Resonance giants

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... 

We note that also other types of isovector giant resonances have been suggested as a source of information on the neutron skin, such as the spin-dipole giant resonance [33] and the isobaric analog state [34], At present studies of these reactions have not led to quantitative constraints for the neutron skin of... 

A giant dipolar resonance (GDR) exists in the majority of photoabsorption and photonuclear reactions. This resonance energy corresponds to the fundamental frequency for absorption of electric dipole radiation by the nucleus acting as a whole. It can be envisioned as an oscillation of neutrons against the protons in a nucleus. The GDR occurs at energies of 20-24 MeV in light material and of 13-15 MeV in heavy nuclei. A compendium of the GDR parameters is found in Ref [3]. 

The chances of such three-body colhsions are very slight because the mediating Be is so ephemeral. This guarantees the red giant phase an enviable longevity of several million years even this collision probabihty is amplified by a perfectly chance resonance, to which we shall return shortly. 

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. 

Fig. 15. Angle-integrated photoelectron energy distribution curves of uranium in the region of the giant 5 d -> 5 f resonance (90 eV < hv < 108 eV). The 5 f intensity at Ep is suppressed by more than a factor of 30 at the 5 ds/2 threshold (see the spectra for hv = 92 and 94 eV) and resonantly enhanced above threshold (see, e.g., the spectrum for hv = 99 e V). At an initial energy 2.3eV below Ep a new satellite structure is observed which is resonantly enhanced at the 5 d5/2 and 5 ds onsets. At threshold the satellite coincides with the Auger electron spectrum, which moves to apparently larger initial energies with increasing photon energy (from Ref. 67)...

In atomic nuclei, SRPA was derived [9,10,19] for the demanding Skyrme functional involving a variety of densities and currents (see [20] for the recent review on Skyrme forces). SRPA calculations for isoscalar and isovector giant resonances (nuclear counterparts of electronic plasmons) in doubly magic nuclei demonstrated high accuracy of the method [10]. 

In study of response of a system to external fields, we are usually interested in the average strength function instead of the responses of particular RPA states. For example, giant resonances in heavy nuclei are formed by thousands of RPA states whose contributions in any case cannot be distinguished experimentally. In this case, it is reasonable to consider the averaged response described by the strength function. Besides, the calculation of the strength function is usually much easier. 

Relative contributions of T-odd densities to a given mode should obviously depend on the character of this mode. Electric multipole excitations (plasmons in atomic clusters, E giant resonances in atomic nuclei) are mainly provided by T-even densities (see e.g. [19]). Instead, T-odd densities and currents might be important for magnetic modes and maybe some exotic (toroidal,. ..) electric modes. 

Vp(fO is peaked at the surface. Many collective oscillations manifest themselves as predominantly surface modes. As a result, already one separable term generating by (74) usually delivers a quite good description of collective excitations like plasmons in atomic clusters and giant resonances in atomic nuclei. The detailed distributions depends on a subtle interplay of surface and volume vibrations. This can be resolved by taking into account the nuclear interior. For this aim, the radial parts with larger powers and spherical Bessel functions can be used, much similar as in the local RPA [24]. This results in the shift of the maxima of the operators (If), (12) and (65) to the interior. Exploring different conceivable combinations, one may found a most efficient set of the initial operators. 

For the description of giant resonances in atomic nuclei, we used the set of initial operators [10]... 

The sets (75)-(77) are optimal for description of electric collective modes EX plasmons in clusters and giant resonances in nuclei). For description of magnetic modes, the initial operator should resemble the T-odd magnetic external field. So, in this case we should start from the initial operators... 

Figure 2. Isoscalar E2 and isovector El giant resonances in calculated with SkM forces. The results are exhibited for fuU (exact) RPA (sohd curve) and SRPA with k = 1 (dotted curve).

The particular SRPA versions for electronic Kohn-Sham and nuclear Skyrme functional were considered and examples of the calculations for the dipole plasmon in atomic clusters and giant resonances in atomic nuclei were presented. SRPA was compared with alternative methods, in particular with EOM-CC. It would be interesting to combine advantages of SRPA and couled-cluster approach in one powerful method. 

Fig. 7. Experimental arrangement of a giant-pulse laser (Q-switching by dye solution). AM, active material (e.g. ruby crystal rod), F, flashlamp, Mj, 2, resonator mirrors, DC, dye cell...

The observations of the lithium resonance line at x6708.8 A were carried out with a SIT vidicon detector attached to the coudi spectrometer of the 1.5 m telescope of the Tartu Astrophysical Observatory. The sample of stars observed consists of 70 K0 - K5 and 75 MO - M4 giants. A set of spectra of K giants with different strengths of lithium resonance doublet is shown in Fig. 1. 

Fig. 1. A set of the spectra of K giants with different strength of the lithium resonance line. ...

Fig. 2. Frequency distribution of the lithium resonance line strengths in red giants. The number of observed stars is indicated in the brackets.

Fig. 5. High resolution spectra of U Cephei In the Mg II resonance doublet region at 2975 and 2802 A, at phase 0.58, during its active mass flow episode in 1986 (McCluskey et al. 1987). The maximum-velocity toward the observer is about 800 km/s. The flat bottom of the broad absorption feature indicates saturation but the absorption does not quite reach zero-flux level, suggesting only a partial covering of the surface of the B star by the plasma flowing out of the G giant.

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... 

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