Fast, Efficient Calculations of the Two-Body Matrix Elements of the Transition Operators for Neutrinoless Double Beta Decay

Abstract

To extract information about the neutrino properties from the study of neutrinoless double-beta (0νββ) decay one needs a precise computation of the nuclear matrix elements (NMEs) associated with this process. Approaches based on the Shell Model (ShM) are among the nuclear structure methods used for their computation. ShM better incorporates the nucleon correlations, but have to face the problem of the large model spaces and computational resources. The goal is to develop a new, fast algorithm and the associated computing code for efficient calculation of the two-body matrix elements (TBMEs) of the 0νββ decay transition operator, which are necessary to calculate the NMEs. This would allow us to extend the ShM calculations for double-beta decays to larger model spaces, of about 9-10 major harmonic oscillator shells. The improvement of our code consists in a faster calculation of the radial matrix elements. Their computation normally requires the numerical evaluation of two-dimensional integrals: one over the coordinate space and the other over the momentum space. By rearranging the expressions of the radial matrix elements, the integration over the coordinate space can be performed analytically, thus the computation reduces to sum up a small number of integrals over momentum. Our results for the NMEs are in a good agreement with similar results from literature, while we find a significant reduction of the computation time for TBMEs, by a factor of about 30, as compared with our previous code that uses two-dimensional integrals.

6 pages, one figure

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Cited by in corpus (13)

• Neutrinoless Double-Beta Decay: a Probe of Physics Beyond the Standard Model
• Shape and pairing fluctuations effects on neutrinoless double beta decay nuclear matrix elements
• Systematic study of nuclear matrix elements in neutrinoless double-beta decay with a beyond mean-field covariant density functional theory
• Relativistic description of nuclear matrix elements in neutrinoless double-$\beta$ decay
• Neutrinoless double beta decay of 48Ca in the shell model: Closure versus nonclosure approximation
• Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism
• Shell model analysis of competing mechanism to the double-beta decay of ${}^{48}$Ca
• Analysis of mechanisms that could contribute to the neutrinoless double-beta decay
• Shell model study on the possibility of using an effective field theory for disentangling several contributions to the neutrinoless double-beta decay
• Study of Nuclear Effects in the Computation of the 0νββ Decay Matrix Elements
• Present Status of Nuclear Shell-Model Calculations of Neutrinoless Double-Beta Decay Matrix Elements
• Short-range correlations for neutrinoless double-beta decay and low-momentum NN potentials
• Effect of Spin-Dependent Short-Range Correlations on Nuclear Matrix Elements for Neutrinoless Double Beta Decay of ${}^{48}$Ca