In this article, we have modified the r 2 correlated kernel. Under this modification, the kernel remains V 3 0r 2δ(τ) at small r and when r is large enough, it tends to be Aδ(τ), where A is a constant. Thus, the kernel no longer corresponds to a complete confinement potential. By solving the Gap equation, we found that the contribution of the modification to quark-antiquqrk condensation is obvious, though the main results of vacuum condensation remain.
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