Corrections to the Neutrinoless Double-Beta-Decay Operator in the Shell Model

Abstract

We use diagrammatic perturbation theory to construct an effective shell-model operator for the neutrinoless double-beta decay of 82Se. The starting point is the same Bonn-C nucleon-nucleon interaction that is used to generate the Hamiltonian for recent shell-model calculations of double-beta decay. After first summing high-energy ladder diagrams that account for short-range correlations and then adding diagrams of low order in the G matrix to account for longer-range correlations, we fold the two-body matrix elements of the resulting effective operator with transition densities from the recent shell-model calculation to obtain the overall nuclear matrix element that governs the decay. Although the high-energy ladder diagrams suppress this matrix element at very short distances as expected, they enhance it at distances between one and two fermis, so that their overall effect is small. The corrections due to longer-range physics are large, but cancel one another so that the fully corrected matrix element is comparable to that produced by the bare operator. This cancellation between large and physically distinct low-order terms indicates the importance of a reliable nonperturbative calculation.

7 pages, 6 figures

References in corpus (9)

• The Shell Model as Unified View of Nuclear Structure
• Double Beta Decay, Majorana Neutrinos, and Neutrino Mass
• Disassembling the Nuclear Matrix Elements of the Neutrinoless double beta Decay
• Anatomy of nuclear matrix elements for neutrinoless double-beta decay
• The influence of pairing on the nuclear matrix elements of the neutrinoless double beta decays
• The realistic collective nuclear Hamiltonian
• Shell-model calculations and realistic effective interactions
• Improved short-range correlations and 0nbb nuclear matrix elements of 76Ge and 82Se
• Short-range correlations and neutrinoless double beta decay

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