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).

Bargmann transform techniques used to calculate norm kernels for nuclear cluster systems have been generalized to evaluate interaction kernels for central interactions of gaussian form for binary cluster systems made up of SU(4}scalar (A = 4n) cluster fragments with internal func tions of good SU(3) symmetry and equal oscillator width parameters . The technique involves a reduction from A-particle orbital states of space symmetry characterized by 4-columned Young tableaux to 4A-particle states of single-column symmetry . The interaction kernels are built partly through a convolution of the single~olumn Bargmann transforms of the Fourier components of basic one-body operators . Bargmann transforms of single-column type have been evaluated in algebraic form for a two-body gaussian interaction and for the one-body Fourier kernel,~~E xp (iq~r;), for the following A-particle systems and cluster decompositions : A = 12, x+"Be : A = 16, x+' 2 C, "Be+"Be ; A = 20, x+"'O, "Be+`Z C ; and A = 24, ' zC+' zC, "Be+'`'O, x+ Z°Ne .The construction of the Bargmann transform for the full A-particle system is illustrated with a simple example. The example also shows how the coordinate space matrix elements needed for the evaluation of RGM and GCM kernels can be extracted from appropriate expansions of this Bargmann transform by purely algebraic techniques . *