Cluster sum rules for three-body systems with angular-momentum dependent interactions

Abstract

We derive general expressions for non-energy weighted and energy-weighted cluster sum rules for systems of three charged particles. The interferences between pairs of particles are found to play a substantial role. The energy-weighted sum rule is usually determined by the kinetic energy operator, but we demonstrate that it has similar additional contributions from the angular momentum and parity dependence of two- and three-body potentials frequently used in three-body calculations. The importance of the different contributions is illustrated with the dipole excitations in ${}^6$He. The results are compared with the available experimental data.

Comments: 11 pages, 3 figures, 2 tables