Contribution to the "Handbook of Nuclear Physics", Springer, 2022, I. Tanihata, H. Toki and T. Kajino, Eds. (small issue with \hbar when submitting, this character does not show up as it should)
The Random Phase Approximation (RPA) and its variations and extensions are, without any doubt, the most widely used tools to describe Giant Resonances within a microscopic theory. In this chapter, we will start by discussing how RPA comes out naturally if one seeks a state with a harmonic time dependence in the space of one particle-one hole excitations on top of the ground state. It will be also shown that RPA is the simplest approach in which a ``collective'' state emerges. These are basic arguments that appear in other textbooks but are also unavoidable as a starting point for further discussions. In the rest of the chapter, we will give emphasis to developments that have taken place in the last decades: alternatives to RPA like the Finite Amplitude Method (FAM), state-of-the-art calculations with well-established Energy Density Functionals (EDFs), and progress in {\em ab initio} calculations. We will discuss extensions of RPA using as a red thread the various enlargements of the one particle-one hole model space. The importance of the continuum, and the exclusive observables like the decay products of Giant Resonances, will be also touched upon.
Effect of ground-state deformation on the Isoscalar Giant Monopole Resonance and the first observation of overtones of the Isoscalar Giant Quadrupole Resonance in rare-earth Nd isotopes
[Background] Giant resonance (GR) is a typical collective mode of vibration. The deformation splitting of the isovector (IV) giant dipole resonance is well established. However, the splitting of GRs with other multipolarities is not well understood. [Purpose] I explore the IV monopole and quadrupole excitations and attempt to obtain the generic features of IV giant resonances in deformed nuclei by investigating the neutral and charge-exchange channels simultaneously. [Method] I employ a nuclear energy-density functional (EDF) method: the Skyrme-Kohn-Sham-Bogoliubov and the quasiparticle random…
The remaining uncertainties of isovector nuclear interactions call for reliable experimental measurements of isovector probes in finite nuclei. Based on the Bayesian analysis, although the neutron-skin thickness data or the isovector giant dipole resonance data in $^{208}$Pb can constrain only one isovector interaction parameter, correlations between other parameters are built. Using combined data of both the neutron-skin thickness and the isovector giant dipole resonance helps to constrain significantly all isovector interaction parameters, thus serves as a useful way in the future analysis.
We review the phenomenon of fine structure of nuclear giant resonances and its relation to different resonance decay mechanisms. Wavelet analysis of the experimental spectra provides quantitative information on the fine structure in terms of characteristic scales. A comparable analysis of resonance strength distributions from microscopic approaches incorporating one or several of the resonance decay mechanisms allows conclusions on the source of the fine structure. For the isoscalar giant quadrupole resonance (ISGQR), spreading through the first step of the doorway mechanism, i.e.\ coupling be…
Giant multipole resonances in Nd and Sm isotopes are studied by employing the quasiparticle-random-phase approximation on the basis of the Skyrme energy-density-functional method. Deformation effects on giant resonances are investigated in these isotopes which manifest a typical nuclear shape change from spherical to prolate shapes. The peak energy, the broadening, and the deformation splitting of the isoscalar giant monopole (ISGMR) and quadrupole (ISGQR) resonances agree well with measurements. The magnitude of the peak splitting and the fraction of the energy-weighted strength in the lower …
Giant resonances encapsulate the dynamic response of the nuclear ground state to external perturbations. As such, they offer a unique view of the nucleus that is often not accessible otherwise. Although interesting in their own right, giant resonances are also enormously valuable in providing stringent constraints on the equation of state of asymmetric matter. We this view in mind, we focus on two modes of excitation that are essential in reaching this goal: the isoscalar giant monopole resonance (GMR) and the isovector giant dipole resonance (GDR). GMR energies in heavy nuclei are sensitive t…
Giant resonances--highly collective, high-frequency oscillations of the atomic nucleus--are the focus of this chapter. We discuss the isoscalar excitations, where the protons and neutrons oscillate in phase, up to angular-momentum transfers $L$ = 3. The procedures of experiments and data analysis employed in extracting the strength distributions associated with these resonances are discussed. The experimentally extracted strength distributions are presented, along with information on the properties of these resonances available to date. The effect of deformation of the nuclear ground state on …
The energetic beam of (spin and isospin zero) $α$-particles remains a very efficient probe for the nuclear isoscalar giant resonances. In the present work, a microscopic folding model study of the isoscalar giant resonances in $^{208}$Pb induced by inelastic \aPb scattering at $E_{\rm lab}=240$ and 386 MeV has been performed using the (complex) CDM3Y6 interaction and nuclear transition densities given by both the collective model and Random Phase Approximation (RPA) approach. The fractions of energy weighted sum rule around the main peaks of the isoscalar monopole, dipole and quadrupole giant …
The thermal pairing gap obtained by embedding the exact solutions of the pairing problem into the canonical ensemble is employed to calculate the width and strength function of the giant dipole resonance (GDR) within the phonon damping model. The results of calculations describe reasonably well the data for the GDR width as well as the GDR linearized strength function, recently obtained for $^{201}$Tl in the temperature region between 0.8 and 1.2 MeV, which other approaches that neglect the effect of non-vanishing thermal pairing fail to describe.
Updated values and corresponding uncertainties of Isovector Giant Dipole Resonance (GDR) parameters which are obtained by the least-squares fitting of theoretical photoabsorption cross sections to experimental data are presented. The theoretical photoabsorption cross sections are taken as a sum of the components corresponding to the excitation of the GDR and quasideuteron photodisintegration. The current compilation is an extension and improvement of the earlier compilations of Lorentzian parameters for ground-state photoneutron and photoabsorption cross sections and covers experimental data m…
Fine structure of giant resonances (GR) has been established in recent years as a global phenomenon across the nuclear chart and for different types of resonances. A quantitative description of the fine structure in terms of characteristic scales derived by wavelet techniques is discussed. By comparison with microscpic calculations of GR strength distributions one can extract information on the role of different decay mechanisms contributing to the width of GRs. The observed cross-section fluctuations contain information on the level density (LD) of states with a given spin and parity defined …
The compression-mode giant resonances, namely the isoscalar giant monopole and isoscalar giant dipole modes, are examples of collective nuclear motion. Their main interest stems from the fact that one hopes to extrapolate from their properties the incompressibility of uniform nuclear matter, which is a key parameter of the nuclear Equation of State (EoS). Our understanding of these issues has undergone two major jumps, one in the late 1970s when the Isoscalar Giant Monopole Resonance (ISGMR) was experimentally identified, and another around the turn of the millennium since when theory has been…
The properties of the isoscalar giant monopole resonance (ISGMR) for the double magic $^{48}$Ca are analyzed in the framework of a microscopic model based on Skyrme-type interactions. A method for simultaneously taking into account the coupling between one-, two-, and three-phonon terms in the wave functions of $0^{+}$ states has been developed. The inclusion of three-phonon configurations leads to a substantial redistribution of the ISGMR strength to lower energy $0^{+}$ states and also higher energy tail. Our results demonstrate that the developed approach enables to us to describe a gross s…
We have studied the isoscalar giant quadruple resonance (ISGQR) and the isovector giant dipole resonance (IVGDR) in $^{208}$Pb based on an improved isospin-dependent Boltzmann-Uehling-Uhlenbeck transport approach using an improved isospin- and momentum-dependent interaction. With the isoscalar nucleon effective mass and the nucleon-nucleon cross section which reproduces respectively the excitation energy and the width of the ISGQR strength function, the slope parameter of the symmetry energy and the neutron-proton effective mass splitting are constrained respectively within $36<L<62$ MeV and $…
We present an ab-initio calculation of the giant dipole resonance in 16O based on a nucleon-nucleon (NN) interaction from chiral effective field theory that reproduces NN scattering data with high accuracy. By merging the Lorentz integral transform and the coupled-cluster methods, we extend the previous theoretical limits for break-up observables in light nuclei with mass numbers (A<=7), and address the collective giant dipole resonance of 16O. We successfully benchmark the new approach against virtually exact results from the hyper-spherical harmonics method in 4He. Our results for 16O reprod…
The assumption of an exact isospin symmetry would imply equal strengths for mirror E1 transitions (at least, in the long-wavelength limit). Actually, large violations of this symmetry rule have been indicated by a number of experimental results, the last of which is the 67As - 67Se doublet investigated at GAMMASPHERE. Here, we examine in detail various possible origins of the observed asymmetry. The coherent effect of Coulomb-induced mixing with the high-lying Giant Isovector Monopole Resonance is proposed as the most probable process to produce a large asymmetry in the E1 transitions, with co…
We put a stringent constraint on the isovector nuclear interactions in the Skyrme-Hartree-Fock model from the centroid energy $E_{-1}$ of the isovector giant dipole resonance in $^{208}$Pb as well as its electric polarizability $α_D$. Using the Bayesian analysis method, $E_{-1}$ and $α_D$ are found to be mostly determined by the nuclear symmetry energy $E_{sym}$ at about $ρ^\star=0.05$ fm$^{-3}$ and the isovector nucleon effective mass $m_v^\star$ at the saturation density. At $90\%$ confidence level, we obtain $E_{sym}(ρ^\star) = 16.4 ^{+1.0}_{-0.9}$ MeV and $m_v^\star/m = 0.79 ^{+0.06}_{-0.0…
Proton capture reaction is an important process concerning the astrophysical origin of the elements. In present work, we focus on giant dipole resonance (GDR) in proton capture reactions, such as $^{11}$B$(p, γ)^{12}$C, $^{27}$Al$(p, γ)^{28}$Si, $^{39}$K$(p, γ)^{40}$Ca, and $^{67}$Co$(p, γ)^{68}$Ni in a framework of an extended quantum molecular dynamics model. The systematic properties of GDR parameters including the peak energy, the strength and full width at half maximum (FWHM) have been studied. The dependence of FWHM on temperature has also been discussed. Some comparisons with experiment…
The nuclear giant resonances are studied by using a Fermi-liquid method, and the nuclear collective excitation energies of different values of $l$ are obtained, which are fitted with the centroid energies of the giant resonances of spherical nuclei, respectively. In addition, the relation between the isovector giant resonance and the corresponding isoscalar giant resonance is discussed.
The isoscalar giant monopole, dipole, and quadrupole strength distributions have been deduced in $^{90, 92}$Zr, and $^{92}$Mo from "background-free" spectra of inelastic $α$-particle scattering at a beam energy of 385 MeV at extremely forward angles, including 0$^{\circ}$. These strength distributions were extracted by a multipole-decomposition analysis based on the expected angular distributions of the respective multipoles. All these strength distributions for the three nuclei practically coincide with each other, affirming that giant resonances, being collective phenomena, are not influence…
A closed expression is obtained for the cross-section for Coulomb excitation of levels of the giant dipole resonance of given angular momentum and phonon number. Applications are made to the Goldhaber-Teller and Steinwedel-Jensen descriptions of the resonance, at non-relativistic and relativistic bombarding energies.
With a newly improved isospin- and momentum-dependent interaction and an isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, we have investigated the effects of the slope parameter $L$ of the nuclear symmetry energy and the isospin splitting of the nucleon effective mass $m_{n-p}^*=(m_n^*-m_p^*)/m$ on the centroid energy of the isovector giant dipole resonance and the electric dipole polarizability in $^{208}$Pb. With the isoscalar nucleon effective mass $m_s^*=0.7m$ constrained by the empirical optical potential, we obtain a constraint of $L=64.29\pm11.84 (\rm MeV)$ and $m_{n-p}^*=…
The damping of isoscalar giant quadrupole resonance in $^{16}$O is studied using extended random-phase-approximation approaches derived from the time-dependent density-matrix theory. It is pointed out that the effects of ground-state correlations bring strong fragmentation of quadrupole strength even if the number of two particle--two hole configurations is strongly limited.
We study the Coulomb excitation of pygmy dipole resonances (PDR) in heavy ion reactions at 100 MeV/nucleon and above. The reactions 68Ni+197Au and 68Ni+208Pb are taken as a practical examples. Our goal is to address the question of the influence of giant resonances on the PDR as the dynamics of the collision evolves. We show that the coupling to the giant resonances affects considerably the excitation probabilities of the PDR, a result that indicates the need of an improved theoretical treatment of the reaction dynamics at these bombarding energies.
While bulk properties of stable nuclei are successfully reproduced by mean-field theories employing effective interactions, the dependence of the centroid energy of the electric giant dipole resonance on the nucleon number A is not. This problem is cured by considering many-particle correlations beyond mean-field theory, which we do within the "Quasiparticle Time Blocking Approximation". The electric giant dipole resonances in $^{16}$O, $^{40}$Ca, and $^{208}$Pb are calculated using two new Skyrme interactions.
The isoscalar giant resonances for $^{86}\textrm{Ge}$ are studied by the quasiparticle finite amplitude method based on the covariant density functional theory. In addition to the well-known monopole-quadrupole coupling that splits the isoscalar giant monopole resonance in axially deformed nuclei, a monopole-quadrupole-hexadecupole coupling is identified in the triaxially deformed nucleus $^{86}\textrm{Ge}$, leading to the emergence of a distinct resonance peak at the low energy side of the isoscalar monopole strength function. The transition density of the triaxiality induced resonance peak s…
The basic version of the semi-microscopic particle-hole dispersive optical model is implemented to describe main properties of the Gamow-Teller and charge-exchange giant spin-monopole resonances in medium-heavy closed-shell parent nuclei. Calculation results obtained for $^{48}Ca$, $^{90}Zr$, $^{132}Sn$, and $^{208}Pb$ are compared with available experimental data.
The extraction of the nuclear incompressibility from the isoscalar giant monopole resonance (GMR) measurements is analysed. Both pairing and mutually enhanced magicity (MEM) effects play a role in the shift of the GMR energy between the doubly closed shell $^{208}$Pb nucleus and other Pb isotopes. Pairing effects are microscopically predicted whereas the MEM effect is phenomenologically evaluated. Accurate measurements of the GMR in open-shell Pb isotopes are called for.
