Response of nonrelativistic confined systems

We study the nonrelativistic response of a ‘‘diquark’’ bound by confining forces, for which perturbation theory in the interaction fails. As nonperturbative alternatives we consider the Gersch-Rodriguez-Smith (GRS) theory and a summation method. We show that, contrary to the case of singular repulsive forces, the GRS theory can generally be applied to confined systems. When expressed in the GRS-West kinematic variable y, the response has a standard asymptotic limit and calculable dominant corrections of orders 1/q, 1/${\mathit{q}}^2$. That theory therefore clearly demonstrates how constituents, confined before and after the absorption of the transferred momentum and energy, behave as asymptotically free particles. We compare the GRS results with those of a summation method for harmonic and square-well confinement and also discuss the convergence of the GRS series for the response in powers of 1/q.