Equations of the resonating group method for a given permutation symmetry [f] and scattering of lightest clusters by each other

With the help of a projection operator P defined on a nonstandard basis of the permutation group, the equations of the resonating group method are written for the case of a given permutation symmetry [ f]. Construction of the operator P is discussed for the example of d+d scattering, and the integral equations of the resonating group method are presented for several different symmetries [ f]. It is shown that these equations satisfy the quasiclassical criterion of the existence of effective local potentials. The potentials obtained are close to the phenomenological ones. Thus, a basis is provided for the generalized potential approach to d+d, d+p, d+h, d+6Li, etc. scattering, including the inelastic spin-flip and isospin-flip channels. The formal problem solved in the present paper is also of relevance for the N+N system on the quark level