Neutron scattering and magnetic observables for S=1/2 spin clusters and molecular magnets

In this paper we report results for magnetic observables of finite spin clusters composed of $S=1∕2$ ions. We consider clusters of two, three, and four spins in distinct spatial arrangements, with isotropic Heisenberg interactions of various strengths between ion pairs. In addition to the complete set of energy eigenvalues and eigenvectors, specific heat and magnetic susceptibility, we also quote results for the single crystal and powder average inelastic neutron scattering structure factors. Examples of the application of these results to experimental systems are also discussed.