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Self-consistent theory frameworks have been introduced for description of excitations in nuclei at finite temperature, based on energy density functionals formulated using i) relativistic mean field Lagrangian with density dependent meson-nucleon vertex functions, and ii) Skyrme-type functionals. Finite temperature random phase approximation (FTRPA) has been employed in description of multipole excitations and charge-exchange modes. It is shown that in the temperature range T = 1–2 MeV additional transition strength appears at low energies due to thermal unblocking of single-particle orbitals close to the Fermi level. Within the finite temperature Hartree-Fock+RPA based on Skyrme functionals, the electron capture cross sections have been studied for target nuclei at temperatures relevant in modeling the supernova evolution.

We show some results of systematic calculation on electric dipole responses of even-even nuclei, employing a Hartree-Fock plus RPA approach. For an easy implementation of the fully self-consistent calculation, a finite amplitude method which we proposed recently is employed. We show a systematic comparison of calculated peak energies of giant dipole resonances and an importance of low-angular momentum orbit for emergence of pygmy dipole resonances.

Collisional damping widths of isoscalar giant monopole, isovector giant dipole and isoscalar giant quadrupole excitations for ¹²⁰Sn and ²⁰⁸Pb at zero and finite temperatures are calculated within Thomas-Fermi approximation by employing a recently proposed modified Skyrme force and the results are compared with previous works.

The low-lying dipole and quadrupole states in neutron rich nuclei are studied within the fully self-consistent relativistic quasiparticle random-phase approximation (RQRPA), formulated in the canonical basis of the Relativistic Hartree–Bogoliubov model (RHB), which is extended to include the density dependent interactions. In heavier nuclei, the low-lying E1 excited state is identified as a pygmy dipole resonance (PDR), i.e. as a collective mode of excess neutrons oscillating against a proton–neutron core. Isotopic dependence of the PDR is characterized by a crossing between the PDR and one-neutron separation energies. Already at moderate proton–neutron asymmetry the PDR peak is calculated above the neutron emission threshold, indicating important implications for the observation of the PDR in (γ, γ′) scattering, and on the theoretical predictions of the radiative neutron capture rates in neutron-rich nuclei. In addition, a novel method is suggested for determining the neutron skin of nuclei, based on measurement of excitation energies of the Gamow–Teller resonance relative to the isobaric analog state.

Electric dipole strength below the particle emission threshold both in stable nuclei and short-lived isotopes has received increasing interest due to its astrophysical impact. In analogy to the giant dipole resonance, this strength is commonly referred to as pygmy resonance. Coulomb dissociation of neutron-rich unstable isotopes and nuclear resonance fluorescence photon scattering have begun to provide systematic data on electric dipole strength in various isotope chains. We review the present state of the art of theoretical approaches and point out some open problems. We emphasize the necessity of a simultaneous theoretical treatment of the nucleon separation energies and the energetically low-lying dipole strength because the presently available data do not exclude a non-collective nature of the pygmy strength.

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.

γ-ray strength function is the key input for the photonuclear reactions, which have a special astrophysical importance, and should be renormalized by using the nuclear level density for calculating the theoretical average radiative capture width, but performing such renormalization is challenging for light nuclei. With this motivation, recently introduced level density parameter formula including collective effects is used to calculate the average radiative capture width of light nuclei, and therefore to renormalize their γ-ray strength functions. Obtained normalization factors are tested in (n, γ) reactions for the necessity of renormalization for light nuclei.

Fully consistent axially-symmetric-deformed HFB+QRPA calculations have been performed, where the same Gogny D1S effective force has been used both in the HFB and QRPA approaches. Results on dipole pygmy states in ²⁶Ne are shown and compared with recent experimental data. Giant dipole resonances calculated in the s-d shell nuclei ^26–30Si and ^22–28Mg are presented and the splitting of the resonance in the deformed nuclei is discussed.

We briefly review the continuum mechanical approach to the excitation of collective modes in homogenous nuclear matter. The main point of this treatment is that nuclear matter around the saturation density displays characteristics analogous to a linear elastic continuum. Giant resonances are discussed as typical cases of elastic disturbances in nuclear matter. Within such a macroscopic approach it is possible to understand the gross properties of isoscalar electric and magnetic resonances. We sketch also how this framework can be extended to the case of inhomogenous nuclear matter.

I undertake an anatomy of the nuclear electric-dipole spectrum and discuss selected observations. First, using data and calculations on ²⁰⁸Pb as a representative case, I identify five conspicuous structures in the spectra of heavy nuclei: (1) the giant dipole resonance (GDR), (2) the dipole compression mode, (3) the isoscalar low-energy dipole mode (ISLED), (4) the IS mode in the region of the GDR, and (5) a concentration of “pygmy” dipole strength (PDS) between the latter two. Next, compiling the data from Texas A&M I show that the energy of (4) follows roughly a A^−1/6 dependence on the mass number. Finally, I summarize recent theoretical studies on the PDS in exotic nuclei, which suggest a strong influence of shell effects and loose binding.

Second RPA calculations with a Skyrme force are performed to describe both high- and low-lying excited states in ¹⁶O and ⁴⁸Ca. The coupling between 1 particle-1 hole and 2 particle-2 hole as well as that between 2 particle-2 hole configurations are fully taken into account and the residual interaction is considered with the proper rearrangement terms. A several-MeV shift to lower energies is systematically found with respect to the RPA distributions for the strength distributions of giant resonances. The nature of the low-energy dipole excitations is analyzed in ⁴⁸Ca: it is found that in general these excitations cannot be in interpreted in terms of oscillations of the neutron skin against the core, with the exception of the peak with the largest B(E1) value, which is located at 9.09 MeV. For this peak the neutron transition density dominates and the neutron and proton transition densities oscillate out of phase in the internal part of the nucleus leading to a strong mixing of isoscalar and isovector components. Therefore, this state shows some features usually associated to pygmy resonances.

Isoscalar giant resonances in exotic nuclei can be studied using inelastic alpha scattering in inverse kinematics. In particular, the compression modes, i.e. isoscalar giant monopole and dipole resonances, are very interesting because they can furnish information on the different terms of the nuclear incompressibility, especially if measured in long isotopic chains including nuclei far from the valley of stability. As beams of exotic nuclei have relatively low intensities thick targets have to be used in order to get a reasonable yield. However, this leads to degradation of the energy resolution and stops low-energy recoil particles. Two good alternatives exist. The first method is to use an active target, such as MAYA, which is a time-projection chamber and therefore can be used for detection of low-energy recoil particles. Furthermore, its thickness can be increased by increasing the length of the detection volume or the gas pressure without severe loss of energy resolution. The second method is to use a storage ring for storing the exotic nuclei, which then interact with target nuclei from a gas-jet target. Here, the luminosity and hence the yield are increased because the exotic nuclei circulate in the ring at a frequency of around 10⁶ turns/s. Low-energy recoil particles traverse the gas-jet with little loss of energy and can be detected in solid-state detectors. Pioneering experiments with both methods have been performed for inelastic scattering of secondary ⁵⁶Ni beam off helium nuclei. Here, preliminary results of the experiment with the active target MAYA will be presented.