Giant dipole resonance

Nuclear science in particular obtains from laser-driven electron sources a brand new input to perform interesting measurements in the context of many laboratories equipped with ultrashort powerful lasers. The ultrashort duration of these particle bunches represent a further attractive feature for these kinds of studies. In the following, we will focus on nuclear reaction induced by gamma radiation produced by bremsstrahlung of laser-produced electrons in suitable radiator targets. This way is usually mentioned as photo-activation and is particularly efficient for photons of energy close to the Giant Dipole Resonance of many nuclei. 

Giant dipole resonance. Isovector giant resonances contain information about the SE through the restoring force. In particular the excitation of the isovector giant dipole resonance (GDR) with isoscalar probes has been used to extract A R/R [32], In the distorted wave Bom approximation optical model analysis of the cross section the neutron and proton transition densities are needed as an input. For example, in the Goldhaber-Teller picture these are... 

In the 1950s, many basic nuclear properties and phenomena were qualitatively understood in terms of single-particle and/or collective degrees of freedom. A hot topic was the study of collective excitations of nuclei such as giant dipole resonance or shape vibrations, and the state-of-the-art method was the nuclear shell model plus random phase approximation (RPA). With improved experimental precision and theoretical ambitions in the 1960s, the nuclear many-body problem was born. The importance of the ground-state correlations for the transition amplitudes to excited states was recognized. 

This bump is called the giant dipole resonance (GDR). Goldhaber and Teller (1948) provided a model for this reaction in which the giant dipole resonance is... 

The organisation of the present chapter is as follows first, we describe different kinds of clusters which can be formed and the shapes which are commonly found. Next, we give an example of how clusters can be used to bridge the gap from the atom to the solid and, finally, we discuss the subject of giant dipole resonances in clusters. 

The shell model for metal clusters, described above, has an important implication which will not have escaped the reader if electrons become delocalised from individual atoms and can roam freely over the whole cluster to form a closed shell, then this shell should be able to oscillate collectively, and should therefore exhibit giant dipole resonances analogous to those which were described in chapter 5 for free atoms. 

The second, and more important kind is the giant dipole resonance intrinsic to the delocalised closed shell of a metallic cluster. Such resonances have received a great deal of attention [684]. They occur at energies typically around 2-3 eV for alkali atoms, and have all the features characteristic of collective resonances. In particular, they exhaust the oscillator strength sum rule, and dominate the spectrum locally. 

Fig. 12.15. Example of a giant dipole resonance in a metal cluster with a closed shell, in this case a singly ionised K cluster with eight delocalised electrons (after C. Brechignac and J.-P. Connerade [714]).

Clusters also demonstrate the ubiquity and generality of the basic principles of physics the stability of metal clusters is governed by a shell closure closely related to that of nuclear physics. Indeed, the collective, giant dipole resonances in clusters and in nuclei obey the same laws over changes of fourteen decades in scale size. 

Calculated cross sections for Coulomb excitation of °S in the first excited state (2, the giant dipole resonance (GDR), and the giant quadrupole resonance (GQR) in s using a °S beam incident on Au, versus the beam energy. The calculation assumes a minimum impact parameter of 16 fm (From Glasmacher 1998)... 

The first depletion spectra obtained for neutral sodium clusters N = 2-40 were characterized by structureless broad features containing one or two bands. The results were interpreted in terms of collective resonances of valence electrons (plasmons) for all clusters larger than tetramers [2, 52-55]. The analogies between findings for metallic clusters and observations of giant dipole resonances in nuclei have attracted a large attention. Therefore the methods employed in nuclear physics, such as different versions of RPA in connection with the jellium model, have also been applied for studying the optical properties of small clusters. Another aspect was the onset of conductivity in metal-insulator transitions. 

In a next step, we compare nuclear and cluster response in the generic case of Coulomb excitation, as modeled by an initial shift of the electrons (respectively neutrons) with respect to ions (respectively protons). We first consider the nuclear giant dipole resonance. The lower panel of Figure 7.9 shows the power spectrum of the dipole along the z axis (symmetry axis) of after Coulomb excitation for several amplitudes with average excitation energies as indicated. The small-amplitude case represents the nuclear excitation spectrum in the linear regime as it is known from nuclear RPA calculations. We... 

It has been deduced that the effective cross-section in the interval of giant dipole resonance is expressed by equation... 

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