Isospin corrections for superallowed Fermi beta decay in self-consistent relativistic random phase approximation approaches

Self-consistent random phase approximation (RPA) approaches in the relativistic framework are applied to calculate the isospin symmetry-breaking corrections $\delta_c$ for the $0^+\to0^+$ superallowed transitions. It is found that the corrections $\delta_c$ are sensitive to the proper treatments of the Coulomb mean field, but not so much to specific effective interactions. With these corrections $\delta_c$, the nucleus-independent $\mathcal{F}t$ values are obtained in combination with the experimental $ft$ values in the most recent survey and the improved radiative corrections. It is found that the constancy of the $\mathcal{F}t$ values is satisfied for all effective interactions employed. Furthermore, the element $V_{ud}$ and unitarity of the Cabibbo-Kobayashi-Maskawa matrix are discussed.Comment: 7 pages, 2 figures, 4 table

RPA Correlations and Nuclear Densities in Relativistic Mean Field Approach

The relativistic mean field approach (RMF) is well known for describing accurately binding energies and nucleon distributions in atomic nuclei throughout the nuclear chart. The random phase approximation (RPA) built on top of the RMF is also a good framework for the study of nuclear excitations. Here, we examine the consequences of long range correlations brought about by the RPA on the neutron and proton densities as given by the RMF approach.Comment: 15 pages, 13 figure

Fine structure of charge-exchange spin-dipole excitations in 16^{16}O

The charge-exchange spin-dipole (SD) excitations for both $(p,n)$ and $(n,p)$ channels in $^{16}$O are investigated in the fully self-consistent random phase approximation based on the covariant density functional theory. The fine structure of SD excitations in the most up-to-date $^{16}$O($\vec p, \vec n$)$^{16}$F experiment is excellently reproduced without any readjustment in the functional. The characteristics of SD excitations are understood with the delicate balance between the $\sigma$- and $\omega$-meson fields via the exchange terms. The fine structure of SD excitations for $^{16}$O($n,p$)$^{16}$N channel is predicted for future experiments.Comment: 5 pages, 4 figure

Feasibility of the finite amplitude method in covariant density functional theory

Self-consistent relativistic random-phase approximation (RPA) in the radial coordinate representation is established by using the finite amplitude method (FAM). Taking the isoscalar giant monopole resonance in spherical nuclei as example, the feasibility of the FAM for the covariant density functionals is demonstrated, and the newly developed methods are verified by the conventional RPA calculations. In the present relativistic RPA calculations, the effects of the Dirac sea can be automatically taken into account in the coordinate-space representation. The rearrangement terms due to the density-dependent couplings can be implicitly calculated without extra computational costs in both iterative and matrix FAM schemes.Comment: 12 pages, 5 figure

Finite-amplitude method: An extension to the covariant density functionals

The finite-amplitude method (FAM) is one of the most promising methods for optimizing the computational performance of the random-phase approximation (RPA) calculations in deformed nuclei. In this report, we will mainly focus on our recent progress in the self-consistent relativistic RPA established by using the FAM. It is found that the effects of Dirac sea can be taken into account implicitly in the coordinate-space representation and the rearrangement terms due to the density-dependent couplings can be treated without extra computational costs.Comment: 5 pages, 2 figures, Proceedings of the 20th Nuclear Physics Workshop "Marie & Pierre Curie", Kazimierz, Poland, 25-29 September, 201