Phenomenological Three-Body Interactions in the UCOM Framework

In the Unitary Correlation Operator Method (UCOM) the short-range central and tensor correlations induced by the nuclear interaction are treated explicitly by a unitary transformation. This method is employed to transform the Argonne V18 potential into a phase-shift equivalent correlated interaction VUCOM which is used for the following calculations [1]. Previous investigations of ground states and collective excitations based on the two-body interaction VUCOM revealed systematic deviations of different observables for heavier nuclei. Figure 1 shows the binding energies per nucleon (upper part) and charge radii (lower part) of closedshell nuclei obtained in a Hartree-Fock (HF) calculation using VUCOM (disks). The range of the tensor correlator was fixed in few-body calculations (Iθ = 0.09 fm) [1]. The HF approximation underestimates the binding energies, since long-range correlations cannot be described. Their inclusion within many-body perturbation theory leads to a good agreement of the binding energies with experiment [2]. Furthermore, the charge radii are clearly too small for heavier nuclei and the inclusion of long-range correlations via perturbation theory does not lead to a substantial improvement. Besides ground-state properties, collective excitations were investigated within the Random Phase Approximation (RPA) [3] using VUCOM. An example is shown in Figure 2, where the response function of the isoscalar quadrupole resonance of Zr is displayed. The solid line represents the results with the two-body interaction VUCOM. The strength is concentrated at energies ∗Supported by DFG through SFB 634.