N c is the number of colors, M B ( ~ 1 GeV) is an infrared mass which is interpreted as the ground state mass of the two gluons bound to by the basic string, μ 0 = 1.1 (GeV), Λ V = 0.385 (GeV) as in Refs. The string tension σ = 0.18 Ge V 2 in Ref. In addition, the anisotropy in the present potential with respect to the direction of the magnetic field is not breaking the translational invariance of space, (for detail, see Ref. The effect of the magnetic field will be appearing through the Debye mass. This potential depends on the radial distance. So, the potential takes the following form as in Ref. In the present work, the radial Schrödinger equation is employed which means potential interaction is symmetry. Following radial, SE is obtained by applying the wave function Where l, N & μ are angular momentum quantum numbers, dimensional numbers, & reduced mass. 49, in N-dimensional space, the Schrödinger equation for two particles which interact with symmetrical potentials takes form The Solution of the Schrödinger Equation in the Presence of a Strong Magnetic Field.Īs in Ref. This is possible if the discrimination is zero. (9) is possible to determine whether expression under square root is square of expression. Where B n is a constant of normalization and ρ(s) is a function of weight that follows the next equation X(s) = x n(s) is an n degree polynomial which fulfils the form of the Rodrigues Then, the new eigenvalue equation becomes Where π(s) is the first-degree polynomial 47 By using the transformation of s = s (r), Where σ(s) and σ(s) are max-second degree polynomials and τ(s) is the first-degree maximal polynomials. The NU method 47 used to solve the second-order differential equation in form is defined as follows 4, we discuss the results, and a summary & conclusion are given in Sec.5. In Sec.3, the method is used to solve N-dimensional SE. In addition, the effect of a number of flavors is studied on the binding energy and dissociation temperature of quarkonium. For our best knowledge, the previous works are not solved the present potential analytically. The aim of the present work, we have analytically solved the Schr odinger equation using NU method in which the finite temperature and magnetic field are included in the potential interaction.
On the other hand, the magnetic field pays an important in the non-fluid mechanics such as in Refs. 16, the real part of the potential is included in SE in order to determine energy eigenvalues and energy eigenfunctions of the states of the c c.
The effect of finite T and eB on the real part of Q Q potential in form of destructive thermal QCD & dissociation of heavy quarkonia due to color screening have been studied 46. In presence of an external magnetic field, vacuum quantum with harmonic oscillators and Cornell potential 39,42 were recently mechanically investigated with quarkonium and heavy meson spectroscopy, with an additional spin-spin interaction component. One of the study influences on the features of nuclear matter under extreme settings has been heavy quarkonia., as quarkonia form in URHICs field as at a very period of ∼1/2 m Q (where m Q is mass of charm or bottom quark), this is equivalent to time scale at which magnetic field is produced. In serval approach models, the effect of eB on QCD thermo-dynamics has been examined 16-38.Ī few studies have looked into the effect of magnetic fields on the static characteristics of quarkonium. Dissociation is currently considered primarily to be due to the increase in the resonance distance either due to an inelastic mechanism of spatially mediated dispersion by a patron such as gluons, known as Landau damping 14, or because of a process glue-dissociation in which involves hard thermal gluon in one-tone color state 15. potential is too small to keep pair appointed by Q Q.
Over the last two decades, the dynamics of the dissociation of quarkonium have been seen in a medium where, in the beginning, the resonance was assumed to be dissociated if screening is robust enough, i.e. The dissociation of quarkonia necessitates the measuring of heavy quarkonium potentials in a disordered manner. The Higgs field gradients rendered an extraordinarily enormous magnetic field (∼10 23Gauss), during the electroweak stage transition in the early cosmos 9. It is capable of achieving levels in extreme situations. The strength of the magnetic field is dependent on the centrality and could be between m π 2 (?10 18 Gauss) at RHIC 8 to 10 m π 2 at LHC 1. The URHIC events have recently been reported when the magnetic field effect is combined with an exceptionally strong magnetic field 3-7. In the mid-seventies, scientists investigated the possibility of quark-gluon plasma (QGP).