Trivial center element and Coulombic potential of the thick center vortex model

The thick center vortex potentials in the SU(3) gauge group have been calculated by means of the modified inter-quark potential which consists of two terms. One term is the result of the area law fall-off for the large Wilson loop which leads to the linear potentials. The second term represents vacuum fluctuations leading to the perimeter law fall-off believed to contain the trivial center element. We introduce a new Gaussian flux limited to vary in a finite region of space which causes the corresponding group factor to have only some small deviations from the trivial center element. So, this flux increases the role of the trivial center element and W0 is enhanced in the induced potential of the model at small quark separations. Using both trivial and non-trivial center elements in the potential between static color sources, results in the correct 3-ality dependence at large quark separations and a very good agreement with Casimir scaling at short and intermediate distances. In fact, the ratios of the potential of each representation to that of the fundamental one have been improved - in comparison with the previous work on the short distance potentials, remarkably. So, one might use the thick center vortex model to describe the inter-quark potential of every regime.