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Evolution of the Giant Dipole Resonance Properties with Excitation Energy

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Evolution of the Giant Dipole Resonance Properties with Excitation Energy EPJ manuscript No. (will be inserted by the editor) Evolution of the Giant Dipole Resonance Properties with Excitation Energy D.Santonocito1 and Y.Blumenfeld2 1 INFN - Laboratorio Nazionale del Sud, Via S.Sofia 62, 95123, Catania, Italy 2 Institut de Physique Nucl´aire, IN2P3-CNRS, 91406 Orsay, France Received: date / Revised version: date Abstract. The studies of the evolution of the hot Giant Dipole Resonance (GDR) properties as a function of excitation energy are reviewed. The discussion will mainly focus on the A ∼ 100 − 120 mass region where a large amount of data concerning the width and the strength evolution with excitation energy are available. Models proposed to interpret the main features and trends of the experimental results will be presented and compared to the available data in order to extract a coherent scenario on the limits of the development of the collective motion in nuclei at high excitation energy. Experimental results on the GDR built in hot nuclei in the mass region A ∼ 60 − 70 will be also shown allowing to investigate the mass dependence of the main GDR features. The comparison between limiting temperatures for the collective motion and critical temperatures extracted from caloric curve studies will suggest a possible link between the disappearance of collective motion and the liquid-gas phase transition. PACS. 24.30.Cz, 25.70Ef GDR – 25.70Gh Hot Nuclei 1 Introduction teresting discrepancy between data and theoretical model at temperatures T ∼ 1 − 1.5 MeV which deserves further A well-established result of nuclear physics is the observa- investigation. tion of giant resonances, small amplitude, high frequency, collective modes of excitation in nuclei which are expected Conversely, populating nuclei at progressively higher to be chaotic systems due to their intrinsic complexity. thermal energies up to the limits of the their existence Among all possible modes of collective excitation, the Gi- one can follow the evolution of the collective motion in ant Dipole Resonance (GDR), a collective vibration of pro- extreme conditions up to its disappearance. The investi- tons against neutrons with a dipole spatial pattern, has gation of the GDR features at high excitation energy is been widely investigated and is now considered a general particularly interesting because it also opens up the pos- feature of all nuclei. sibility to investigate the limits of validity of the standard The experiments performed over many years have statistical scenario in describing the decay properties of shown that the GDR is an efficient tool to probe nuclear hot nuclei. The statistical model assumes, in fact, that properties of the ground state as well as at finite tem- the system reaches thermal equilibrium before it decays. perature. In fact, the gamma-ray emission following the Increasing the excitation energy, the compound nucleus GDR decay is sufficiently fast to compete with other de- lifetime decreases significantly and collective degrees of cay modes with a sizable branching ratio and therefore to freedom might not reach equilibrium before the system probe the characteristics of the nuclear system prevailing decays. Therefore the GDR strength distribution will re- at that time. The resonance energy being proportional flect the relative influence of the different time scales which to the inverse of the nuclear radius, the investigation of come into play, the population and decay time of the GDR the strength distribution gives access to the study of the on one hand and the equilibration and decay time of hot nuclear deformations in the ground state but also to the nuclei on the other. In the following the experimental re- shape evolution of nuclei as a function of spin and tem- sults collected up to E∗ ∼ 500 MeV will be presented and perature of the system. Shape evolution and shape fluc- compared to statistical model calculations. The evidence tuations are the main issues in the study of the GDR in in the gamma spectra of a vanishing of the GDR strength nuclei populated at low excitation energy (E∗ < 100 MeV) at high excitation energies relative to the standard statis- and spin up to the fission limit. This region has been ex- tical calculation led to the development of different theo- tensively studied and the GDR properties, which are ex- retical models whose main features will be discussed in the pected to be influenced by the shell effects, are rather well text. The comparison between data and statistical calcu- understood [1,2] even if some recent results indicate an in- lations including different model prescriptions will allow 2 D.Santonocito, Y.Blumenfeld: Evolution of the Giant Dipole Resonance Properties with Excitation Energy us to draw some conclusions concerning the effects lead- in terms of the Energy Weighted Sum Rule (EWSR) for ing to the GDR disappearance. Eventually, the existence dipole radiation. This sum rule, also known as Thomas- of a limiting temperature for the collective motion will be Reiche-Kuhn sum rule gives the total integrated cross sec- discussed and compared to the limiting temperature for tion for electric dipole photon absorption. It is given by: the existence of nuclei in different mass regions. This will 30 2 2 allow to investigate a link between the liquid gas phase 2π e ¯h NZ σabs(Eγ )dEγ = transition and the disappearance of collective motion. 0 Mc A NZ (3) 60 (MeV · mb) A 2 GDR built on the ground state: general where N, Z and A are respectively the neutron, the proton features and the mass number and M is the nucleon mass [6]. The systematics show that a large fraction of the EWSR is The GDR was first observed in 1947 by Baldwin and exhausted [6]. Kleiber in photo-absorption and photo-fission experiments [3,4]. They observed an increase of the absorption cross- section above 10 MeV in several nuclei with resonance 3 GDR built on excited states: historical energies between 16 and 30 MeV. The observed peak in the photo-absorption spectrum The field of the study of Giant Resonances built on excited was interpreted by Goldhaber and Teller [5] as the exci- states was launched by Brink [8] who stated the hypoth- tation of a collective nuclear vibration in which all the esis that Giant Resonances could be built on all nuclear protons in the nucleus move collectively against all the states and that their characteristics, aside from the depen- neutrons creating an electric dipole moment. Since then, dence on the shape, should not depend significantly on the the GDR has been extensively studied and broad system- nuclear state. This opened up the possibility of investigat- atics for almost all stable nuclei exist on the GDR built ing nuclear shapes also in excited nuclei and to study the on ground state. Most of the information was extracted evolution of the properties of collective motion up to the from photo-absorption experiments because of the high limits of existence of nuclei. Indeed the disappearance of selectivity of this reaction to E1 transitions [6]. collective motion has been considered a further signature The shape of the resonance in the photo-absorption for a phase transition in nuclear matter. spectrum can be approximated, in the case of a spherical Evidence in favor of the Brink hypothesis was extracted γ nucleus, by a single Lorentzian distribution [6,7]: for the first time in 1974, in the study of the -ray spec- trum emitted from spontaneous fission of 252Cf [9]. The 2 2 γ σ0Eγ ΓGDR enhancement observed in the spectrum above 10 MeV σabs(Eγ )= (1) was, in fact, correctly attributed to the de-excitation of (E2 − E2 )2 + E2Γ 2 γ GDR γ GDR the GDR built on excited states of the fission products. where σ0, EGDR and Γ are respectively the strength, the The first evidence for the existence of the GDR built on an centroid energy and the width of Giant Dipole Resonance. excited state using a reaction study emerged in a proton capture (p,γ) experiment on 11B where the GDR built on In nuclei with a static deformation the GDR splits in two 12 components corresponding to oscillations along and per- the first excited state of C was observed [10]. From sub- γ γ pendicular to the symmetry axis and the photo-absorption sequent (p, )and(n, ) experiments on various other light cross-section can be well reproduced by the superposition nuclei emerged a coherent picture supporting the Brink of two Lorentzian distributions. This particular feature al- hypothesis [11]. An important step further in the study lows one to extract the nuclear deformation from the cen- of the GDR properties was made with the use of heavy troid energies of the two components and to distinguish, ion reactions which opened up the possibility to populate from the relative intensities, prolate from oblate deforma- highly excited continuum states through the mechanism of tions. complete fusion in a wide variety of nuclei. The first obser- The systematics show that the resonance energy de- vation of the gamma-decay of the GDR built on highly ex- cited states in nuclei formed in fusion reaction was made in creases gradually with increasing mass number. This mass 40 82 110 dependence can be reproduced by [6]: 1981 studying Ar induced reactions on Se, Pd, and 124Sn targets [12]. The importance of these measurements −1/3 −1/6 EGDR =31.2A +20.6A (2) stems from the fact that they demonstrated the possibil- ity to study the GDR in the γ-ray de-excitation spectra which is a linear combination of the mass dependencies following fusion reactions where the statistical emission predicted by Goldhaber-Teller and Steinwedel-Jensen of high energy gamma-rays occurs from an equilibrated macroscopic models for the energy of the GDR [5,7] .
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