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We use a solvable model to examine double-beta decay, focusing on theneutrinoless mode. After examining the ways in which the neutrino propagatoraffects the corresponding matrix element, we address the problem of finitemodel-space size in shell-model calculations by projecting our exact wavefunctions onto a smaller subspace. We then test both traditional and morerecent prescriptions for constructing effective operators in small modelspaces, concluding that the usual treatment of double-beta-decay operators inrealistic calculations is unable to fully account for the neglected parts ofthe model space. We also test the quality of the Quasiparticle Random PhaseApproximation and examine a recent proposal within that framework to usetwo-neutrino decay to fix parameters in the Hamiltonian. The procedureeliminates the dependence of neutrinoless decay on some unfixed parameters andreduces the dependence on model-space size, though it doesn't eliminate thelatter completely.Comment: 10 pages, 8 figure

physical review. c. nuclear physics/physical review. c, nuclear physics

Effective operators for double-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:math>decay

Effective operators for double-βdecay