Effective operators for double-β decay -: art. no. 034304

We use a solvable model to examine double- beta decay, focusing on the neutrinoless mode. After examining the ways in which the neutrino propagator affects the corresponding matrix element, we address the problem of finite model-space size in shell-model calculations by projecting our exact wave functions onto a smaller subspace. We then test both traditional and more recent prescriptions for constructing effective operators in small model spaces, concluding that the usual treatment of double- beta-decay operators in realistic calculations is unable to fully account for the neglected parts of the model space. We also test the quality of the quasiparticle random phase approximation and examine a recent proposal within that framework to use two-neutrino decay to fix parameters in the Hamiltonian. The procedure eliminates the dependence of neutrinoless decay on some unfixed parameters and reduces the dependence on model-space size, though it does not eliminate the latter completely.