• Volume 75, Issue 4

October 2010,   pages  565-755

• Travelling wave solutions for ($N + 1$)-dimensional nonlinear evolution equations

In this paper, we implement the exp-function method to obtain the exact travelling wave solutions of ($N + 1$)-dimensional nonlinear evolution equations. Four models, the ($N + 1$)-dimensional generalized Boussinesq equation, ($N + 1$)-dimensional sine-cosine-Gordon equation, ($N + 1$)-double sinh-Gordon equation and ($N + 1$)-sinh-cosinh-Gordon equation, are used as vehicles to conduct the analysis. New travelling wave solutions are derived.

• Quarkonium and hydrogen spectra with spin-dependent relativistic wave equation

The non-linear non-perturbative relativistic atomic theory introduces spin in the dynamics of particle motion. The resulting energy levels of hydrogen atom are exactly the same as that of Dirac theory. The theory accounts for the energy due to spin-orbit interaction and for the additional potential energy due to spin and spin-orbit coupling. Spin angular momentum operator is integrated into the equation of motion. This requires modification to classical Laplacian operator. Consequently, the Dirac matrices and the k operator of Dirac’s theory are dispensed with. The theory points out that the curvature of the orbit draws on certain amount of kinetic and potential energies affecting the momentum of electron and the spin-orbit interaction energy constitutes a part of this energy. The theory is developed for spin-1/2 bound state single electron in Coulomb potential and then extended further to quarkonium physics by introducing the linear confining potential. The unique feature of this quarkonium model is that the radial distance can be exactly determined and does not have a statistical interpretation. The established radial distance is then used to determine the wave function. The observed energy levels are used as the input parameters and the radial distance and the string tension are predicted. This ensures 100% conformance to all observed energy levels for the heavy quarkonium.

• Eigenvalue spectra of a $\mathcal{PT}$ -symmetric coupled quartic potential in two dimensions

The Schrödinger equation was solved for a generalized $\mathcal{PT}$-symmetric quartic potential in two dimensions. It was found that, under a suitable ansatz for the wave function, the system possessed real and discrete energy eigenvalues. Analytic expressions for the energy eigenvalues and the eigenfunctions for the first four states were obtained. Some constraining relations among the wave function parameters rendered the problem quasi-solvable.

• Solitary wave solutions of selective nonlinear diffusion-reaction equations using homogeneous balance method

An auto-Bäcklund transformation derived in the homogeneous balance method is employed to obtain several new exact solutions of certain kinds of nonlinear diffusion-reaction (D-R) equations. These equations arise in a variety of problems in physical, chemical, biological, social and ecological sciences.

• A primer for electroweak induced low-energy nuclear reactions

Under special circumstances, electromagnetic and weak interactions can induce low-energy nuclear reactions to occur with observable rates for a variety of processes. A common element in all these applications is that the electromagnetic energy stored in many relatively slow-moving electrons can – under appropriate circumstances – be collectively transferred into fewer, much faster electrons with energies sufficient for the latter to combine with protons (or deuterons, if present) to produce neutrons via weak interactions. The produced neutrons can then initiate low-energy nuclear reactions through further nuclear transmutations. The aim of this paper is to extend and enlarge upon various examples analysed previously, present order of magnitude estimates for each and to illuminate a common unifying theme amongst all of them.

• Search for $B_{s} \rightarrow \phi \mu \mu$ decay at the Large Hadron Collider

As $B_{s}$ -mesons will be produced abundantly at the LHC, the observability of the flavour-changing-neutral-current decay mode $B_{s} \rightarrow \phi \mu^{+} \mu^{-}$ has been studied in CMS at the LHC centre-of-mass energy of 10 TeV. With an integrated luminosity of 100 pb-1, an upper limit of $6.7 \times 10^{−6}$ on the branching ratio is expected to be obtained. The potential at 7 TeV with a luminosity of 1 fb-1 is expected to be better .

• Gamow–Teller 1+ states in 112-124Sb isotopes

The violated supersymmetry property of the pairing interaction between nucleons were restored using the Pyatov method [Pyatov and Salamov, Nucleonica 22, 127 (1977)]. The eigenvalues and eigenfunctions of the restored Hamiltonian with the separable residual Gamow–Teller effective interactions in the particle–hole and particle–particle channels were solved within the framework of proton–neutron quasirandom phase approximation (pnQRPA). The Gamow–Teller resonance energies for 112-124Sb isotopes and the differential cross-sections for Sn(3He, 𝑡)Sb reactions at 𝐸(3He) = 200 MeV occurring by the excitation of the Gamow–Teller resonance state were calculated. The calculated values were compared with other calculations and the corresponding experimental data.

• $\omega (\rightarrow \pi^{+} \pi^{-} \pi^{0})$ meson photoproduction on proton

The cross-section for the $\pi^{+} \pi^{-} \pi^{0}$ invariant mass distribution in the $\gamma p$ reaction in the GeV region is calculated. This reaction is assumed to proceed through the formation of the 𝜔-meson in the intermediate state, because the production cross-section for this meson in the $\gamm p$ reaction in the GeV region is significant and it has a large branching ratio (88.8%) in the $\pi^{+} \pi^{−} \pi^{0}$ channel. The cross-sections for this reaction are calculated using the energy-dependent reaction amplitude, $f_{\gamma p \rightarrow \omega p (0)$, extracted from the latest 𝜔-meson photoproduction data. We use established procedure to calculate other factors, like width and propagator of the 𝜔-meson, so that our calculation can provide reliable cross-section. The calculated results reproduce the measured $\pi^{+} \pi^{-} \pi^{0}$ invariant mass distribution spectra in the $\gamma p$ reaction.

• Nucleation efficiency of R134a as a sensitive liquid for superheated drop emulsion detector

Superheated emulsion detector is known to detect neutrons, γ-rays and other charged particles. The present work includes the study of nucleation efficiency of super-heated drops of one of the CFC-free liquids, R134a (C2H2F4), to fast neutrons, its response to 𝛾-rays from 241Am and 137Cs and compare its nucleation efficiency with that of R12. The observation indicates that because of the presence of hydrogen, the nucleation efficiency is less in R134a than in R12 in the present neutron energy range of considera-tion. R134a is one of the most environment-friendly, commercially available liquid that is suitable for superheated drop detector, specially in neutron dosimetry and one needs to investigate it in detail.

• Crystal growth and comparison of vibrational and thermal properties of semi-organic nonlinear optical materials

Single crystals of urea thiourea mercuric sulphate (UTHS) and urea thiourea mercuric chloride (UTHC), semi-organic nonlinear optical materials, were grown by low-temperature solution growth technique by slow evaporation method using water as the solvent. Good quality single crystals were grown within three weeks. The nonlinear nature of the crystals was confirmed by SHG test. The UV–Vis spectrum showed the transmitting ability of the crystals in the entire visible region. FTIR spectrum was recorded and vibrational assignments were made. The degree of dopant inclusion was ascertained by AAS. The TGA–DTA studies showed the thermal properties of the crystals.

• Comparative study of runaway electron diffusion in the rise phase of low $q_{a}$ and normal $q_{a}$ discharges in the SINP tokamak

The behaviour of runaway electrons in the SINP tokamak, which can be operated in a normal edge safety factor ($q_{a}$) (NQ) discharge configuration as well as in a low $q_{a}$ (LQ) configuration, was experimentally investigated, during the initial plasma generation phase. An energy analysis of the runaway electron dynamics in the rise phase of the SINP tokamak discharges was also made. A comparison of the runaway electron diffusion coefficients in NQ and LQ is carried out in this paper.

• On complexly coupled modified KdV equations

We introduced complexly coupled modified KdV (ccmKdV) equations, which could be derived from a two-layer fluid model [Yang and Mao, Chin. Phys. Lett. 25, 1527 (2008); Hu, J. Phys. A: Math. Theor. 43, 185207 (2009)], and used the Miura transformation to construct expressions for their alternative Lax pair representations. We derived a Lagrangian-based approach to study the Hamiltonian structures of the ccmKdV equations and observed that the complexly coupled mKdV equations have an additional analytic structure. The coupled equations were characterized by two alternative Lagrangians not connected by a gauge term. We examined how the alternative Lagrangian descriptions of the system affect the bi-Hamiltonian structures.

• Collisional effect on the Weibel instability in the limit of high plasma temperature

The Weibel instability (WI) of relativistic electron beam (REB) penetrating an infinite collisional plasma was studied in the following models: (i) REB model, where the total equilibrium distribution function $f_{0} (\bar{p})$ is approximated by nonrelativistic back-ground electron and REB distribution functions and (ii) relativistic monoenergetic beam (RMB) model, where $f_{0}(\bar{p})$ is approximated by nonrelativistic background electrons and RMB distribution functions.

The dispersion equation including the effect of collision for a purely transverse mode describing each model was derived and solved analytically to obtain growth rates and conditions of excitation of the WI in the limit of high plasma temperature.

The purpose of this paper is to determine the effect of collision within the plasma on the growth rate of the WI for the two models. It was proved that the plasma collision frequency reduces the growth rate of WI at high plasma temperature. That is to say, collisions are inversely proportional to the growth rate. This leads to the important result: WI can be stabilized by increasing the plasma temperature.

Comparing the growth rate of WI in the two models (RMB and REB models), we came to the conclusion that growth rate of WI is more in the second case (REB case).

• Scattered ionizing radiations from low-energy focus plasma and radiation dosimetery assessment

Scattered ionizing radiation emissions from a low-energy plasma focus (0.1 kJ Mather-type) device operating with different gases were studied. The plasma focus device was powered by a capacitor bank of 1 𝜇F at 18 kV maximum charging voltage. The radiation emissions were investigated using time-integrated thermoluminescence TLD-500. These detectors were calibrated against standard X-ray machine as well as standard 𝛾 sources (60Co and 137Ca). Calibration of detectors showed linear relation over all the region of measurements. It was found that radiation levels would be minimum for different gases, when the gas pressure was between 0.5 and 0.8 Torr. Only helium deviated from this phenomenon as it gave maximum radiation level at 0.8 Torr pressure. It was also found that, for all the gases used, the radiation levels were maximum when the applied voltage was 15 keV.

• Molecular dynamics of liquid alkaline-earth metals near the melting point

Results of the studies of the properties like binding energy, the pair distribution function $g(r)$, the structure factor $S(q)$, specific heat at constant volume, velocity autocorrelation function (VACF), radial distribution function, self-diffusion coefficient and coordination number of alkaline-earth metals (Be, Mg, Ca, Sr and Ba) near melting point using molecular dynamics (MD) simulation technique using a pseudopotential proposed by us are presented in this article. Good agreement with the experiment is achieved for the binding energy, pair distribution function and structure factor, and these results compare favourably with the results obtained by other such calculations, showing the transferability of the pseudopotential used from solid to liquid environment in the case of alkaline-earth metals.

• Effect of magnetic field on the impurity binding energy of the excited states in spherical quantum dot

The effect of external magnetic field on the excited state energies in a spherical quantum dot was studied. The impurity energy and binding energy were calculated using the variational method within the effective mass approximation and finite barrier potential. The results showed that by increasing the magnetic field, the energy would be increased. The results obtained by this method were compared with the previous investigations.

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