Using the asymptotic iteration and wave function ansatz method, we present exact solutions of the Klein-Gordon equation for the quark-antiquark interaction and harmonic oscillator potential in the case of the position-dependent mass.

We have examined the anomalous electromagnetic moments of the tau lepton in the processes e − γ → ν e τν τ (γ is the Compton backscattering photon) and e − e + → e − γ * e + → ν e τν τ e + (γ * is the Weizsacker-Williams photon) with unpolarized and polarized electron beams at the CLIC. We have obtained 95% confidence level bounds on the anomalous magnetic and electric dipole moments for various values of the integrated luminosity and center-of-mass energy. Improved constraints of the anomalous magnetic and electric dipole moments have been obtained compared to the LEP sensitivity.

We numerically solve the Schr€odinger equation, using a more general exponential cosine screened\ud Coulomb (MGECSC) potential with an electric field, in order to investigate the screening and weak\ud external electric field effects on the hydrogen atom in plasmas. The MGECSC potential is\ud examined for four different cases, corresponding to different screening parameters of the potential\ud and the external electric field. The influences of the different screening parameters and the weak\ud external electric field on the energy eigenvalues are determined by solving the corresponding\ud equations using the asymptotic iteration method (AIM). It is found that the corresponding energy\ud values shift when a weak external electric field is applied to the hydrogen atom in a plasma. This\ud study shows that a more general exponential cosine screened Coulomb potential allows the\ud influence of an applied, weak, external electric field on the hydrogen atom to be investigated in\ud detail, for both Debye and quantum plasmas simultaneously. This suggests that such a potential\ud would be useful in modeling similar effects in other applications of plasma physics, and that AIM\ud is an appropriate method for solving the Schr€odinger equation, the solution of which becomes\ud more complex due to the use of the MGECSC potential with an applied external electric field

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In this study, we investigate the potential of the process pp → pγ * p → pτν τ q ′ X at the LHC to examine the anomalous electromagnetic moments of the tau lepton. We obtain 95% confidence level bounds on the anomalous coupling parameters with various values of the integrated luminosity and center-of-mass energy. The improved bounds have been obtained on the anomalous coupling parameters of electric and magnetic moments of the tau lepton a τ and |d τ | compared to the current experimental sensitivity bounds. The γp mode of photon reactions at the LHC have shown that it has great potential for the electromagnetic dipole moments studies of the tau

The influence of relativistic and plasma screening effects on energies of hydrogen-like atoms embedded in plasmas has been studied. The Dirac equation with a more general exponential cosine screened potential has been solved numerically and perturbatively, by employing the direct perturbation theory. Properties of spectra corresponding to bound states and to different sets of the potential parameters have been studied both in nonrelativistic and relativistic approximations. Binding energies, fine-structure splittings, and relativistic energy shifts have been determined as functions of parameters of the potential. The results have been compared with the ones known from the literature.

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