The role of charge-symmetry invariance in the σ−1 “bremsstrahlung-weighted” photo-absorption sum rules for the non-relativistic and relativistic few-body systems

Abstract

Within the non-relativistic approach to photo-absorption sum rules for the 3N(4N)-nuclei the new σ−1 sum rules proposed which are based on general charge-symmetry (CS) consequences for a pair of the “CS-conjugated” triton and 3He nuclei and for the “self-conjugated” nucleus 4He. The numerical deviations from the less general “charge-independent” approach leading to the long-known Foldy-Khokhlow sum rules are estimated. In the relativistic domain the functional inapplicability is demonstrated of the “charge independence” approximation in the derivation of the σ−1 - type sum rules in the case of nucleons. With application of the relevant “charge symmetry” approach, the general system of the sum rules is derived and the inevitable isospin-dependent dynamics of the constituent quarks is underlined.