Sensitive behavior of image-decay amplitude within QRPA and broken image symmetry in nuclei Original Research Article

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 View the MathML source for realistic View the MathML source (with View the MathML source 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 View the MathML source in the QRPA) and passes through zero at the point View the MathML source 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 View the MathML source 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.