Two-neutrino double-βdecay Fermi transition and two-nucleon interaction

Abstract

An exactly solvable model for a description of the two-neutrino double beta decay transition of the Fermi type is considered. By using perturbation theory an explicit dependence of the twoneutrino double beta decay matrix element on the like-nucleon pairing, particle-particle and particlehole proton-neutron interactions by assuming a weak violation of isospin symmetry of Hamiltonian expressed with generators of the SO(5) group. It is found that there is a dominance of double beta decay transition through a single state of the intermediate nucleus. Then, an energy weighted sum rule connecting ∆Z=2 nuclei is presented and discussed. It is suggested that this sum rule can be exploited to study the residual interactions of the nuclear Hamiltonian.

Multiple $SO(5)$ isovector pairing and seniority $Sp(2Ω)$ multi-$j$ algebras with isospin

“…For the first papers on single-j shell pairing Sp(2j + 1) algebra and the corresponding SO (5) algebra see [8][9][10][11][12][13]. Similarly, for technical work on these algebras (for example deriving analytical formulas for the Wigner coefficients of SO( 5)) see [12,[14][15][16][17][18] and for recent applications see [19][20][21][22][23] and references therein. Although many of the single-j shell results extend to the multi-j shell systems, for the multi-j shell situation a crucial aspect is that there will be multiple SO(5) algebras as the isovector pair creation operator here is no longer unique.…”

Comment on "Structure of the two-neutrino double-β decay matrix elements within perturbation theory" by Dušan Štefánik, Fedor Šimkovic, Amand Faessler, arXiv:1506.00835 [nucl-th], Phys.Rev.C91 (2015) 6, 064311

“…[17] the double Fermi and GT sum rules associated with ∆Z = 2 nuclei were introduced. ", where a previous paper [2] by the same authors has been given the priority (explicit representations for the sum rules are given in Eqs. ( 27),(28) of [1]).…”

“…In fact, the sum rules were first introduced in [3] 15 years prior to the publication [2], see Eq. ( 5) of [3] (the notation used in [3] is somewhat different from that of [1,2]).…”

“…In fact, the sum rules were first introduced in [3] 15 years prior to the publication [2], see Eq. ( 5) of [3] (the notation used in [3] is somewhat different from that of [1,2]). A model-independent, identity transformation of the amplitude M 2ν of 2νββ decay, introduced for the first time in [3], allows one to partition M 2ν into two terms that are sensitive to different parts of a nuclear Hamiltonian.…”

“…Note, that the authors of [1,2] must have been aware of publications [4,5], since first, [4,5] were cited in [2], see entries [26,27] in the list of references, and second, one of the authors of [1,2] was also a co-author of [4,5].…”