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 Schrodinger eq uation 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 pro blem is shown to be exactly soluble for the admissible states of isospin I = 2 provided that the pairwise interactions between the quarks are suppleme nted by some four-body counter terms (interpreted as four-body forces), Thi s model correctly simulates the color with orbital structure expected of th e 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 ful l q(6) problem in SU(3) color with spin-dependent forces, (C) 2001 Publishe d by Elsevier Science B.V.