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

TL;DR

This paper derives generalized sum rules for three-body charged systems, highlighting the significant role of interference effects and potential dependencies on angular momentum and parity, with applications to $^6$He dipole excitations.

Contribution

It introduces new expressions for cluster sum rules that incorporate angular-momentum dependent interactions and interference effects in three-body systems.

Findings

Interference effects significantly influence sum rules.

Angular momentum and parity dependencies contribute to energy-weighted sum rules.

Comparison with experimental data validates the theoretical expressions.

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.