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Giant Modes in Cold and Hot Nuclei

Since their discovery giant resonances have attracted much attention because of their fundamental nature. They provide insight into both the effective nucleon-nucleon interaction and other basic properties of nuclei, such as shape and compressibility. The giant monopole resonance (GMR) represents a compression oscillation, providing information about the compression modulus of infinite nuclear matter. While in heavy nuclei with A>100 the GMR has been consistently found with its full energy-weighted sum rule (EWSR), only a part of the EWSR could be identified in light-mass nuclei, probably due to the fragmentation of the resonance strength. If this turns out to be generally true, it will imply a much higher centroid energy for this resonance than expected both on the basis of extrapolations from the A>100 region and of the predictions of calculations with effective interactions and with coupling to the continuum and to doorway states taken into account. These questions form a very lively experimental programme. The isovector giant dipole resonance (GDR) can be excited in small angle inelastic scattering of isoscalar probes, e.g. 200 MeV $\alpha$-particles, via both the Coulomb and the nuclear interactions. The nuclear excitation matrix element is proportional to the neutron skin thickness, which occurs because of the different density distributions of protons and neutrons. In inverse kinematics, this offers a novel method of measuring the neutron skin thickness of unstable nuclei. Giant resonances represent collective oscillations of all the nucleons in a nucleus. Such oscillations occur also in spin-isospin space, where protons and neutrons with spin-up and spin-down may move out of phase $\Delta S$=1, $\Delta T$=1. We are dealing with spin-isospin excitations, which are governed by the spin-isospin dependent part of the nucleon-nucleon (N-N) interaction in the nuclear medium. The Gamov-Teller resonance (GT, $\Delta L$=0) has been well established in charge-exchange reactions. However, the mechanism responsible for the depletion of its strength has not been resolved satisfactorily as yet. Much less is known about the spin-flip $\Delta L$ = 1 (SDR) and higher $\Delta L$ resonances. The use of polarised beams can be of great help in sorting out information on the different SDR excitations, as well as for the identification and delineation of the isovector M1 and $\Delta L$=1 spin-flip modes in sd- and light fp-shell nuclei, which play a central role in the astrophysics context. The study of the microscopic structure of a giant resonance requires measurements of nuclear decay to final hole states since it is a coherent superposition of 1p-1h states. Such studies will benefit greatly from the new accelerators at Groningen and Catania and from a range of new neutron and charged particle detection systems. Giant Resonances can be understood as first oscillator quanta of the collective vibration. The recent discovery of the double GDR and GQR, the second oscillator quanta, has strengthened this picture, see figure . Rather different reaction mechanisms have been used to study multiphonon excitations: pion double-charge exchange, relativistic heavy-ion Coulomb scattering and medium-energy heavy-ion inelastic scattering. The existing data indicate that, to first order, these multiphonons can be thought of as consisting of independent phonons, although in several experiments the excitation cross section is about twice that implied by the independent phonon picture. If verified, this may point to small anharmonicities in the two-phonon structure or small non-linearities in the excitation process. A better theoretical understanding of the width and decay of the double GDR is still needed.  

Figure: Comparison of various experimental quantities X for the two-phonon giant dipole resonance in ²⁰⁸Pb with those obtained in the harmonic limit X^harm. Results are shown for the resonance energy E₀, width $\Gamma$, integrated cross section $\sigma$ (averaged over all targets), decay branching ratio T_2g/T_n and neutron decay probability T_n. In all cases, the harmonic values X^harm are obtained using the known values of the single GDR.

 

When the N/Z ratio differs appreciably from that in stable nuclei one expects exotic collective modes of excitation. This will be a very active area of research at the new radioactive beam facilities. Giant resonances can be built on any nuclear state. The study of their decay provides information on nuclear structure at very high temperature and angular momentum. So far only the GDR built on excited states has been studied; its characteristic $\gamma$-decay has been measured and the strength function extracted for many different reactions. This has provided information on how the nuclear shape evolves with temperature and angular momentum. A consistent picture emerges with a constant collisional damping width up to about 2 MeV per nucleon in excitation and a gradual weakening of the GDR strength above 3 MeV per nucleon. The explanation requires more refined measurements. In fusion-fission reactions the total $\gamma$-yield from the initial state to the scission point is a measure of the relative partial decay widths, $\Gamma_g/\Gamma_fiss$. Since $\gamma$-decay is mediated through the GDR, it can be used as an accurate clock to obtain the time evolution of the fission process. As for neutrons and charged particles, these studies have recently shown that the yield of pre-scission $\gamma$-rays is larger than expected on the basis of the Bohr-Wheeler description of the fission partial decay width, and could be explained by delaying the fission process through an increase in the viscosity of the nucleus. Evidence for a sharp onset of the nuclear viscosity as a function of the excitation energy has been reported for Th and Cf nuclei. A satisfactory theory is still lacking. Furthermore, on the theoretical side, it is worthwhile remembering that isospin restoration in highly excited compound nuclei, predicted over 30 years ago, and found in recent dedicated experiments, still lacks a quantitative description.