In this paper we study the powerlike confining potentials $r^{\alpha }.$ The region of allowed $\alpha ’\mathrm{s}$ is identified, the mass-gap equation is constructed for an arbitrary $\alpha$ and solved for several values of the latter, and the vacuum energy and the chiral condensate are calculated. The question of replica solutions to the mass-gap equation for such potentials is addressed, and it is demonstrated that the number of replicas is infinite for any $\alpha ,$ as a consequence of the peculiar behavior of the quark self-energy in the infrared domain.

• Received 26 May 2003

DOI:https://doi.org/10.1103/PhysRevD.68.065021