is given in (\[3.2\]). The analytic solutions outside this region are not as simple, but can be represented graphically. As an example, the coefficient function $\lambda ^T_3$ is shown in Fig.\[fig4\] for $C_{Pq}=0$. The exhibited continuous spectrum arises from the fact that the gluon two-point function (\[3.1\]) provides a constant, or infinite-range, interaction between the quarks in coordinate space. The quarks are therefore allowed to propagate throughout space uninhibited by the presence of the vacuum. This situation is analogous to that of the constant mean-field case discussed previously.

Several observations can be made from this example. First, the absence of a mass pole in the vacuum Green’s function of a colored object is sufficient for a description of confinement provided the subsequent interactions with other colored objects contain a scale beyond which the interaction diminishes allowing the presence of the vacuum to become apparent. This defines a confinement scale that is largely responsible for the characteristics of bound states. The effect of such a scale is investigated in the numerical work to follow in Sec.4, however, one can anticipate that as the range of the interaction increases, the density of bound-state poles increases; finally giving rise to a continuous spectrum 