Interaction kernels for A = 4n binary cluster systems

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 functions of good SU(3) symmetry and equal oscillator width parameter. The technique involves a reduction from A-particle orbital states of space symmetry characterized by 4-columned Young tableaux to 1/4A-particle states of single-column symmetry. The interaction kernels are built partly through a convolution of the single-column 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, Σsub(j) exp(iqxrsub(j)), for the following A-particle systems and cluster decompositions: A = 12, α + 8Be; A = 16, α + 12C, 8B + 8Be; A = 20, α + 16O, 8Be + 13C; and A = 24, 12C + 12C, 8Be + 16O, α + 20Ne. 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. (orig.)