Description of the 2ννββ2\nu\nu\beta\beta decay within a fully renormalized pnQRPA approach with a restored gauge symmetry

A many body Hamiltonian involving the mean field for a projected spherical single particle basis, the pairing interactions for alike nucleons and the dipole-dipole proton-neutron interactions in the particle-hole ($ph$) and particle-particle ($pp$) channels is treated by the projected gauge fully renormalized proton-neutron quasiparticle random phase approximation (PGFRpnQRPA) approach. The resulting wave functions and energies for the mother and the daughter nuclei are used to calculate the $2\nu\beta\beta$ decay rate and the process half life. For illustration, the formalism is applied for the decay $^{100}$Mo$\to$ $^{100}$Ru. The results are in good agreement with the corresponding experimental data. The Ikeda sum rule ($ISR$) is obeyed. The gauge projection makes the $pp$ interaction inefficient.Comment: 11 pages, 1 figur

Remarks on monopole charge properties within the Generalized Coherent State Model

The Generalized Coherent State Model, proposed previously for a unified description of magnetic and electric collective properties of nuclear systems, is used to study the ground state band charge density as well as the E0 transitions from $0^+_{\beta}$ to $0^+_g$. The influence of the nuclear deformation and of angular momentum projection on the charge density is investigated. The monopole transition amplitude has been calculated for ten nuclei. The results are compared with some previous theoretical studies and with the available experimental data. Our results concerning angular momentum projection are consistent with those of previous microscopic calculations for the ground state density. The calculations for the E0 transitions agree quite well with the experimental data. Issues like how the shape transitions or shape coexistence are reflected in the $\rho(E0)$ behavior are also addressed.Comment: 32 pages, 7 figure

New features of the triaxial nuclei described with a coherent state model

Supplementing the Liquid Drop Model (LDM) Hamiltonian, written in the intrinsic reference frame, with a sextic oscillator plus a centrifugal term in the variable $\beta$ and a potential in $\gamma$ with a minimum in $\frac{\pi}{6}$, the Sch\"{o}dinger equation is separated for the two variables which results in having a new description for the triaxial nuclei, called Sextic and Mathieu Approach (SMA). SMA is applied for two non-axial nuclei, $^{180}$Hf and $^{182}$W and results are compared with those yielded by the Coherent State Model (CSM). As the main result of this paper we derive analytically the equations characterizing SMA from a semi-classical treatment of the CSM Hamiltonian. In this manner the potentials in $\beta$ and $\gamma$ variables respectively, show up in a quite natural way which contrasts their ad-hoc choice when SMA emerges from LDM.Comment: 13 figures, 13 page