restricted ourselves to four nucleon systems in the present paper, the formulation of the TGVR itself can be applied to more than four-body systems as in the previous studies of the Global Vector Representation methods (GVR) [@GVR]. Furthermore, for scattering problems, the TGVR can deal with more complicated systems than the double (or single) global vector which was given in the previous papers [@DGVR; @GVR], because we need three representative orbital angular momenta, the total internal orbital momenta of both clusters and the orbital momentum of their relative motion, in order to reasonably describe the scattering states. In other words, the first global vector represents the angular momentum of cluster $a$, the second global vector represents the angular momentum of cluster $b$, and the third global vector represents the relative angular momentum between the clusters.

In this paper, we will investigate the effect of the distortion of clusters on the $d$+$d$ elastic-scattering by comparing the phase shifts calculated with a realistic and an effective interaction. In section 2, we explain the MRM in brief. In section 3, the correlated Gaussian (CG) method with the TGVR, which has newly been developed for the present analysis, will be presented. In section 4, 