New results for the fully renormalized proton–neutron quasiparticle random phase approximation

Abstract

A many-body Hamiltonian describing a system of Z protons and N neutrons moving in spherical shell model mean field and interacting among themselves through proton-proton and neutronneutron pairing and a dipole-dipole proton-neutron interaction of both particle-hole and particleparticle type, is treated within a fully renormalized (FR) pnQRPA approach. Two decoupling schemes are formulated. One of them decouples the equations of motion of particle total number conserving and non-conserving operators. One ends up with two very simple dispersion equations for phonon operators which are formally of Tamm-Dancoff types. For excitations in the (N-1,Z+1) system, Ikeda sum rule is fully satisfied provided the BCS equations are renormalized as well and therefore solved at a time with the FRpnQRPA equations. Next, one constructs two operators R † 1µ , R 1,−µ (−) 1−µ which commutes with the particle total number conserving operators, A † 1µ and A 1,−µ (−) 1−µ , and moreover could be renormalized so that they become bosons. Then, a phonon operator is built up as a linear combination of these four operators. The FRpnQRPA equations are written down for this complex phonon operator and the ISR is calculated analytically. This formalism allows for an unified description of the dipole excitations in four neighboring nuclei (N-1,Z+1),(N+1,Z-1),(N-1,Z-1),(N+1,Z+1). The phonon vacuum describes the (N,Z) system ground state.

Description of the 2ννββ decay within a gauge restored of a fully renormalized pnQRPA approach

“…In this paper the results of [15] are improved in three respects: (a) aiming at providing a unitary description of the process for the situations when the nuclei involved are spherical or deformed, here we use the projected spherical single particle basis defined in [16] and used for double beta decay in [17,18]; (b) the space of proton-neutron dipole configurations is split into three subspaces, one being associated with the single β − , one to the β + process, and one spanned by the unphysical states; (c) the correlations for the second leg of the process are mainly determined by the ph dipole-pairing term. A compact expression for the dispersion equation of energies is obtained from the linearized equations of motion of the basic transition operators corresponding to the two coupled processes.…”

“…It is believed that such a violation is caused by the gauge symmetry breaking. Consequently, a method of restoring this symmetry was formulated by the present authors in [15].…”

Equation of Motion Method to strongly correlated Fermi systems and Extended RPA approaches

“…This drawback is cured in Refs. [86,87] within the fully renormalized pnQRPA (FR-pnQRPA), by considering the scattering terms in the structure of the QRPA phonon. Later on, a new method of restoring the gauge symmetry breaking was formulated to cure this drawback within the so-called GPFR-pnQRPA [88].…”

FRpnQRPA approach with the gauge symmetry restored. Application for the 2νββdecay

“…[7] were improved in two respects: a) aiming at providing a unitary description of the process for the situations when the involved nuclei are spherical or deformed, here we use a projected spherical single particle basis; b) the space of proton-neutron dipole configurations is split in three subspaces, one being associated to the single β − decay, one to the single β + process, and one spanned by the unphysical states. A set of GRFRpnQRPA equations is written down in the first two subspaces mentioned above, by linearizing the equations of motion of the basic transition operators corresponding to the two coupled processes.…”