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.

11 pages, 3 figures, 2 tables

References in corpus (6)

• Structure of ground and excited states of ${}^{12}$C
• Three-body continuum states on a Lagrange mesh
• The ${}^{10}$Li spectrum and the ${}^{11}$Li properties
• Three-body structure of the low-lying ${}^{17}$Ne-states
• Structure of low-lying 12C-resonances
• Electron scattering on two-neutron halo nuclei: The case of ${}^6$He

Cited by in corpus (8)

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• Above threshold s-wave resonances illustrated by the 1/2${}^{+}$ states in ${}^9$Be and ${}^9$B
• Electric dipole response of low-lying excitations in the two-neutron halo nucleus ${}^{29}$F
• The triple alpha reaction rate and the 2${}^{+}$ resonances in ${}^{12}$C
• Radiative capture reaction for ${}^{17}$Ne formation within a full three-body model
• Exploring the halo character and dipole response in the dripline nucleus ${}^{31}$F