International Journal of Modern Physics E

The phenomenological classification of collective quadrupole excitations by means of the Bohr–Hamiltonian (BH) is reviewed with focus on signatures for triaxility. The variants of the microscopic BH derived by means of the Adiabatic Time-Dependent Mean Field theory from the Pairing-plus-quadrupole–quadrupole interaction, the Shell Correction Method, the Skyrme Energy Density Functional, the Relativistic Mean Field Theory and the Gogny interaction are discussed and applications to concrete nuclides reviewed. The Generator Coordinate Method for the five-dimensional quadrupole deformation space and first applications to triaxial nuclei are presented. The phenomenological classification in the framework of the Interacting Boson Model is discussed with a critical view on the boson number counting rule. The recent success in calculating the model parameters by mapping the mean field deformation energy surface on the bosonic one is discussed and the applications listed. A critical assessment of the models is given with focus on the limitations due to the adiabatic approximation. The Tidal Wave approach and the Triaxial Projected Shell Model are presented as practical approaches to calculate spectral properties outside the adiabatic region.

Through ab initio approaches in nuclear theory, we may now seek to quantitatively understand the wealth of nuclear collective phenomena starting from the underlying internucleon interactions. No-core configuration interaction (NCCI) calculations for p-shell nuclei give rise to rotational bands, as evidenced by rotational patterns for excitation energies, electromagnetic moments and electromagnetic transitions. In this review, NCCI calculations of ^7–9Be are used to illustrate and explore ab initio rotational structure, and the resulting predictions for rotational band properties are compared with experiment. We highlight the robustness of ab initio rotational predictions across different choices for the internucleon interaction.

Density functional theory provides the most promising, and likely unique, microscopic framework to describe nuclear systems ranging from finite nuclei to neutron stars. Properly optimized energy density functionals define a new paradigm in nuclear theory where predictive capability is possible and uncertainty quantification is demanded. Moreover, density functional theory offers a consistent approach to the linear response of the nuclear ground state. In this paper, we review the fundamental role played by nuclear collective modes in uncovering novel excitations and in guiding the optimization of the density functional. Indeed, without collective excitations the determination of the density functional remains incomplete. Without collective excitations, the equation of state of neutron-rich matter continues to be poorly constrained. We conclude with a discussion of some of the remaining challenges in this field and propose a path forward to address these challenges.

Relativistic energy density functionals have become a standard framework for nuclear structure studies of ground state properties and collective excitations over the entire nuclide chart. In this paper, we review recent developments in modeling nuclear weak-interaction processes: Charge-exchange excitations and the role of isoscalar proton–neutron pairing, charged-current neutrino–nucleus reactions relevant for supernova evolution and neutrino detectors and calculation of β-decay rates for r-process nucleosynthesis.

In the last 10 years, we have observed an important increase of interest in the application of time-dependent energy density functional (TD-EDF) theory. This approach allows to treat nuclear structure and nuclear reaction from small to large amplitude dynamics in a unified framework. The possibility to perform unrestricted three-dimensional simulations using state-of-the-art effective interactions has opened new perspectives. In the present paper, an overview of applications where the predictive power of TD-EDF has been benchmarked is given. A special emphasize is made on processes that are of astrophysical interest. Illustrations discussed here include giant resonances, fission, binary and ternary collisions leading to fusion, transfer and deep inelastic processes.

The neutron star inner crust is assumed to be superfluid at relevant temperatures. The contribution of neutron quasiparticles to thermodynamic and transport properties of the crust is therefore strongly suppressed by the pairing gap. Nevertheless, the neutron gas still has low-energy excitations, namely long-wavelength collective modes. We summarize different approaches to describe the collective modes in the crystalline phases of the inner crust and present an improved model for the description of the collective modes in the pasta phases within superfluid hydrodynamics.

In this paper, I will review the theory behind the gravitational wave (GW) driven r-mode instability in rapidly rotating neutron stars (NSs) and discuss which constraints can be derived from observations of spins and temperatures in low mass X-ray binaries (LMXBs). I will discuss how a standard, 'minimal' NS model is not consistent with the data, and discuss some of the additional physical mechanisms that could reconcile theory with observations. In particular, I will focus on additional forms of damping due to exotic cores and on strong mutual friction due to superfluid vortices cutting through superconducting flux tubes, and examine the repercussions these effects could have on the saturation amplitude of the mode. Finally I will also discuss the possibility that oscillations due to r-modes may have been recently observed in the X-ray light curves of two LMXBs.

Neutrino oscillations in a hot and dense astrophysical environment such as a core-collapse supernova pose a challenging, seven-dimensional flavor transport problem. To make the problem even more difficult (and interesting), neutrinos can experience collective oscillations through nonlinear refraction in the dense neutrino medium in this environment. Significant progress has been made in the last decade towards the understanding of collective neutrino oscillations in various simplified neutrino gas models with imposed symmetries and reduced dimensions. However, a series of recent studies seem to have "reset" this progress by showing that these models may not be compatible with collective neutrino oscillations because the latter can break the symmetries spontaneously if they are not imposed. We review some of the key concepts of collective neutrino oscillations by using a few simple toy models. We also elucidate the breaking of spatial and directional symmetries in these models because of collective oscillations.

Neutrinos propagate in astrophysical and cosmological environments modifying their flavor in intriguing ways. The study of neutrino propagation in media is based on the mean-field, extended mean-field and Boltzmann equations. We summarize salient features of these evolution equations and the methods employed so far to derive them. We emphasize applications to situations of observational interest.