Exact wave functions of a four-body system

In this Letter the exact wave functions of a model four-quark system in SU(2) color are calculated for spinless but isospinor quarks in Schrödinger equation as an analogue to the actual six-quark problem in SU(3) color which arises naturally in the study of dibaryon states. This model four-quark problem is shown to be exactly soluble for the admissible states of isospin I=2 provided that the pairwise interactions between the quarks are supplemented by some four-body counter terms (interpreted as four-body forces). This model correctly simulates the color with orbital structure expected of the corresponding fermionic 4N problem. Further the possible exact solutions such as these can prove to be useful as test cases for the study of the full q⁶ problem in SU(3) color with spin-dependent forces.