  The mass and wave function of a six-quark system with quantum numbers
J^P=0^-, T=0, called d', are calculated. We use a colored diquark-tetraquark
cluster model for the six-quark wave function. A constituent quark model
Hamiltonian with a two-body confinement potential, and residual one-gluon,
one-pion, and one-sigma exchange interactions is used. The complications due to
the quark exchange interactions between tetraquark and diquark clusters (Pauli
principle) are taken into account within the framework of the Resonating Group
Method. The calculated d' mass is some 350 MeV above the empirical value if the
same two-body confinement strength as in the nucleon and Delta is used. This
paper also examines the validity of the usual assumption of a universal
two-quark confinement strength. We propose that the effective two-body
confinement strength in an exotic six-quark system, such as the d', could be
weaker than in a single baryon. The weaker confinement hypothesis leads to a d'
mass of M=2092 MeV and a d' radius of r=1.53 fm.
