Regge poles in the collective model of the nuclear giant multipole resonances

Giant nuclear resonance states, of higher multipolarity than dipole, have recently been observed in hadron and electron scattering. They may possibly be described by the collective Goldhaber-Teller model as extended to the higher multipolarity case, and as generalized to include spin-isospin vibrations and spin waves. Based on such a model, we show that the multipole resonances, together with the conventional dipole resonances, can be generated by the motion of a few basic Regge poles through the complex angular momentum plane. This viewpoint unifies all the resonances with a given spin-isospin character but arbitrary value of the multipolarity, and suggests the existence of the higher-multipole resonances as a consequence of the existence of the dipole resonance. We also analyze these Regge poles in terms of collective surface waves (“creeping waves”) circumnavigating the nucleus, and we determine their phase velocities and attenuations. Finally, the giant resonances them selves are explained as a resonant reinforcement of phase-matched surface waves.     

Differences between dynamical theories of giant resonances

It is the objective of dynamical theories of collective excitations to describe the influence of particle-vibration coupling on the excitation energies of giant resonances. This yields dynamical corrections to the energies calculated in the random-phase approximation (RPA). The existing dynamical theories can be characterized by the effective particle-hole gap which they prescribe for RPA-type calculations of collective excitations. We investigate three dynamical theories in the framework of a schematic model for the nucleon self-energy. In the case of the giant dipole resonance in ²⁰⁸Pb, the microscopic dynamical model prescribes an effective p-h gap which is smaller than the experimental value; in contradistinction, the effective p-h gap is larger than the experimental value in the case of the isoscalar octupole surface vibration. These dynamical corrections are opposite to the corrections predicted by two other models which have been proposed. The origin of these differences is discussed.     

Semiclassical description of isoscalar giant multipole resonances

The scaling approximation in a semiclassical theory of nuclear collective motions based on the Vlasov equation is applied to the study of isoscalar giant resonances. Analytic forms are obtained for the frequencies of any multipolarity, expressed just in terms of local density distributions, using realistic nuclear effective forces. The importance of non local interactions and diffuse surfaces is clearly shown. The limits of the scaling picture in describing high multipolarity resonances are finally discussed.     

Role of the nuclear surface in a unified description of the damping of single-particle states and giant resonances

The damping widths of single-particle states and of giant resonances are estimated in spherical nuclei, based on the excitation of surface modes.A Skyrme III interaction with an effective mass consistent with that resulting from infinite nuclear matter calculations with “realistic” forces $\text{(m}{}^1\text{/m = 0.76)}$, was utilized. The single-particle basis needed to construct the unperturbed nuclear response function for each multipolarity was obtained, treating this force in the Hartree-Fock approximation. Diagonalizing a schematic interaction in this basis, the surface modes were calculated. They are used to dress the single-particle and single-hole states and to renormalize the vertex interaction, taking into account the proper energy dependence of the couplings.The essential new feature of the present calculation as compared to the calculations reported in ref.¹) is that the energy dependence of the real and imaginary part of the self-energy is taken into account. This is done utilizing a strength function model.About 70 % of the damping widths arise from the coupling to specific intermediate states containing one low-lying collective surface vibration. The rest, from the coupling to many nonspecific states.Qualitative agreement is found with the experimental data for spherical nuclei throughout the mass table for both the single-particle states and the giant resonances. The model seems however to predict widths which are smaller than those experimentally observed.     

Collective potentials and dipole and quadrupole giant resonances

The dynamic collective model is extended into the energy region immediately above the giant dipole resonances, i.e. into an energy region between 20 and 28 MeV. The total Hamiltonian is constructed and the dynamical problem is solved by diagonalizing the Hamiltonian in the basis of a five-dimensional harmonic oscillator. In schematical studies the splitting of giant quadrupole resonances is shown. For some elements the potential energy surfaces (PES) are constructed within the collective model developed by Gneuss et al. and the quadrupole resonances have been calculated in the framework of the dynamic collective model. In the last part the agreement with experimental data is shown.     

Life time of soft multipole excitations

Decay of soft multipole excitations in halo nuclei is studied in comparison with the potential resonance state. Although the soft excitation has a sharp peak just above the particle threshold and carries extremely large transition strength, the decay rate looks much faster than that expected for a resonance state. Consequently, the half life is shown to be several orders of magnitude shorter than what one naively expects from the uncertainty principle. It is shown also that the soft excitations accumulate large transition strength as a non-resonant single-particle excitation, but not as particle-hole collective excitations like giant resonances.     

Microscopic description of giant resonances in highly excited nuclei

Giant resonances of general multipolarity in highly excited nuclei, which are produced in compound nuclear and deep inelastic heavy ion reactions, are described microscopically in the finite temperature linear response formalism. The linear response function is calculated in the finite temperature (FT) quasi-particle RPA approximation (FT-HFB-RPA) and is based on the corresponding self-consistent quasi-particle basis (FT-HFB). The theory is derived from the small amplitude limit of FT-TDHFB. The inclusion of cranking constraints allows the investigation of giant resonances in nuclei with large intrinsic excitation energy and high spin. A schematic model for the FT-HFB-RPA is developed and applied to the isovector giant dipole resonance in hot spherical nuclei. It is shown that the energy of the resonance depends only weakly on temperature in these systems. The experimentally observed lowering of the giant mode in highly excited nuclei is to be attributed to different effects. The descritpion of resonance damping lies beyond the scope of the random phase approximation. Possible extensions in this direction and qualitative features of the width of giant resonances at finite temperature are discussed.     

Particle-hole optical model and strength functions for high-energy giant resonances

A formulation of the particle-hole optical model is proposed for describing the contribution of the fragmentation effect to the formation of strength functions for high-energy giant resonances. The model is based on the Bethe-Goldstone equation for the energy-averaged particle-hole Green’s function. In this equation, the particle-hole interaction that is induced by a virtual excitation of multiquasiparticle configurations and in which, upon averaging over energy, an imaginary part is contained is taken into account. An analogy with the single-quasiparticle optical model is discussed.     

Nuclear effective interactions and spin excitations

In view of the one-boson-exchange model for the nucleon-nucleon interaction and the Hartree-Fock (HF) interaction, we formulate the effective interactions for particle-hole states in terms of the exchange of the fields which are confined in the nucleus. This theory, as an extension to the nuclear field theory (NFT), takes into account the propagation of the fields which is neglected in NFT. The effective interactions thus obtained reproduce the energies of a sequence of electric giant resonances and the core polarizabilities associated with the resonances. It is found that the coupling constants of the σ- and ω-fields are suppressed for the particle-hole interaction by 60% with respect to the HF interaction. As for the effective interactions involving nucleon spins, we consider the fields coupled to nucleon spins. The effective interactions obtained, essentially different from those in NFT, have a tensor component. We analyse the energies and cross sections for excitation of stretched spin particle-hole states which are the most sensitive to the tensor force. The effective interaction responsible for the stretched spin states is shown to be consistent with that for the magnetic resonances observed in the (p, n) reactions.     

Phase transition from deformed to γ-instable Os isotopes and the structure of the giant resonances

The collective potential energy surfaces and kinetic energies are constructed empirically by using the experimental low energy spectra for the Os isotopes. Giant dipole resonances and photon scattering are calculated within the DCM based in the so-obtained collective Hamiltonian. The potential energy surfaces show a phase transition from prolately deformed (Os) to γ-instable (Os) nuclei. This is also reflected in the structure of the giant resonances.     

Muonic atoms in the neighbourhood of lead

In a previous paper the electroexcitation of various giant multipole resonances in heavy nuclei has been discussed in Born approximation. This has given only the qualitative features of the cross section, since the electron wave functions in heavy nuclei are considerably distorted by the nuclear charge. Therefore we derive in this paper the corresponding cross sections using a phase shift analysis for the electron wave functions. Moreover, the coupling between giant resonances and surface oscillations has been taken into account. This leads to transitions not only to the several giant resonances itself but also to their “satellites” (i.e. giant resonance plus surface oscillations). Since the giant resonances have rather large widths, the calculated differential cross sections have been folded using a Lorentz shape and plotted against excitation energy. It is shown that the quadrupole giant resonance levels should be observed very clearly at scattering angles of the electron of about 40° (primary energy of the electrons about 200 MeV). It seems, however, unlikely to observe the monopole giant resonance as a distinct peak of the electron cross section because of the relatively large damping to be expected.     

On an intermediate structure of giant analog resonances in medium and heavy nuclei

The effect of coupling of the usual particle-hole states to particle-hole states built above a collective state on the decay characteristics and structure of a giant resonance with higher isospin (T _>) has been estimated. Numerical calculations are carried out for⁶⁰Ni,⁹⁰Zr and²⁰⁸Pb.     

Excitation of isovector giant resonances by inelastic scattering of positive pions on90Zr at 226 MeV

We studied the region of giant resonances with positive pions of 226 MeV scattered inelastically on⁹⁰Zr. Two groups of resonances were seen: the first structure between 12 and 19 MeV excitation energy is explained as a sum of the isoscalar quadrupole resonance at 14 MeV, the isovector dipole resonance at 16.5 MeV and possibly some E₀ strength. The second group between 24 and 34 MeV excitation energy also corresponds to more than a simple multipolarity and may be described as a sum of a monopole and a quadrupole isovector resonance.     

Nonlinear dynamics of giant resonances in atomic nuclei

The dynamics of monopole giant resonances in nuclei is analyzed in the time-dependent relativistic mean-field model. The phase spaces of isoscalar and isovector collective oscillations are reconstructed from the time series of dynamical variables that characterize the proton and neutron density distributions. The analysis of the resulting recurrence plots and correlation dimensions indicates regular motion for the isoscalar mode, and chaotic dynamics for the isovector oscillations. Information-theoretic functionals identify and quantify the nonlinear dynamics of giant resonances in quantum systems that have spatial as well as temporal structure.     

Pion electroproduction from nuclei near threshold

The electroproduction of low energy pions is calculated for experimental situations corresponding to the detection of only one of the outgoing particles. The final nuclear state is a superposition of particle-hole states, corresponding to the giant resonances. A comparison with the predictions of the Fermi gas model is made. The effect of final state interactions was included by using a distorted wave impulse approximation to describe electroproduction from nuclei. Distortion effects near threshold have a significant effect on the magnitude of the electroproduction cross section.     

Giant resonances in90Zr and116Sn

The giant resonance region in⁹⁰Zr and¹¹⁶Sn excited by 270 MeV helions has been measured up to about 35 MeV excitation energy. The low and the high energy octupole resonances are seen prominently in addition to the quadrupole and the monopole resonances. The angular distribution data for the various multipoles are satisfactorily explained by the collective model calculations. The percentatge energy weighted sum rule strengths have been determined for all the prominent resonances.     

Scaling- and antiscaling-type oscillations in isoscalar and isovector nuclear monopole vibrations

Isoscalar (T = 0) and isovector (T = 1) giant monopole resonances are studied using a localscale version of the ATDHF theory developed on the basis of a rigorous energy-density functional approach. Due to the strong coupling between the bulk and surface density vibrations, the monopole collective motion is split into four normal modes. Two of them, lower in energy, correspond to scaling-type density vibrations. The other two are of antiscaling-type in which the nuclear surface oscillates opposite in phase to the scaling-type vibrations. Excitation energies, transition densities, T = 0 and T = 1 energy weighted sum rules and other properties of breathing even-even nuclei are calculated using different Skyrme-type effective forces. The strong sensitivity of the antiscaling-type vibrations to the particular form of the approximate energy-density functionals is demonstrated.