R. G. Lovas

Matrix elements between Slater determinants

Expressing the wavefunction in terms of Slater Determinants means that at some point we will have to evaluate matrix elements of the Hamiltonian and other operator between these determinants. The rules for doing so where worked out some time ago by Slater and Condon and are appropriately enough called the Slater-Condon rules which we will now derive. Consider the Slater determinant ˆ (1, 2,3, , ) (1) (2) (3) ( ) N a b c d Ψ = L L A N where the elements are orthonormal spin-orbitals, 1 a a b b c c d d = = = = = L

Numerically exact description of multicluster bound states

SummaryWe present the variational few-body approach to multiparticle bound states called the correlated-Gaussian stochastic variational method (CGSVM) and show how it can be applied to systems of nuclear clusters. It will be demonstrated that the treatment of the intercluster motion is numerically exact and the method provides a virtually perfect realization of the conventional cluster model.

Microscopic Versus Macroscopic Treatment of Clusters in Nuclei

We test the limitations of the macroscopic and microscopic versions of the nuclear cluster model by studying their applicability to the description of the fragmentation of the nucleus 6Li into clusters. The models considered are the microscopic α+d breathing cluster model and the macroscopic α+p+n three-particle model. Both models prove reasonably successful, but the minor discrepancies found reveal some important defects of the presently used versions. For the microscopic description to be improved, the inter-cluster motion should be described in as sophisticated a manner as in the three-particle model. For the macroscopic description to be improved, the spectroscopic amplitude should be re-defined in accord with the microscopic approach. This modified definition contains information on the cluster internal structures through norm operators.