Solution of Dirac equation for Eckart potential and trigonometric Manning Rosen potential using asymptotic iteration method

The Dirac equation for Eckart potential and trigonometric Manning Rosen potential with exact spin symmetry is obtained using an asymptotic iteration method. The combination of the two potentials is substituted into the Dirac equation,then the variables are separated into radial and angular parts. The Dirac equation is solved by using an asymptotic iteration method that can reduce the second order differential equation into a differential equation with substitution variables of hypergeometry type. The relativistic energy is calculated using Matlab 2011. This study is limited to the case of spin symmetry. With the asymptotic iteration method, the energy spectra of the relativistic equations and equations of orbital quantum number l can be obtained, where both are interrelated between quantum numbers. The energy spectrum is also numerically solved using the Matlab software, where the increase in the radial quantum number nr causes the energy to decrease. The radial part and the angular part of the wave function are defined as hypergeometry functions and visualized with Matlab 2011. The results show that the disturbance of a combination of the Eckart potential and trigonometric Manning Rosen potential can change the radial part and the angular part of the wave function.     

Electro-optic response of metal halide $$\hbox {CsPbI}_3$$: A first-principles study

In this work, we have obtained energy levels and charge radius for the β-stability line nucleus, in relativistic shell model. In this model, we considered a close shell for each nucleus containing double magic number and a single nucleon energy level. Here we have taken ⁴¹Ca with a single neutron in the ⁴⁰Ca core as an illustrative example. Then we have selected the Eckart plus Hulthen potentials for interaction between the core and the single nucleon. By using parametric Nikiforov–Uvarov (PNU) method, we have calculated the energy values and wave function. Finally, we have calculated the charge radius for ¹⁷O, ⁴¹Ca, ⁴⁹Ca and ⁵⁷Ni. Our results are in agreement with experimental values and hence this model can be applied for similar nuclei.     

Ab-initio calculations of structural,phonon and thermal properties of $$\hbox {Al}_x \hbox {Ga}_{1-x} \hbox {As}$$ alloy

We provide the energy spectrum of an electron in a degenerately doped semiconductor of parabolic band. Knowing the energy spectrum, the density-of-states (DOS) functions are obtained, considering the Gaussian distribution of the potential energy of the impurity states, showing a band tail in them e.g., energy spectrum and density-of-states. Therefore, Fermi integrals (FIs) of DOS functions, having band tail, are developed by the exact theoretical calculations of the same. It is noticed that with heavy dopings in semiconductors, the total FI demonstrates complex functions, containing both real and imaginary terms of different FI functions. Their moduli possess an oscillatory function of \(\eta \) (reduced \(\hbox {Fermi energy} = E_{\mathrm{f}}/k_{\mathrm{B}}T\), \(k_{\mathrm{B}}\) is the Boltzmann constant and T is the absolute temperature) and \(\eta _{e}\) (impurity screening potential), having a series solutions of confluent hypergeometric functions, \(\Phi (a, b; z)\), superimposed with natural cosine functions of angle \(\theta \). The variation of \(\theta \) with respect to \(\eta \) indicated a resonance at \(\eta =1.5\). The oscillatory behaviour of FIs show the existence of ‘band-gaps’, both in the real as well as in the forbidden bands as new band gaps in the semiconductor.     

Electronic structure and optical properties of prominent phases of $$\hbox {TiO}_{2}$$: First-principles study

We present the properties of the C-parameter as an event-shape variable. We calculate the coupling constants in the perturbative and also in the non-perturbative parts of the QCD theory, using the dispersive as well as the shape function models. By fitting the corresponding theoretical predictions to our data, we find \(\alpha _{\mathrm {s}} (M_{Z^{0}})\) = 0.117 ± 0.014 and α ₀(μ _I ) = 0.491 ± 0.043 for dispersive model and \(\alpha _{\mathrm {s}} (M_{Z^{0}})\) = 0.124 ± 0.015 and λ ₁ = 1.234 ± 0.052 for the shape function model. Our results are consistent with the world average value of \(\alpha _{\mathrm {s}} (M_{Z^{0}})\) = 0.118 ± 0.002. All these features are explained in the main text.     

Magnetic interactions and electronic structure of $$\hbox {Pt}_{2}\hbox {Mn}_{1-x}\hbox {Y}_{x} \hbox {Ga (Y = Cr and Fe)}$$ system: An ab-initio calculation

Structural, optical, electrical conductivity and dielectric relaxation properties of bulk 4-amino-3-mercapto-6-(2-(2-thienyl)vinyl)-1,2,4-triazin-5(4H)-one donor (AMT) are studied. The structure of AMT in its powder form was analysed by X-ray diffraction (XRD), infrared spectroscopy (FT-IR) and atomic force microscopy (AFM). AC measurements (impedance, capacitance and phase angle) are done over the temperature range 303–373 K and in the frequency range from 42 Hz to 5 MHz. Analytical approaches for the experimental results of the σ _AC(ω, T) and the temperature behaviour of the frequency exponent show that the correlated barrier hopping (CBH) model is a good model to explain the AC electrical conductivity of bulk AMT organic semiconductor material. Application of the dielectric modulus formulism gives a simple method for evaluating the activation energy of the dielectric relaxation. The activation energy from the DC conductivity and the relaxation time are quite similar suggesting a hopping mechanism for AMT. The optical band gap of AMT is investigated using spectrophotometric measurement of transmittance at normal incidence of light in the wavelength range 300–1100 nm.     

Sextonions,Zorn matrices,and $$\mathbf {e}_{\mathbf{7} \frac{\mathbf{1}}{\mathbf{2}}}$$

By exploiting suitably constrained Zorn matrices, we present a new construction of the algebra of sextonions (over the algebraically closed field \(\mathbb {C}\)). This allows for an explicit construction, in terms of Jordan pairs, of the non-semisimple Lie algebra \(\mathbf {e}_{\mathbf{7} \frac{\mathbf{1}}{\mathbf{2}}}\), intermediate between \(\mathbf {e_7}\) and \(\mathbf {e_8}\), as well as of all Lie algebras occurring in the sextonionic row and column of the extended Freudenthal Magic Square.     

Structural characterization of Mg substituted on A/B sites in $$\hbox {NiFe}_2\hbox {O}_4$$ nanoparticles using autocombustion method

A compact quantitative model based on oxide semiconductor interface density of states (DOS) is proposed for Al_0.25Ga_0.75N/GaN metal oxide semiconductor high electron mobility transistor (MOSHEMT). Mathematical expressions for surface potential, sheet charge concentration, gate capacitance and threshold voltage have been derived. The gate capacitance behaviour is studied in terms of capacitance–voltage (CV) characteristics. Similarly, the predicted threshold voltage (V _T) is analysed by varying barrier thickness and oxide thickness. The positive V _T obtained for a very thin 3 nm AlGaN barrier layer enables the enhancement mode operation of the MOSHEMT. These devices, along with depletion mode devices, are basic constituents of cascode configuration in power electronic circuits. The expressions developed are used in conventional long-channel HEMT drain current equation and evaluated to obtain different DC characteristics. The obtained results are compared with experimental data taken from literature which show good agreement and hence endorse the proposed model.     

Density functional study of $$\hbox {AgScO}_2$$: Electronic and optical properties

Dielectric relaxation studies of binary (jk) polar mixtures of tetrahydrofuran with N-methyl acetamide, N,N-dimethyl acetamide, N-methyl formamide and N,N-dimethyl formamide dissolved in benzene(i) for different weight fractions (w _{j k} ’s) of the polar solutes and mole fractions (x _j ’s) of tetrahydrofuran at 25 ^°C are attempted by measuring the conductivity of the solution under 9.90 GHz electric field using Debye theory. The estimated relaxation time (τ _{j k} ’s) and dipole moment (μ _{j k} ’s) agree well with the reported values signifying the validity of the proposed methods. Structural and associational aspects are predicted from the plot of τ _{j k} and μ _{j k} against x _j of tetrahydrofuran to arrive at solute–solute (dimer) molecular association upto x _j =0.3 of tetrahydrofuran and thereafter solute–solvent (monomer) molecular association upto x _j =1.0 for all systems except tetrahydrofuran + N,N-dimethyl acetamide.     

Characterisation of electric discharge in hollow electrode Z-pinch device by means of Rogowski coils

In this paper, the energy spectra of the general molecular potential are obtained using the asymptotic iteration method within the framework of non-relativistic quantum mechanics.With the energy spectrum obtained, the vibrational partition function is calculated in a closed form and is used to obtain an expression for other thermodynamic functions such as vibrational mean energy U, vibrational mean free energy F, vibrational entropy S and vibrational specific heat capacity C. These thermodynamic functions are studied for the electronic state \(\mathrm{X}^{1}\Sigma _g^+ \) of \(K_2\) diatomic molecules.     

Low-energy electron impact cross-sections and rate constants of $$\hbox {NH}_2$$

In this paper, we have studied the anisotropic and homogeneous Bianchi type-VI ₀ Universe filled with dark matter and holographic dark energy components in the framework of general relativity and Lyra’s geometry. The Einstein’s field equations have been solved exactly by taking the expansion scalar (??) in the model is proportional to the shear scalar (σ). Some physical and kinematical properties of the models are also discussed.     

X-ray spectra and valence states of cations in nanostructured half-doped $$\hbox {La}_{0.5}\hbox {Ca}_{0.5}\hbox {MnO}_{3}$$ manganite

Soft X-ray absorption (XAS) and emission (XES) spectroscopies were applied to determine valence states of manganese ions in nanostructured powder of half-doped \(\hbox {La}_{0.5}\hbox {Ca}_{0.5}\hbox {MnO}_{3}\) manganite obtained by milling in a ball mill. XAS spectra were measured both in surface-sensitivity total electron-yield and in bulk-sensitivity total fluorescence-yield modes. O K\(_{\upalpha }\) XES and O 1s XAS spectra characterized the occupied and unoccupied partial O 2p densities of states are compared with band-structure calculations made using the TB-LMTO-ASA codes. Experimental Mn 2p, Ca 2p, and La 3\(d\) XAS spectra are compared with results of crystal field atomic multiplet calculations. For the nanostructured system of \(\hbox {La}_{0.5}\hbox {Ca}_{0.5}\hbox {MnO}_{3}\), concentrations of Mn\(^{4+}\) ions are found to be increased with increasing the time of milling.     

Spectral and Scattering Theory of Space-cutoff Charged $${P(\varphi)_{2}}$$ Models

We consider in this paper space-cutoff charged \({P(\varphi)_{2}}\) models arising from the quantization of the non-linear charged Klein–Gordon equation:

$(\partial_{t}+\i V(x))^{2}\phi(t, x)+ (-\Delta_{x}+ m^{2})\phi(t,x)+ g(x)\partial_{\overline{z}}P(\phi(t,x), \overline{\phi}(t,x))=0,$

where V(x) is an electrostatic potential, g(x) ≥ 0 a space-cutoff, and \({P(\lambda, \overline{\lambda})}\) a real bounded below polynomial. We discuss various ways to quantize this equation, starting from different CCR representations. After describing the construction of the interacting Hamiltonian H we study its spectral and scattering theory. We describe the essential spectrum of H, prove the existence of asymptotic fields and of wave operators, and finally prove the asymptotic completeness of wave operators. These results are similar to the case when V = 0.

     

Study of the weak annihilation contributions in charmless $$\varvec{B_s\rightarrow VV}$$ decays

In this paper, in order to probe the spectator-scattering and weak annihilation contributions in charmless \(B_s\rightarrow VV\) (where V stands for a light vector meson) decays, we perform the \(\chi ^2\)-analyses for the endpoint parameters within the QCD factorization framework, under the constraints from the measured \(\bar{B}_{s}\rightarrow \) \(\rho ^0\phi \), \(\phi K^{*0}\), \(\phi \phi \) and \(K^{*0}\bar{K}^{*0}\) decays. The fitted results indicate that the endpoint parameters in the factorizable and nonfactorizable annihilation topologies are non-universal, which is also favored by the charmless \(B\rightarrow PP\) and PV (where P stands for a light pseudo-scalar meson) decays observed in previous work. Moreover, the abnormal polarization fractions \(f_{L,\bot }(\bar{B}_{s}\rightarrow K^{*0}\bar{K}^{*0})=(20.1\pm 7.0)\%,(58.4\pm 8.5)\%\) measured by the LHCb collaboration can be reconciled through the weak annihilation corrections. However, the branching ratio of \(\bar{B}_{s}\rightarrow \phi K^{*0}\) decay exhibits a tension between the data and theoretical result, which dominates the contributions to \(\chi _\mathrm{min}^2\) in the fits. Using the fitted endpoint parameters, we update the theoretical results for the charmless \(B_s\rightarrow VV\) decays, which will be further tested by the LHCb and Belle-II experiments in the near future.     

Probing neutrino and Higgs sectors in $$\text{ SU(2) }_1 \times \text{ SU(2) }_2 \times \text{ U(1) }_Y $$ model with lepton-flavor non-universality

The neutrino and Higgs sectors in the \(\text{ SU(2) }_1 \times \text{ SU(2) }_2 \times \text{ U(1) }_Y \) model with lepton-flavor non-universality are discussed. We show that active neutrinos can get Majorana masses from radiative corrections, after adding only new singly charged Higgs bosons. The mechanism for the generation of neutrino masses is the same as in the Zee models. This also gives a hint to solving the dark matter problem based on similar ways discussed recently in many radiative neutrino mass models with dark matter. Except the active neutrinos, the appearance of singly charged Higgs bosons and dark matter does not affect significantly the physical spectrum of all particles in the original model. We indicate this point by investigating the Higgs sector in both cases before and after singly charged scalars are added into it. Many interesting properties of physical Higgs bosons, which were not shown previously, are explored. In particular, the mass matrices of charged and CP-odd Higgs fields are proportional to the coefficient of triple Higgs coupling \(\mu \). The mass eigenstates and eigenvalues in the CP-even Higgs sector are also presented. All couplings of the SM-like Higgs boson to normal fermions and gauge bosons are different from the SM predictions by a factor \(c_h\), which must satisfy the recent global fit of experimental data, namely \(0.995<|c_h|<1\). We have analyzed a more general diagonalization of gauge boson mass matrices, then we show that the ratio of the tangents of the W–\(W'\) and Z–\(Z'\) mixing angles is exactly the cosine of the Weinberg angle, implying that number of parameters is reduced by 1. Signals of new physics from decays of new heavy fermions and Higgs bosons at LHC and constraints of their masses are also discussed.     

Coulomb Problem for <Emphasis Type="Italic">Z</Emphasis> &gt; Z<Subscript>cr</Subscript> in Doped Graphene

The dynamics of charge carriers in doped graphene, i.e., graphene with a gap in the energy spectrum depending on the substrate, in the presence of a Coulomb impurity with charge Z is considered within the effective two-dimensional Dirac equation. The wave functions of carriers with conserved angular momentum J = M + 1/2 are determined for a Coulomb potential modified at small distances. This case, just as any two-dimensional physical system, admits both integer and half-integer quantization of the orbital angular momentum in plane, M = 0, ±1, ±2, …. For J = 0, ±1/2, ±1, critical values of the effective charge Z_cr(J, n) are calculated for which a level with angular momentum J and radial quantum numbers n = 0 and n = 1 reaches the upper boundary of the valence band. For Z < Z_cr (J, n = 0), the energy of a level is presented as a function of charge Z for the lowest values of orbital angular momentum M, the level with J = 0 being the first to descend to the band edge. For Z>Z_cr (J, n = 0), scattering phases are calculated as a function of hole energy for several values of supercriticality, as well as the positions ε₀ and widths γ of quasistationary states as a function of supercriticality. The values of ε₀* and width γ* are pointed out for which quasidiscrete levels may show up as Breit–Wigner resonances in the scattering of holes by a supercritical impurity. Since the phases are real, the partial scattering matrix is unitary, so that the radial Dirac equation is consistent even for Z > Z_cr. In this single-particle approximation, there is no spontaneous creation of electron–hole pairs, and the impurity charge cannot be screened by this mechanism.     

Proton-antiproton annihilation into a \Lambda_{c}^{+} \bar{{\Lambda}}_{c}^{-} pair

The process p $ \bar{{p}}$ $ \rightarrow$ $ \Lambda_{c}^{+}$ $ \bar{{\Lambda}}_{c}^{-}$ is investigated within the handbag approach. It is shown to lowest order of perturbative QCD that, under the assumption of restricted parton virtualities and transverse momenta, the dominant dynamical mechanism, characterized by the partonic subprocess u $ \bar{{u}}$ $ \rightarrow$ c $ \bar{{c}}$ , factorizes in the sense that only the subprocess contains highly virtual partons, namely a gluon, while the hadronic matrix elements embody only soft scales and can be parameterized in terms of helicity flip and non-flip generalized parton distributions. Modelling the latter functions by overlaps of light-cone wave functions for the involved baryons we are able to predict cross-sections and spin correlation parameters for the process of interest.     

A Chiang-type lagrangian in $$\mathbb {CP}^2$$

We analyse a monotone lagrangian in \(\mathbb {CP}^2\) that is hamiltonian isotopic to the standard lagrangian \(\mathbb {RP}^2\), yet exhibits a distinguishing behaviour under reduction by one of the toric circle actions, namely it intersects transversally the reduction level set and it projects one-to-one onto a great circle in \(\mathbb {CP}^1\). This lagrangian thus provides an example of embedded composition fitting work of Wehrheim–Woodward and Weinstein.     

Polarized angular distributions in the decays of the singlet D2 state of charmonium originating from $\bar{p}p$ collisions

Using the helicity formalism, we calculate the combined angular distribution function of the neutral pion (π ⁰) and the polarized electron (e ^?) and photon (γ) produced in the triple cascade process \(\bar{p}+p\rightarrow{}^{1}D_{2}\rightarrow{}^{1}P_{1}+\gamma\rightarrow(\psi +\pi^{0})+\gamma \rightarrow(e^{-}+e^{+})+\pi^{0}+\gamma\), when \(\bar{p}\) and p are unpolarized. We also present the partially integrated angular distribution functions in three different cases where the combined angular distribution function of the three particles is integrated over the direction of one of the particles. Our results show that by measuring the two-particle angular distribution of the electron and the photon with the polarization of either particle, one can determine the relative magnitudes as well as the relative phases of all the angular-momentum helicity amplitudes in the two decay processes ¹ D ₂→¹ P ₁+γ and ¹ P ₁→ψ+π ⁰.     

Dirac equation with spin symmetry for the modified Pöschl–Teller potential in <Emphasis Type="Italic">D</Emphasis> dimensions

We present solutions of the Dirac equation with spin symmetry for vector and scalar modified Pöschl–Teller potentials within the framework of an approximation of the centrifugal term. The relativistic energy spectrum is obtained using the Nikiforov–Uvarov method and the two-component spinor wave functions obtained are in terms of the Jacobi polynomials. It is found that there exist only positive energy states for bound states under spin symmetry, and the energy of a level with fixed value of n, increases with increase in dimension of space time and the potential range parameter α.     

The Semileptonic Decay Modes {\bar{B} \rightarrow D\ell \bar{\nu}} and {\bar{B}_{s} \rightarrow D_{s} \ell \bar{\nu}}: A New Analysis in Potential Model

We consider the Schrödinger equation with a combination of Deng–Fan-type and harmonic terms. To solve the corresponding differential equation, we split the equation to two parts: the parent and the perturbation terms. We use the Nikiforov–Uvarov technique to solve the parent part. For the perturbation part, we apply the series expansion method. Next, using the calculated wave function, we investigate some bottom and charm mesons within the Isgur–Wise function formalism. We present especially semileptonic \({\bar{B} \rightarrow D\ell \bar{\nu}}\) and \({\bar{B}_{s} \rightarrow D_s \ell \bar{\nu }}\) decay widths, branching ratios and \({|V_{cb}|}\) (element of the CKM matrix). Masses of some pseudoscalar mesons are also indicated. Comparisons of our results with experimental values and other approaches are included.