Charge-symmetry breaking forces and isospin mixing in 8Be

We report Green's function Monte Carlo calculations of isospin-mixing (IM) matrix elements for the 2⁺, 1⁺, and 3⁺ T=0 and 1 pairs of states at 16-19 MeV excitation in 8Be. The realistic Argonne v ₁₈ (AV18) two-nucleon and Illinois-7 three-nucleon potentials are used to generate the nuclear wave functions. Contributions from the full electromagnetic interaction and strong class III charge-symmetry breaking (CSB) components of the AV18 potential are evaluated. We also examine two theoretically more complete CSB potentials based on ρ-ω mixing, tuned to give the same neutron-neutron scattering length as AV18. The contribution of these different CSB potentials to the 3H-3He, 7Li-7Be, and 8Li-8B isovector energy differences is evaluated and reasonable agreement with experiment is obtained. Finally, for the 8Be IM calculation we add the small class IV CSB terms coming from one-photon, one-pion, and one-ρ exchange, as well as ρ-ω mixing. The expectation values of the three CSB models vary by up to 20% in the isovector energy differences, but only by 10% or less in the IM matrix element. The total matrix element gives 85-90% of the experimental IM value of -145 keV for the 2⁺ doublet, with about two thirds coming from the Coulomb interaction. We also report the IM matrix element to the first 2⁺ state at 3 MeV excitation, which is the final state for various tests of the standard model for β decay.