• Volume 87, Issue 1

July 2016

• Editorial

• General editorial on publication ethics

• Energy distribution of cosmic rays in the Earth’s atmosphere and avionic area using Monte Carlo codes

Cosmic rays cause significant damage to the electronic equipments of the aircrafts. In this paper, we have investigated the accumulation of the deposited energy of cosmic rays on the Earth’s atmosphere, especially in the aircraft area. In fact, if a high-energy neutron or proton interacts with a nanodevice having only a few atoms, this neutron or proton particle can change the nature of this device and destroy it. Our simulation based on Monte Carlo using Geant4 code shows that the deposited energy of neutron particles ranging between 200MeV and 5 GeV are strongly concentrated in the region between 10 and 15 km from the sea level which is exactly the avionic area. However, the Bragg peak energy of proton particle is slightly localized above the avionic area.

• Influence of nuclear dissipation on fission dynamics of the excited nucleus $^{248}$Cf within a stochastic approach

A stochastic approach to fission dynamics based on two-dimensional Langevin equations was applied to calculate the anisotropy of the fission fragments angular distribution and average pre-scission neutron multiplicities for the compound nucleus 248Cf formed in the {16}$O+$^{232}$Th reactions. Postsaddle nuclear dissipation strength of$(12–14) \times 10^{21} s^{−1}$was extracted for Cf nucleus by fitting the results of calculations with the experimentaldata. Furthermore, it was found that the results of calculations for the anisotropy of the fission fragments angular distribution and pre-scission neutron multiplicities are very sensitive to the magnitude of post-saddle nucleardissipation. • Significance of power average of sinusoidal and non-sinusoidal periodic excitations in nonlinear non-autonomous system Additional sinusoidal and different non-sinusoidal periodic perturbations applied to the periodically forced nonlinear oscillators decide the maintainance or inhibitance of chaos. It is observed that the weak amplitude of the sinusoidal force without phase is sufficient to inhibit chaos rather than the other non-sinusoidal forces and sinusoidal force with phase. Apart from sinusoidal force without phase, i.e., from various non-sinusoidal forces and sinusoidal force with phase, square force seems to be an effective weak perturbation to suppress chaos. The effectiveness of weak perturbation for suppressing chaos is understood with the total power average of the external forces applied to the system. In any chaotic system, the total power average of the external forces isconstant and is different for different nonlinear systems. This total power average decides the nature of the force to suppress chaos in the sense of weak perturbation. This has been a universal phenomenon for all the chaoticnon-autonomous systems. The results are confirmed by Melnikov method and numerical analysis. With the help of the total power average technique, one can say whether the chaos in that nonlinear system is to be supppressed or not. • Effect of barium doping on the physical properties of zinc oxide nanoparticles elaborated via sonochemical synthesis method The aim of this work is to study the effect of barium (Ba) doping on the optical, morphological and structural properties of ZnO nanoparticles. Undoped and Ba-doped ZnO have been successfully synthesized via sonochemical method using zinc nitrate, hexamethylenetetramine (HMT) and barium chloride as startingmaterials. The structural characterization by XRD and FTIR shows that ZnO nanoparticles are polycrystalline with a standard hexagonal ZnO wurtzite crystal structure. Decrease in lattice parameters from diffraction data shows the presence of Ba$^{2+}$in the ZnO crystal lattice. The morphology of the ZnO nanoparticles has been determined by scanning electron microscopy (SEM). Incorporation of Ba was confirmed from the elemental analysis using EDX. Optical analysis depicted that all samples exhibit an average optical transparency over 80%, in the visible range. Room-temperature photoluminescence (PL) spectra detected a strong ultraviolet emission at 330 nmand two weak emission bands were observed near 417 and 560 nm. Raman spectroscopy analysis of Ba-doped samples reveals the successful doping of Ba ions in the host ZnO. • Stability analysis and quasinormal modes of Reissner–Nordstrøm space-time via Lyapunov exponent We explicitly derive the proper-time (τ ) principal Lyapunov exponent (λp) and coordinate-time (t ) principal Lyapunov exponent$(\lambda_c)$for Reissner–Nordstrøm (RN) black hole (BH). We also compute their ratio. For RN space-time, it is shown that the ratio is$(\lambda_{p}/\lambda_{c}) = r_{0}/\sqrt{r^{2}0 − 3Mr_{0} + 2Q^{2}}$for time-like circulargeodesics and for Schwarzschild BH, it is$(\lambda_{p}/\lambda_{c}) = \sqrt{r_{0}}/\sqrt{r_{0} − 3M}. We further show that their ratio $\lambda_{p}/\lambda_{c}$ may vary from orbit to orbit. For instance, for Schwarzschild BH at the innermost stable circular orbit (ISCO), the ratio is $(\lambda_{p}/\lambda_{c})_{|rISCO}=6M = \sqrt{2}$ and at marginally bound circular orbit (MBCO) the ratio is calculated to be $(\lambda_{p}/\lambda_{c})|_{rmb}=4M = 2$. Similarly, for extremal RN BH, the ratio at ISCO is $(\lambda_{p}/\lambda_{c})|_{rISCO}=4M = 2\sqrt{2}/\sqrt{3}$. We also further analyse the geodesic stability via this exponent. By evaluating the Lyapunov exponent, it is shown that in the eikonal limit, the real and imaginary parts of the quasinormal modes of RN BH is given by the frequency and instability time-scale of the unstable null circular geodesics.

• Experimental study of soft X-ray intensity with different anode tips in Amirkabir plasma focus device

To study the effect of different anode tip geometries on the intensity of soft X-rays emitted from a 4 kJ plasma focus device (PFD), we considered five different anode tips which were cylindrical-flat, cylindricalhollow, spherical-convex, cone-flat and cone-hollow tips. BPX-65 PIN diodes covered by four different filters are used to register the intensity of soft X-rays. The use of cone-flat anode tip has augmented the emitted X-ray three times compared to the conventional cylindrical-flat anode.

• Lifetime measurements in the yrast band of the gamma-soft nuclei $^{131}$Ce and $^{133}$Pr

Lifetimes of excited states in the yrast band of the gamma-soft nuclei $^{131}$Ce and 133Pr have been measured using the recoil distance Doppler shift and Doppler shift attenuation methods. The yrast bands in $^{131}$Ce and $^{133}$Pr are based on odd decoupled neutron $νh_{11/2}$ high $\Omega$ and proton $\pi h_{11/2}$ low $\Omega$ orbitals, respectively. Thetriaxiality parameter extracted from the experimentally deduced values of transition quadrupole moments, within the framework of cranked Hartree–Fock–Bogoliubov (CHFB) and total Routhian surface (TRS) calculatons, is$\gamma ~ −80{^o}$ for the band in $^{131}$Ce at high spins, while for the band in $^{133}$Pr, the value of $\gamma$ is close to $0^{o}$. Thisagrees well with the $\gamma$ shape polarization property of high and low $\Omega_{11/2}$ orbitals in these gamma-soft nuclei.

• The dependence of scattering length on van derWaals interaction and reduced mass of the system in two-atomic collision at cold energies

The static exchange model (SEM) and the modified static exchange model (MSEM) recently introduced by Ray in {\it Pramana – J. Phys.} 83, 907 (2014) are used to study the elastic collision between two hydrogen-like atoms when both are in ground states by considering the system as a four-body Coulomb system in the centre of mass frame, in which all the Coulomb interaction terms in direct and exchange channels are treated exactly. The SEM includes the non-adiabatic short-range effect due to electron exchange. The MSEM added init, the long-range effect due to induced dynamic dipole polarizabilities between the atoms e.g., the van der Waals interaction. Applying the SEM code in different H-like two-atomic systems, a reduced mass $(\mu)$ dependence on the scattering length is observed. Again, applying the MSEM code on H(1s)–H(1s) elastic scattering and varying the minimum values of interatomic distance $R_0$, the dependence of scattering length on the effective interatomic potential consistent with the existing physics is observed. Both these basic findings in low and cold energy atomic collision physics are quite useful and are being reported for the first time.

• Shock wave propagation in soda lime glass using optical shadowgraphy

Propagation of shock waves in soda lime glass, which is a transparent material, has been studied using the optical shadowgraphy technique. The time-resolved shock velocity information has been obtained (1) in single shot, using the chirped pulse shadowgraphy technique, with a temporal resolution of tens of picoseconds and (2) in multiple shots, using conventional snapshot approach, with a second harmonic probe pulse. Transient shock velocities of $(5–7) \times 10^{6}$ cm/s have been obtained. The scaling of the shock velocity with intensity in the $2 \times 10^{13}–10^{14}$ W/cm$^2$ range has been obtained. The shock velocity is observed to scale with laser intensity as $I^{0.38}$. The present experiments also show the presence of ionization tracks, generated probably due to X-ray hotspots from small-scale filamentation instabilities. The results and various issues involved in these experiments are discussed

• Quantum mechanics of $PT$ and non-$PT$ -symmetric potentials in three dimensions

With a view of exploring new vistas with regard to the nature of complex eigenspectra of a non-Hermitian Hamiltonian, the quasi-exact solutions of the Schrödinger equation are investigated for a shifted harmonic potential under the framework of extended complex phase-space approach. Analyticity property ofthe eigenfunction alone is found sufficient to throw light on the nature of the eigenvalues and eigenfunctions of a system. Explicit expressions of eigenvalues and eigenfunctions for the ground state as well as excited state including their $PT$-symmetric version are worked out.

• Effect of dust size distribution and dust charge fluctuation on dust ion-acoustic shock waves in a multi-ion dusty plasma

The effects of dust size distribution and dust charge fluctuation of dust grains on the small but finite amplitude nonlinear dust ion-acoustic shock waves, in an unmagnetized multi-ion dusty plasma which contains negative ions, positive ions and electrons, are studied in this paper. A Burgers equation and its stationary solutions are obtained by using the reductive perturbation method. The analytical and numerical results show that the height with polynomial dust size distribution is larger than that of the monosized dusty plasmas with the same dustgrains, but the thickness in the case of different dust grains is smaller than that of the monosized dusty plasmas. Furthermore, the moving speed of the shock waves also depend on different dust size distributions.

• Measurement of attenuation cross-sections of some fatty acids in the energy range 122–1330 keV

The mass attenuation coefficients $(\mu m)$ have been measured for undecylic acid (C$_{11}$H$_{22}$O$_2$), lauric acid (C$_{12}$H$_{24}$O$_2$), tridecylic acid (C$_{13}$H$_{26}$O$_2$), myristic acid (C$_{14}$H$_{28}$O$_2$), pentadecylic acid (C$_{15}$H$_{30}$O$_2$) andpalmitic acid (C$_{16}$H$_{32}$O$_2$) using $^{57}$Co, $^{133}$Ba, $^{137}$Cs, $^{60}$Co and $^{22}$Na emitted γ radiation with energies 122, 356,511, 662, 1170, 1275 and 1330 keV, respectively. The accurate values of the effective atomic number (Zeff), atomic cross-section $(\sigma t,)$, electronic cross-section $(\sigma e)$ and the effective electron density (Neff) have great significance in radiation protection and dosimetry. These quantities were obtained by utilizing experimentally measured values of mass attenuation coefficients $(\mu m)$. A NaI(Tl) scintillation detector with 8.2% (at 662 keV) resolution was used for detecting of attenuated γ -photons. The variation in Zeff and Neff of fatty acids with energy is discussed. The experimental and theoretical results are in good agreement within 2% deviation.

• Similarities between 2D and 3D convection for large Prandtl number

Using direct numerical simulations of Rayleigh–Bénard convection (RBC), we perform a comparative study of the spectra and fluxes of energy and entropy, and the scaling of large-scale quantities for large and infinite Prandtl numbers in two (2D) and three (3D) dimensions. We observe close similarities between the 2D and 3D RBC, in particular, the kinetic energy spectrum $E^{u}(k) ∼ k^{−13/3}$, and the entropy spectrum exhibits a dual branch with a dominant $k^{−2}$ spectrum. We showed that the dominant Fourier modes in 2D and 3D flows are very close. Consequently, the 3D RBC is quasi-two-dimensional, which is the reason for the similarities between the 2D and 3D RBC for large and infinite Prandtl numbers.

• Signature splitting in two quasiparticle rotational bands of $^{180,182}$Ta

The signature splittings in $K^{\pi} =1^{+}: 7/2[404]_{\pi}\bigotimes 9/2[624]_{\nu}$ , $K^{\pi} =0^{−}: 9/2[514]_{\pi}\bigotimes 9/2[624]_{\nu}$ bands of $^{180}$Ta and $K^{\pi} = 0^{−}: 7/2[404]_{\pi}\bigotimes 7/2[503]_{\nu}$ , $K_{\pi} = 1^{−}: 5/2[402]_{\pi}\bigotimes 3/2[512]_{\nu$ , $K^{\pi} = 1^{+}: 7/2[404]_{\pi}\bigotimes9/2[624]_{\nu}$ bands of $^{182}$Ta are analysed within the framework of two-quasiparticle rotor model. The phase as well as magnitudeof the experimentally observed signature splitting in $K^{\pi} = 1^{+}$ band of $^{180}$Ta, which could not be explained in earlier calculations, is successfully reproduced. The conflict regarding placement of a 12$^+$ level in $K^{\pi} = 1^{+}: 7/2+[404]_{\pi}\bigotimes 9/2+[624]_{\nu}$ ground-state rotational band of $^{180}$Ta is resolved and tentative nature of $K^{\pi} = 0^{−}:7/2[404]_{\pi}\bigotimes7/2[503]_{\nu}$ ,$K^{\pi} = 1^{+}: 7/2[404]_{\pi}\bigotimes 9/2[624]_{\nu}$ bands observed in $^{182}$Ta is confirmed. As a future prediction for experimentalists, these two-quasiparticle structures observed in $^{180}$Ta and $^{182}$Ta are extended to higherspins.

• The modified simple equation method for solving some fractional-order nonlinear equations

Nonlinear fractional differential equations are encountered in various fields of mathematics, physics, chemistry, biology, engineering and in numerous other applications. Exact solutions of these equations play a crucial role in the proper understanding of the qualitative features of many phenomena and processes in various areas of natural science. Thus, many effective and powerful methods have been established and improved. In this study, we establish exact solutions of the time fractional biological population model equation and nonlinearfractional Klein–Gordon equation by using the modified simple equation method.

• Entanglement dynamics of two interacting qubits under the influence of local dissipation

We investigate the dynamics of entanglement given by the concurrence of a two-qubit system in the non-Markovian setting. A quantum master equation is derived, which is solved in the eigenbasis of the system Hamiltonian for X-type initial states. A closed formula for time evolution of concurrence is presented for a pure state. It is shown that under the influence of dissipation non-zero entanglement is created in unentangled twoqubit states which decay in the same way as pure entangled states. We also show that under real circumstances,the decay rate of concurrence is strongly modified by the non-Markovianity of the evolution.

• # Pramana – Journal of Physics

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December 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019