Nuclear Structure Aspects of Neutrinoless Double-βDecay

Abstract

We decompose the neutrinoless double-beta decay matrix elements into sums of products over the intermediate nucleus with two less nucleons. We find that the sum is dominated by the J π = 0 + ground state of this intermediate nucleus for both the light and heavy neutrino decay processes. This provides a new theoretical tool for comparing and improving nuclear structure models. It also provides the connection to two-nucleon transfer experiments.PACS numbers: 23.40. Bw, 21.60.Cs, 23.40.Hc, 14.60.Pq Neutrinoless double beta decay 0νββ is one of the most important current topics in physics that provides unique information on the neutrino properties [1], [2], [3]. The 0νββ decay process and the associated nuclear matrix elements (NME) were investigated by using several approaches including the quasiparticle random phase approximation (QRPA) [1], the interacting shell model [4], [5], the interacting boson model [6], [7], the generator coordinate method [8], and the projected Hartree-Fock Bogoliubov model [9]. It is critical to assess which nuclei are the best candidates for experimental study.Since the experimental decay rate is proportional to the square of the calculated nuclear matrix elements, it is important to calculate these matrix elements with high accuracy to be able to extract the neutrino effective mass which can be used to determine the absolute scale of neutrino masses. However, the theoretical methods used give results that differ from one another by factors of up to 2-3. It is important to understand the nuclear structure aspects of these matrix elements and why the models give differing results. In this Letter we present a new theoretical tool for understanding 0νββ matrix elements by expanding them in terms of a summation over states in the nucleus with two less nucleons (A − 2). We show that the matrix elements are dominated by the contribution through the ground state of the (A − 2) intermediate nucleus. We also show that the lightneutrino matrix elements are dominated by the GamowTeller type operator that is proportional to a schematic interaction of the form σ 1 · σ 2 /r. This opens up new ways of comparing theoretical models and improving the accuracy of the NME for 0νββ decay.The 0νββ process can be naturally described in 2 nd order perturbation theory, in which the energies of the virtual states of the intermediate nucleus obtained by a single beta decay of the parent nucleus enter into the propagator. However, it has been known for some time (see e.g. [10], [11] and references therein) that these energies are small compared to the neutrino exchange energy, and therefore the widely used closure approximation replaces these energies by a constant value and sums-out the contribution of the intermediate states. We will start with the case for the 0νββ decay of 76 Ge that is shown in Fig. 1. Previously, the structure dependence has been analyzed in terms of the "chargeexchange" to intermediate states in 76 As. In contrast, we will show the results for expanding in terms of the intermediate stat...

Change of nuclear configurations in the neutrinoless double-βdecay ofTe130→Xe130andEntwisle1, Kay2, Tamii3 et al. 2016Phys. Rev. C295340View full textAdd to dashboardCite

“…For example, Ref. [51] discusses the nuclear matrix elements in terms of an expansion over states in the A−2 systems, such that data from the (p,t) and ( There is a quantitative disagreement between the experimental data and recent calculations of the same properties. There is no particular model, at least from comparisons with the results of SM, IBM, and QRPA calculations, that fully describes the experimental occupancy data, and therefore the nuclear structure of the isotopes involved in 0ν2β-decay, better than the others.…”

Evaluation of the theoretical nuclear matrix elements forββdecay ofGe76

“…4. The largest term in the 0ν NME is from the J π pp = 0 + ground state of 74 Ge [56]. In QRPA the NME is nearly constant as the number of orbitals included in the sums increase.…”

“…The results discussed below follow from the expansions of the many-body matrix elements for these three operators in terms of the particle-hole (ph) in 76 As or particle-particle (pp) intermediate states in 74 Ge [56]. The 2ν tensor NME is zero and the Fermi NME is zero since isospin is conserved.…”

“…The J pp intermediate states are dominated by the 0 + ground state of 74 Ge (see Ref. [56] for details on the analysis). In QRPA the NME increases by a factor of R 0N V = 1.9 as the number of orbitals included in the sums increases from jj44 to full (21 orbitals).…”

Analysis of mechanisms that could contribute to neutrinoless double-beta decay

“…[7] shows some of these NME for isotopes of immediate experimental relevance. Here we describe the status of the shell model calculations of these NME [6][7][8][9][10][11][12][13][14][15], and their relevance for discriminating possible competing mechanisms that may contribute to the neutrinoless double-beta decay process.…”