  The scalar field plays an fundamental role in the investigation of
confinement property characterising many particle physics models. This is
achieved by coupling this particle directly with gauge fields at the lagrangian
level. We have adopted the same approach {[}10{]} to determine a potential as a
perturbative series in terms of interquark distance. In order to introduce the
gravitational effects and inspired from bag models, we implement a scalar field
which interacts both with the vacuum and the electron field. In this context
and with presence of the vacuum condensates, it is possible to derive a more
accurate expression of the electron energy.
