Neutrinoless double- β decay matrix elements in large shell-model spaces with the generator-coordinate method

Abstract

We use the generator-coordinate method with realistic shell-model interactions to closely approximate full shell-model calculations of the matrix elements for the neutrinoless double-beta decay of 48 Ca, 76 Ge, and 82 Se. We work in one major shell for the first isotope, in the f 5/2 pg 9/2 space for the second and third, and finally in two major shells for all three. Our coordinates include not only the usual axial deformation parameter β, but also the triaxiality angle γ and neutron-proton pairing amplitudes. In the smaller model spaces our matrix elements agree well with those of full shell-model diagonalization, suggesting that our Hamiltonian-based GCM captures most of the important valence-space correlations. In two major shells, where exact diagonalization is not currently possible, our matrix elements are only slightly different from those in a single shell.

Neutrinoless double- β decay in effective field theory: The light-Majorana neutrino-exchange mechanism

“…(38), describing their relation (when applicable) to the standard treatment of 0νββ matrix elements in the literature. We advocate that many-body calculations with existing methods [77][78][79][80][81][82][83][84][85][86][87][88], as well as with methods under development [89], should be organized according to the EFT power counting scheme, isolating LO, N 2 LO, and ultrasoft contributions. Ideally, the neutrino potential derived here should be used with nuclear wavefunctions also based on chiral EFT and computed at next-to-leading order, or higher.…”

Variational approximations to exact solutions in shell-model valence spaces: Calcium isotopes in the pf shell

“…Similar implementations to the present approach have been recently used to evaluate neutrinoless double-beta decay nuclear matrix elements [15][16][17]. Some of them consider a limited number of collective degrees of freedom as generating coordinates and none of them implements the particle-number variation after projection (PNVAP) method.…”

Union of rotational and vibrational modes in generator-coordinate-type calculations, with application to neutrinoless double- β decay

“…GCM calculation typically focus on collective correlations known to be important in nuclei. Most prominent are quadrupole deformations, originally with axial symmetry [19,20] but later extended to triaxiallydeformed configurations [21][22][23][24]. There are also stud-ies in consideration of octupole modes [25,26], as well as investigations of fluctuations in like-particle pairing [27,28].…”

“…There are also stud-ies in consideration of octupole modes [25,26], as well as investigations of fluctuations in like-particle pairing [27,28]. Recent work has indicated the transition operators of double-beta (ββ) decay are sensitive to protonneutron (pn) pairing correlations [29][30][31][32].The inclusion of pn pairing correlations in GCM calculations [24,[33][34][35] significantly reduces the large difference in the 0νββ nuclear matrix elements between previous GCM and SM predictions [24,34,35]. Despite this success, even if one treats both quadrupole deformation and pn pairing as coordinates, and uses the same SM Hamiltonian, the 0νββ matrix elements of 124 Sn, 130 Te, and 136 Xe given by GCM are still overestimated by about 30% when compared with SM results [35].…”

“…(For other candidate 0νββ targets with naturally triaxial minima, e.g. 76 Ge, full three-dimensional projection unsurprisingly improves results [24]. )…”