Spectroscopic amplitudes for complex cluster systems

By expanding the Bargmann-Segal integral transform of nomi 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 ?, ? ? 4, is combined with a heavy fragment of mass number $\text{A-?,}\text{with}\text{A-? ? 24}$. The $\text{A-?}$ 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 ¹²C+ ¹²C resonances. Eigenvalues and eigenvectors of the antisymmetrizer are evaluated in a “molecular basis” of the ¹²C + ¹²C system, in which each ¹²C nucleus is assumed to have SU(3) symmetry (04) with internal rotational excitations of 0⁺,2⁺ and 4⁺. Reduced width amplitudes are calculated connecting such normalized, fully antisymmetrized molecular basis states to exit channels which include: α+²⁰Ne with ²⁰Ne internal functions of (80) SU(3) symmetry, (K = 0⁺ band, and (82) SU(3) symmetry, (K = 2^? band); ¹⁶O+⁸Be; and ²³Na+p or ²³Mg+n fragments with ²³Na or ²³Mg excitations in $\text{K =}\text{3}\text{2}\text{and}\text{1}\text{2}$ rotational bands of SU(3) symmetry (83).