Sensitive behavior of $2\nu \beta \beta$-decay amplitude within QRPA and broken SU(4) symmetry in nuclei

Abstract

Making use of an identity transformation independent of a nuclear model, we represent the {\bb}-amplitude as a sum of two terms. One term accounts for most of the sensitivity of the original {\bb}-amplitude to $g_{pp}^{\prime }$ for realistic $g_{pp}^{\prime }\simeq 1$ (with $g_{pp}^{\prime }$ being the ratio of the triplet and singlet p-p interaction strengths) and is determined by a specific energy-weighted sum rule. The sum rule depends only on the particle-particle residual interaction (being linear function of $g_{pp}^{\prime }$ in the QRPA) and passes through zero at the point $g_{pp}^{\prime }=1$ where the Wigner SU(4) symmetry is restored in the p-p sector of the Hamiltonian. The second term in the decomposition of the {\bb}-amplitude is demonstrated within the QRPA to be a much smoother function for the realistic values of $g_{pp}^{\prime }$ than the original {\bb}-amplitude. This term is mainly determined by the intensity of the spin-orbit interaction of the nuclear mean field. Thus, the analysis of the present work reveals the reasons for the sensitivity of the {\bb}-amplitude to different components of the nuclear Hamiltonian and thereby can help in constraining nuclear model uncertainties in calculations of the amplitude.

Comments: 14 pages, 3 figures; to be published in Nucl. Phys. A