Symmetry adapted non-spurious wavefunctions for multi-cluster systems

An algorithm for the construction of multi-cluster non-spurious harmonic oscillator wavefunctions with arbitrary permutational symmetry is developed. Each cluster is presented in terms of a harmonic oscillator wavefunction, expressed in an appropriate set of Jacobi coordinates. The single-cluster wavefunctions are constructed recursively, using a new type of harmonic oscillator coefficients of fractional parentage. These coefficients are the eigenvectors of the two-cycle class operator of the intra-cluster symmetric group, in the appropriate basis. The matrix elements of the class operator are evaluated by using a specific version of the harmonic oscillator brackets. The cluster wavefunctions are coupled into non-spurious multi-cluster states with an overall well-defined angular momentum and permutational symmetry. This is achieved by diagonalizing an appropriate set of single-cycle class operation operators of the symmetric group involving all the constituent particles. The technique for the evaluation of the necessary matrix elements is developed. It provides an interesting generalization of the corresponding technique for a system consisting of a single cluster of identical particles. The results are immediately applicable to the study of nuclear cluster models, nuclei as quark clusters, nuclear fusion, fission and multifragmentation, as well as in atomic and molecular physics. (authors)