Non‐relativistic continuous states in arbitrary dimension for a ring‐shaped pseudo‐Coulomb and energy‐dependent potentials

In this research, the non‐relativistic particle scattering has been investigated for an alternative pseudo‐Coulomb potential plus ring‐shaped and an energy‐dependent potentials in D‐dimensional space. The normalized wave functions of continuous states on the k/2π scale are expressed in terms of the hyper‐geometric series, and formula of phase shifts is presented. Analytical properties of the scattering amplitude and thermodynamics properties are discussed. Some of the numerical results of energy levels have been calculated too. Copyright © 2015 John Wiley & Sons, Ltd.     

Analysis of <Emphasis Type="Italic">J</Emphasis>/ψ → ϕ<Emphasis Type="Italic">f</Emphasis><Subscript>0</Subscript>(980) Decay

In this research we analyzed the processes of J/ψ → ?f₀(980) decay by calculating of three amplitude contributions as the electromagnetic (EM) contribution, short-distance (SD) contribution from the \(c\bar c\) annihilation at the wave function origin, and long-distance (LD) contribution from the open charm effects. We obtained the values of these contributions and calculated the branching ratio of this decay.     

Eigen-spectra in the Dirac-attractive radial problem plus a tensor interaction under pseudospin and spin symmetry with the SUSY approach

We approximately solve the Dirac equation for attractive radial potential including a Coulomb-like tensor interaction under pseudospin and the spin symmetry limit for any arbitrary spin-orbit quantum number, by employing the supersymmetric （SUSY） quantum mechanics and supersymmetric shape invariance technique. We obtain the energy eigenvalue equation under the pseudospin and spin conditions. Some numerical results are compared with those obtained by the Nikiforove-Uvarov （NU） method.     

Effects of final state interactions in B^ + \to D_S^ + \bar K^0 decay

We investigate the effects of final state interactions (FSI) contributions in the nonleptonic two body $B^ + \to D_S^ + \bar K^0$ decay, however the hadronic decay of $B^ + \to D_S^ + \bar K^0$ is analyzed by using “QCD factorization” (QCDF) method and final state interaction (FSI). First, the $B^ + \to D_S^ + \bar K^0$ decay is calculated via QCDF method and only the annihilation graphs exist in that method. Hence, the FSI must be seriously considered to solve the $B^ + \to D_S^ + \bar K^0$ decay and the D ⁰π⁺(D ⁰*ρ⁺), D ⁺π⁰(D ⁺*ρ⁰) and D ⁺η _c (D ⁺*J/ψ) via the exchange of K ^+(*), K ^0(*) and D _s ^+(*) mesones are chosen for the intermediate states. To estimate the intermediate states amplitudes, the QCDF method is again used. These amplitudes are used in the absorptive part of the diagrams. The experimental branching ratio of $B^ + \to D_S^ + \bar K^0$ decay is less than 8 × 10^?4 and the predicted branching ratio is 0.23 × 10^?9 in the absence of FSI effects and it becomes 6.74 × 10^?4 when FSI contributions are taken into account.     

Effects of Final State Interactions in Pure Annihilation Decay of B^{0}_{s}\rightarrow\pi^{0}\pi^{0}

We investigate the effects of final state interactions (FSI) contributions in the nonleptonic two body $B^{0}_{s} \rightarrow \pi^{0}\pi^{0}$ decay. The short distance interaction amplitude is calculated by using the annihilation diagrams and a tiny branching ratio is obtained, then the long distance amplitude is considered and calculated within FSI effects. For contributions of FSI, the ρ ⁰ ρ ⁰, π ⁺ π ^?(ρ ⁺ ρ ^?), K ⁺ K ^?(K ^+? K ^??) and $K^{0}\bar{K}^{0}(K^{0*}\bar{K}^{0*})$ are produced for intermediate states, in this case the π ⁰, π ^?(ρ ^?), K ^?(?) and $\bar{K}^{0(*)}$ mesons are exchanged. The absorptive part of the diagrams is directly calculated and the dispersive part of the rescattering amplitude can be obtained from the absorptive part via the dispersion relation. The imaginary and real parts of the amplitudes are summed over all intermediate states. The predicted branching ratio of $B^{0}_{s} \rightarrow \pi^{0}\pi^{0}$ is 0.69×10^?8 in the absence of FSI effects and it becomes 1.86×10^?4 when FSI contributions are taken into account, while the experimental result is less than 2.1×10^?4.     

Effects of Final State Interactions in Pure Annihilation Decay of B+ → D+K0*

The decay of the B ⁺ meson to the D ⁺ and K ⁰* mesons is a pure annihilation decay. For this reason, in the framework of the quantum chromodynamics factorization (QCDF) approach, this decay has a small amplitude and a small branching ratio. In this research we find that, before the D ⁺ and K ⁰* mesons are produced in the final states, pair mesons such as D _s ⁺* and D _s ⁺ρ⁰ are produced. The intermediate-state mesons via the exchange of K ⁰(K ⁰*) and D ⁺(D ⁺*) go to the D ⁺ and K ⁰* final state mesons. However we calculate the B ₊ → D ⁺ K ⁰* decay in two different frameworks. The first framework is the QCDF method and the second one is final state interaction (FSI). The experimental branching ratio of B ₊ → D ₊ K ⁰* decay is less than 3 × 10^–6, and our results obtained by the QCDF method and FSI are (0.35 ± 0.04) × 10^–6 and (2.94 ± 0.10) × 10^–6, respectively.     

Solution of the Dirac Equation with Position-Dependent Mass for q-Parameter Modified P?schl–Teller and Coulomb-like Tensor Potential

In this research, we have been obtained the Dirac equation for q-parameter modified P?schl–Teller potential including a Coulomb-like tensor interaction with arbitrary spin-orbit coupling quantum number by choosing a position-dependent mass. The energy eigenvalues equation and the corresponding unnormalized wave functions have been obtained. The Nikiforov-Uvarov method has been used in the calculations.     

Non-relativistic scattering amplitude for a new multi-parameter exponential-type potential

In this paper, we study the scattering properties of s-wave Schrdinger equation for the multi-parameter potential,which can be reduced into four special cases for different values of potential parameters, i.e., Hulthn, Manning–Rosen,and Eckart potentials. We also obtain and investigate the scattering amplitudes of these special cases. Some numerical results are also obtained and reported.