We examine the leading effects of two-body weak currents from chiral effective field theory on the matrix elements governing neutrinoless double-$\beta$ decay. In the closure approximation these effects are generated by the product of a one-body current with a two-body current, yielding both two- and three-body operators. When the three-body operators are considered without approximation, they quench matrix elements by about 10%, less than suggested by prior work, which neglected portions of the operators. The two-body operators, when treated in the standard way, can produce somewhat larger quenching. In a consistent effective field theory, however, these two-body effects become divergent and must be renormalized by a contact operator, the coefficient of which we cannot determine at present.

Tensor effects on the $N=40$ gap evolution of $N=40$ isotones are studied by employing the Skyrme-Hartree-Fock-Bogoliubov (SHFB) and relativistic Hartree-Fock-Bogoliubov (RHFB) theories. The results with and without the inclusion of the tensor components are compared with each other. It is found that when the tensor force is included, both approaches present the same trend and qualitatively agree with the experimental one indicated by the $\beta$-decay studies, which implies an important role played by the tensor force in the gap evolution of $N=40$. Furthermore, it is shown that the gap evolution is dominated by the corresponding tensor contributions from $\pi$ and $\rho$-tensor coupling in the relativistic framework.

The shape transition and possible occurrence of low-energy shape coexistence and rigid triaxial deformation are analyzed in the six even-even Er, Yb, Hf, W, Os, and Pt isotopic chains with the neutron number $102\le N\le 124$, using a five-dimensional collective Hamiltonian (5DCH) based on covariant density-functional theory. The potential-energy surfaces display a transition from prolate to oblate or triaxial, and then to near spherical shapes as the neutron number increases. The corresponding 5DCH model calculations reproduce the empirical isotopic trend of the characteristic collective observables and confirm the overall shape transition in this region. It is emphasized that a rapid shape transition between prolate and oblate shapes is predicted in Er and Yb isotopic chains while it becomes smooth for higher-$Z$ isotopic chains and signature for rigid triaxial deformation is found in the transitional isotopes, e.g., ${}^{194}\mathrm{W}$ and ${}^{192\text{–}196}\mathrm{Os}$ by analyzing the energy staggering and probability density distribution in the $\gamma$ bands. Finally, the calculated low-lying spectra for ${}^{184}\mathrm{Er}$ and ${}^{186}\mathrm{Yb}$ demonstrate a remarkable multishape coexistence of medium-deformed oblate, medium- and large-deformed prolate shapes in both nuclei.

In a calculation of rotated matrix elements with angular momentum projection, the generalized Wick's theorem may encounter a practical problem of combinatorial complexity when the configurations have more than four quasiparticles (qp's). The problem can be solved by employing the Pfaffian algorithm generally applicable to calculations of matrix elements for Hartree-Fock-Bogoliubov states with any number of qp's. This breakthrough in many-body techniques enables studies of high-spin states in a shell-model framework. As the first application of the Pfaffian algorithm, the configuration space of the projected shell model is expanded to include 6-qp states for both positive and negative parities. Taking $^{166}\mathrm{Hf}$ as an example, we show that 6-qp states become the main configuration of the yrast band beyond spin $I$\approx${}34$\hbar${}$, which explains the observed third back-bending in moment of inertia. Structures of multi-qp high-$K$ isomers in $^{176}\mathrm{Hf}$ are analyzed as another example.

A shell-model method for calculating Gamow-Teller (GT) transition rates in heavy deformed odd-mass nuclei is presented. The method is developed within the framework of the projected shell model. To implement the computation requirement when many multi-quasiparticle configurations are included in the basis, a numerical advancement based on the Pfaffian formula is introduced. With this new many-body technique, it becomes feasible to perform state-by-state calculations for the GT nuclear matrix elements of $\beta$-decay and electron-capture processes, including those at high excitation energies in heavy nuclei which are usually deformed. The first results, ${\beta }^{-}$ decays of the well-deformed $A=153$ neutron-rich nuclei, are shown as the example. The known $log\left(ft\right)$ data corresponding to the $B({\mathrm{GT}}^{-}$) decay rates of the ground state of ${}^{153}\mathrm{Nd}$ to the low-lying states of ${}^{153}\mathrm{Pm}$ are well described. It is further shown that the $B$(GT) distributions can have a strong dependence on the detailed microscopic structure of relevant states of both the parent and daughter nuclei.

The excited-state structure of atomic nuclei can modify nuclear processes in stellar environments. In this Letter, we study the influence of nuclear excitations on Urca cooling (repeated back-and-forth $\beta$ decay and electron capture in a pair of nuclear isotopes) in the crust and ocean of neutron stars. We provide for the first time an expression for Urca process neutrino luminosity which accounts for a thermal Boltzmann distribution of excited states in both members of an Urca pair. We use our new formula with state-of-the-art nuclear structure inputs to compute neutrino luminosities of candidate Urca cooling pairs. Our nuclear inputs consist of the latest experimental data supplemented with calculations using the projected shell model. We show that, in contrast to previous results that only consider the ground states of both nuclei in the pair, our calculated neutrino luminosities for different Urca pairs vary sensitively with the environment temperature and can be radically different from those obtained in the one-transition approximation. We find that nuclear excitations can lead to an enhancement in total Urca neutrino luminosities in the accreted neutron star crust by about 5 times as compared with the previous Urca results, which is expected to cause significant observational effects.