We solve the Dirac equation for the Manning-Rosen plus shifted Deng-Fan potential including a Coulomb-like tensor potential with arbitrary spin–orbit coupling quantum number κ. In the framework of the spin and pseudospin (pspin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions in closed form by using the Nikiforov–Uvarov method. Also Special cases of the potential as been considered and their energy eigen values as well as their corresponding eigen functions are obtained for both relativistic and non-relativistic scope.

An exact analytical and approximate solution of the relativistic and non-relativistic wave equations for central potentials has attracted enormous interest in recent years. By using the basic Nikiforov-Uvarov quantum mechanical concepts and formalism, the energy eigenvalue equations and the corresponding wave functions of the Klein–Gordon and Schrodinger equations with the interaction of Modified Hylleraas-Hulthen Potentials (MHHP) were obtained using the conventional Pekeris-type approximation scheme to the orbital centrifugal term. The corresponding unnormalized eigen functions are evaluated in terms of Jacobi polynomials.

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The present article reports the results of studies related to the synthesis of MgFe 2 O 4 nanocomposite powder by solution combustion process using mixture of fuels containing urea (U) and ammonium acetate (AA). The effect of mixture of fuel and sintering temperature on phase formation, structural, morphological and magnetic properties of MgFe 2 O 4 particles were investigated by X-ray diffraction (XRD), thermogravimetric analysis (TGA), Raman spectroscopy, scanning electron microscopy (SEM), energy dispersive absorption x-ray (EDAX) and vibrating sample magnetometer (VSM). Thermodynamic modeling of the combustion reaction shows that by using a mixture of urea and ammonium acetate fuels, the adiabatic flame temperature (T ad), exothermicity and amount of gases produced during the combustion process as well as product characteristics could be controlled. The use of mixture of fuels (U and AA) in the synthesis of MgFe 2 O 4 was found to produce ferrites with finer agglomerates, higher crystallinity, higher magnetic properties and smaller crystallite sizes than when only urea was used. It was found that only samples prepared with a mixture of fuels (0.5U + 0.5AA) and sintered at 900 o C for 2 h produced pure ferrite spinel phase while the auto-combusted and powders sintered at 600 o C for 2 h had secondary phases. Apart from giving detailed information about the structural order of the samples, Raman spectroscopy also confirmed that MgFe 2 O 4 is a mixed spinel ferrite.