Shape and Pairing Fluctuation Effects on Neutrinoless Double Beta Decay Nuclear Matrix Elements

Nuclear matrix elements (NME) for the most promising candidates to detect neutrinoless double beta decay have been computed with energy density functional methods including deformation and pairing fluctuations explicitly on the same footing. The method preserves particle number and angular momentum symmetries and can be applied to any decay without additional fine tunings. The finite range density dependent Gogny force is used in the calculations. An increase of 10%–40% in the NME with respect to the ones found without the inclusion of pairing fluctuations is obtained, reducing the predicted half-lives of these isotopes.

Figure 1

Left: particle number and angular momentum $I=0$ projected potential energy surfaces: $E^{I=0}({\beta }_2,\delta )=⟨{\Psi }^{I=0}({\beta }_2,\delta )|\widehat{H}|{\Psi }^{I=0}({\beta }_2,\delta )⟩/⟨{\Psi }^{I=0}({\beta }_2,\delta )|{\Psi }^{I=0}({\beta }_2,\delta )⟩$ for (a) ${}^{136}\mathrm{Xe}$ and (b) ${}^{136}\mathrm{Ba}$. Dashed and continuous lines are separated 1 and 2 MeV respectively. The curves are normalized to their corresponding absolute minima. Right: collective wave functions squared $|G^{I=0;\sigma =1}({\beta }_2,\delta ){|}^2=|\sum _{{\beta }_2^{\prime },{\delta }^{\prime }}⟨{\Psi }^{I=0}({\beta }_2,\delta )|{\Psi }^{I=0}({\beta }_2^{\prime },{\delta }^{\prime }){⟩}^{1/2}{g}^{I=0;\sigma =1}({\beta }_2^{\prime },{\delta }^{\prime }){|}^2$ for (c) ${}^{136}\mathrm{Xe}$ and (d) ${}^{136}\mathrm{Ba}$. The dots indicate the values of $\delta$ obtained in a self-consistent one-dimensional calculation along ${\beta }_2$.

Figure 2

Particle number and angular momentum $I=0$ projected GT-NMEs as a function of (a) the quadrupole deformation and (b) pairing of the initial ${}^{136}\mathrm{Xe}$ and final ${}^{136}\mathrm{Ba}$ states. The horizontal and vertical dotted lines delimit the region where the wave functions of both nuclei take the largest values. Contour lines are separated 0.5 units.