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arXiv · 1709.05313

Neutrinoless double-$β$ decay of $^{124}$Sn, $^{130}$Te, and $^{136}$Xe in the Hamiltonian-based generator-coordinate method

C. F. Jiao·M. Horoi·A. Neacsu
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Abstract

We present a generator-coordinate method for realistic shell-model Hamiltonians that closely approximates the full shell model calculations of the matrix elements for the neutrinoless double-$β$ decay of $^{124}$Sn, $^{130}$Te, and $^{136}$Xe. We treat not only quadrupole deformations but also the proton-neutron pairing amplitudes as generator coordinates. We validate this method by calculating and comparing spectroscopic quantities with the exact shell model results and experimental data. Our Hamiltonian-based generator-coordinate method produces $0νββ$ matrix elements much closer to the shell model ones, compared to the existing energy-density-functional-based generator-coordinate approaches. The remaining overestimation of $0νββ$ nuclear matrix element suggests that additional correlations may be needed to be taken into account for $^{124}$Sn, $^{130}$Te, and $^{136}$Xe when calculating with the Hamiltonian-based generator-coordinate method. The validation of this method may open the possibility of calculating $0νββ$ matrix element of $^{150}$Nd in a large shell-model space.

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C. F. Jiao, M. Horoi, A. Neacsu. 2019-01-07. Neutrinoless double-$β$ decay of $^{124}$Sn, $^{130}$Te, and $^{136}$Xe in the Hamiltonian-based generator-coordinate method. https://doi.org/10.1103/physrevc.98.064324

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