Solutions of the Dirac equation in the presence of a static uniform electric fieldɛ in thez-direction and a linear confining potentialAz, are obtained. Generalized reflection and transmission coefficients are derived for such divergent potentials forɛ >A/e. The eigenspectrum and corresponding localized eigenfunctions forɛ <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 fieldɛ 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 fieldɛ in a finite spatial region with the quark (antiquark) being confined in thez direction by the linear potentialAz 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$$q\bar q$$ pairs is enhanced,ɛc(A) >ɛc(A = 0). The rate of pair creation for constantɛ, decreases for non-zeroA, implying longer QGP formation times. Because ofɛc(A) >ɛc(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.
Volume 94, 2019
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