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By combining SU(3) recoupling techniques with the use of the Bergmann-Segal integral transform closed expressions are derived for the interaction kernels of the nuclear cluster model. In a cluster model basis in which the relative motion and internal oscillator wave functions (with arbitrary and different oscillator frequencies) are expanded in SU(3) coupled form, SU(3) reduced matrix elements are evaluated by integral transform methods. Matrix elements in a basis of good angular momentum can be constructed for multi-cluster systems by combining these SU(3) reduced matrix elements with readily available SU(3) Wigner coefficients .

By expanding the Bargmann-Segal integral transform of norm and overlap kernels in appropriately SU(3) coupled Bargmann space functions, the calculation of norm and overlap matrix elements in a cluster model basis is reduced to purely algebraic techniques involving the algebra of SU(3) recoupling transformations. This technique has been further developed to make calculations possible for systems of two heavy fragments other than closed-shell nuclei. In one application of the method, analytic expressions are given for the norms of binary fragment systems in which a light fragment of mass number f, f < 4, is combined with a heavy fragment of mass number A-J with A-f< 24. The A-j' fragment nuclei with different p and sd-shell structure illustrate somewhat different problems in the recoupling technique. In a second application, spectroscopic amplitudes are calculated for the most important open channels of the "C+ "C resonances. Eigenvalues and eigenvectors ofthe antisymmetrizer are evaluated in a "molecular basis" of the "C+ "C system, in which each "C nucleus is assumed to have SU(3) symmetry (04) with internal rotational excitations ofO+, 2+ and 4+. Reduced width amplitudes are calculated connecting such normalized, fully antisymmetrized molecular basis states to exit channels which include: a+20Ne with *ONe internal functions of (80) SU(3) symmetry, (K = O+ band), and (82) SU(3) symmetry, (K = 2-band); 160+sBe; and 23Na+p or 23Mg+n fragments with 23Na or 23Mg excitations in K = jj and f rotational bands of SU(3) symmetry (83).

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