A new parametrization PC-PK1 for the nuclear covariant energy density functional with nonlinear point-coupling interaction is proposed by fitting to observables of 60 selected spherical nuclei, including the binding energies, charge radii, and empirical pairing gaps. The success of PC-PK1 is illustrated in the description of infinite nuclear matter and finite nuclei including the ground-state and low-lying excited states. In particular, PC-PK1 provides a good description for the isospin dependence of binding energy along either the isotopic or the isotonic chain, which makes it reliable for application in exotic nuclei. The predictive power of PC-PK1 is also illustrated for the nuclear low-lying excitation states in a five-dimensional collective Hamiltonian in which the parameters are determined by constrained calculations for triaxial shapes.

Working with Hamiltonians from chiral effective field theory, we develop a novel framework for describing arbitrary deformed medium-mass nuclei by combining the in-medium similarity renormalization group with the generator coordinate method. The approach leverages the ability of the first method to capture dynamic correlations and the second to include collective correlations without violating symmetries. We use our scheme to compute the matrix element that governs the neutrinoless double beta decay of ${}^{48}\mathrm{Ca}$ to ${}^{48}\mathrm{Ti}$, and find it to have the value 0.61, near or below the predictions of most phenomenological methods. The result opens the door to ab initio calculations of the matrix elements for the decay of heavier nuclei such as ${}^{76}\mathrm{Ge}$, ${}^{130}\mathrm{Te}$, and ${}^{136}\mathrm{Xe}$.

The framework of relativistic energy-density functionals is extended to include correlations related to the restoration of broken symmetries and to fluctuations of collective variables. The generator coordinate method is used to perform configuration mixing of angular-momentum-projected wave functions, generated by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The effects of triaxial deformation and of $K$ mixing is illustrated in a study of spectroscopic properties of low-spin states in ${}^{24}\mathrm{Mg}$.

We report a systematic study of nuclear matrix elements (NMEs) in neutrinoless double-$\beta$ decays with a state-of-the-art beyond-mean-field covariant density functional theory. The dynamic effects of particle-number and angular-momentum conservations as well as quadrupole shape fluctuations are taken into account with projections and generator coordinate method for both initial and final nuclei. The full relativistic transition operator is adopted to calculate the NMEs. The present systematic studies show that in most of the cases there is a much better agreement with the previous nonrelativistic calculation based on the Gogny force than in the case of the nucleus ${}^{150}\mathrm{Nd}$ found by Song et al. [ Phys. Rev. C 90, 054309 (2014)]. In particular, we find that the total NMEs can be well approximated by the pure axial-vector coupling term with a considerable reduction of the computational effort.

Background:The discovery of neutrinoless double-$\beta$ ($0\nu \beta \beta$) decay would demonstrate the nature of neutrinos, have profound implications for our understanding of matter-antimatter mystery, and solve the mass hierarchy problem of neutrinos. The calculations for the nuclear matrix elements $M^{0\nu }$ of $0\nu \beta \beta$ decay are crucial for the interpretation of this process.

The recently developed structure model that uses the generator coordinate method to perform configuration mixing of angular-momentum projected wave functions, generated by constrained self-consistent relativistic mean-field calculations for triaxial shapes (3DAMP$+$GCM), is applied in a systematic study of ground states and low-energy collective states in the even-even magnesium isotopes ${}^{20–40}$Mg. Results obtained using a relativistic point-coupling nucleon-nucleon effective interaction in the particle-hole channel and a density-independent $\delta$ interaction in the pairing channel are compared to data and with previous axial 1DAMP$+$GCM calculations, both with a relativistic density functional and the nonrelativistic Gogny force. The effects of the inclusion of triaxial degrees of freedom on the low-energy spectra and $E2$ transitions of magnesium isotopes are examined.