Renormalized Proton-Neutron Quasiparticle Random-Phase Approximation and Its Application to Double Beta Decay

Abstract

A self-consistent method of treating excitations of the proton-neutron quasiparticle random-phase approximation is presented. The non-self-consistent methods violate the Pauli exclusion principle and lead to an eventual collapse of the ground state. This behavior renders a reliable calculation of the nuclear matrix elements, relevant for the prediction of double-beta-decay half-lives, difficult. The present formalism promotes the Pauli exclusion principle and avoids the collapse of the double-betadecay matrix elements. We have applied this formalism to the double beta decay of ' Mo.

Double beta decay and the proton-neutron residual interaction

“…Fig. 3 In all the cases the curve corresponding to M 2ν is very similar to that found in realistic calculations [3,5,6,13], including its cancellation near the collapse of the QRPA description. The RQRPA extends this curve far beyond the value of κ at which the QRPA collapses.…”

“…Contrary to the QRPA in the RQRPA there is no collapse for any set of values of the force's parameters. It was presented as a reliable tool and was applied to the ββ 2ν decay of 100 Mo [13]. Similar results were found with the inclusion of proton-neutron pairing interactions [14].…”

“…A renormalized version of the QRPA (RQRPA) [10,11], which includes some corrections beyond the quasiboson approximation, has been reformulated recently [12] and applied to the ββ 2ν decay [13]. Contrary to the QRPA in the RQRPA there is no collapse for any set of values of the force's parameters.…”

Nuclear matrix elements for double-βdecay

“…Also, the Fermi matrix elements in the DFT are comparable to those in IBM-2 and larger than those in the ISM [44]. (Color online) IBM-2 results for 0νββ nuclear matrix elements compared with QRPA-Tü [13], the ISM [14], QRPA-Jy [36,[54][55][56], QRPA-deformed [41], DFT [43], and HFB [42].…”

Neutrinoless ββ nuclear matrix elements using isovector spin-dipole Jπ=2− data

“…There are many models which have recently been used to compute the 0νββ nuclear matrix elements (NMEs): the quasiparticle random-phase approximation (QRPA), as well as its proton-neutron version (pnQRPA) (see, e.g., [9]) and its renormalized extensions [10,11], the interacting shell model (ISM) [12,13], the microscopic interacting boson model (IBA-2) [14], the Gogny-based energy-density functional (EDF) [15] and its variation [16], and the projected Hartree-FockBogoliubov mean-field scheme (PHFB) [17]. Very recently also the beyond-mean-field covariant density functional theory [18,19] and advanced shell-model frameworks [20][21][22][23] have been used to describe the 0νββ NMEs of nuclei.…”