Isospin selection rules for inelastic electron scattering in the shell model

Abstract

The E1 and M1 isospin selection rules for inelastic electron scattering are studied in terms of the particle-hole model. Form factors calculated for the 1 − levels of O 16 demonstrate the operation of the E1 selection rule in the T=0 levels at low momentum transfer k. Isospin impurities are introduced phenomenologically and are found to break down this selection rule, particularly for the T=0 level calculated at 23.0 MeV. The M1 isospin selection rule is studied for the closed sub-shell nucleus C 12. Here only the configuration 1 p 3 2 ) −11 p 1 2 is considered. Form factor calculations show that for k⪅300 MeV/ c the ΔT=0 transition is suppressed by a factor of about 1 200 relative to the ΔT=1 transition. This is consistent with the absence of the ΔT=0 transition in C 12 electro-excitation cross section measurements, even at fairly high momentum transfer. Isospin mixing in C 12 does not appreciably alter this result.