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 ${}^8$Be. 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 $\rho$-$\omega$ mixing, tuned to give the same neutron-neutron scattering length as AV18. The contribution of these different CSB potentials to the ${}^3$H-${}^3$He, ${}^7$Li-${}^7$Be, and ${}^8$Li-${}^8$B isovector energy differences is evaluated and reasonable agreement with experiment is obtained. Finally, for the ${}^8$Be IM calculation we add the small class IV CSB terms coming from one-photon, one-pion, and one-$\rho$ exchange, as well as $\rho$-$\omega$ 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 $\beta$ decay.

• Received 26 August 2013

DOI:https://doi.org/10.1103/PhysRevC.88.044333