Sensitive behavior of 2νββ-decay amplitude within QRPA and broken SU(4) symmetry in nuclei

Making use of an identity transformation independent of a nuclear model, we represent the 2νββ-amplitude as a sum of two terms. One term accounts for most of the sensitivity of the original 2νββ-amplitude to gpp′ for realistic gpp′≃1 (with gpp′ 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 gpp′ in the QRPA) and passes through zero at the point gpp′=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 2νββ-amplitude is demonstrated within the QRPA to be a much smoother function for the realistic values of gpp′ than the original 2νββ-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 2νββ-amplitude to different components of the nuclear Hamiltonian and thereby can help in constraining nuclear model uncertainties in calculations of the amplitude.