FIELD LOCALIZATION AND PARTICLE CONFINEMENT EFFECTS ON PAIR CREATION BY SCHWINGER MECHANISM

Solutions of the Dirac equation in the presence of a static uniform electric field-epsilon in the z-direction and a linear confining potential Az, are obtained. Generalized reflection and transmission coefficients are derived for such divergent potentials for epsilon > A/e. The eigenspectrum and corresponding localized eigenfunctions for epsilon < A/e are obtained from the reflection coefficient and the continuum solutions respectively. The rate for the electric field to decay into pairs is derived from the transmission coefficient. Neglecting nonabelian effects in quantum chromodynamics we identify the field-epsilon with a colour electric field and the produced particles with a quark and an antiquark. By considering a cylindrical geometry, we thus obtain a generalization of Schwinger's formula, for the field-epsilon in a finite spatial region with the quark (antiquark) being confined in the z direction by the linear potential Az and in the perpendicular direction by the MIT bag boundary condition. The result is used to qualitatively study Schwinger's mechanism of quark-gluon plasma (QGP) formation in ultrarelativistic heavy ion collisions. It is found that the critical strength of the field required to create qqBAR pairs is enhanced, epsilon(c)(A) > epsilon(c)(A = 0). The rate of pair creation for constant-epsilon, decreases for non-zero A, implying longer QGP formation times. Because of epsilon(c)(A) > epsilon(c)(0), QGP is predicted to be formed in the early stages of the nuclear collision. The finite size effects and the MIT bag boundary condition effects on QGP formation are also discussed.