An SU(3) approach to nuclear multi-cluster problems

Abstract

By combining SU(3) recoupling techniques with the use of the Bargmann-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.