬁelds inside the magnet aperture during the whole operating cycle irrespective of their origin. The self-correction coils are short-circuited superconducting coils of required symmetry placed in the useful aperture of the AC dipole magnet. Design and operation mechanism of self-correction coils in a superferric dipole magnet are discussed in this paper.

• Cosmological model of interacting phantom and Yang–Mills ﬁelds

In this paper, we consider a model of interacting phantom and Yang–Mills (YM) ﬁelds by assuming dilaton-type coupling. Using the speciﬁc solution for YM equation previously found by the author, we obtain simple exact solutions for the accelerated expansion of the Friedmann–Robertson–Walker (FRW) cosmological model. Besides, we derive induced potentials of phantom ﬁeld corresponding to some given regimes of expansion. The effective equations of state (EoS) have been reconstructed for all types of models considered here.

• Effect of conduction band nonparabolicity on the optical properties in a single quantum well under hydrostatic pressure and electric ﬁeld

The effect of conduction band nonparabolicity on the linear and nonlinear optical properties such as absorption coefﬁcients, and changes in the refractive index are calculated in the Al0.3Ga0.7As/GaAs heterostructure-based symmetric rectangular quantum well under applied hydrostatic pressure and electric ﬁeld. The electron envelope functions and energies are calculated in the effective mass equation including the conduction band nonparabolicity. The linear and nonlinear optical properties have been calculated in the density matrix formalism with two-level approximation. The conduction band nonparabolicity shifts the positions of the optical properties and decreases their strength compared to those without this correction. Both the optical properties are enhanced with the applied hydrostatic pressure. While the absorption coefﬁcients are bleached under the combined effect of high pressure and electric ﬁeld, the bleaching effect is reduced when nonparabolicity is included.

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