Decay theory of double giant resonances

Abstract

The decay theory of double giant resonances incorporating fluctuation contributions of the BrinkAxel type is developed. The γ and neutron emission decay of Double Giant Dipole Resonances (DGDR) in 208 Pb is discussed in connection with a recent measurement. * Supported in part by FAPESP. * * Supported in part by CNPq.Recently, the decay properties of the double giant dipole resonance (DGDR) in several nuclei has been investigated experimentally in Coulomb excitation reactions at high energies [1]. In particular, the neutron-and γ-decay channels were looked at in Ref. [2]. In analysing the data, the authors rely on a model for the formation of the DGDR that involves the sequential excitation of the two phonon state through the one phonon state. Although it is concluded that the decay of the two phonons seem to follow the harmonic model (namely the two phonons decay independently from each other), we believe that a component essential to the analysis is missing, since the integrated cross sections obtained from the decay data deviate appreciably from the harmonic coupled channel calculations. The purpose of this paper is to develop a new model for the decay of the DGDR using the recently developed Direct + Fluctuation (DF) model of Ref. [3,4] which reproduces the cross section value. We first give a brief description of the DF model. It is argued in Ref. [3] that besides the, direct, g.s. → one-phonon → two-phonon transition, there is another contribution that arises from the coupling of the one-phonon state to the complex background states followed by the excitation of a Brink-Axel phonon.[5] The general structure of the two-step amplitude iswhere G i is the propagator in the region of the GDR, d and b are projectors for the one phonon collective states and for the background states responsible for the damping of the collective states respectively. In writing Eq. (1) it is being assumed that the interaction V i0 , when acting on the initial state, will not excite the background states appreciably. These states will however be reached through the damping mechanisms present in G i , and will thus participate actively in the second step. We next think of the propagator G i as split into a sum of average parts which are essentially diagonal in the subspaces b and d,Ḡ b andḠ d (with complex Q-value), plus an additional fluctuation part with zero average. Thusand the transition amplitude is similarly split as and the average cross section becomesσ

SU(2,1) Model of Multiple Giant Dipole Resonance Coulomb Excitation

“…At low enough bombarding energies, the enhancement factor drops as the bombarding energy grows. This is consistent with the data and gives results similar to those recently obtained in a different context, with a theory based on the concept of fluctuations (damping) and the Brink-Axel mechanism [11], [12]. The interesting property of the full threedimensional results obtained here is that the enhancement factor starts growing again at high bombarding energies (∼ 0.3−0.5GeV• A for heavy colliding nuclei.)…”

“…Validity of this completely linear theory has been questioned by nearly all the experimental data wherever multi-phonon GR has been observed [2]: the double Giant Dipole Resonance (GDR) excitation cross sections [8] are found about 1.3 − 2 bigger than follows from theory. This shortcoming of the linear theory, known as "enhancement factor problem", has been addressed widely in current literature within a number of approaches: higher order perturbation theory [9], anharmonic effects [7], [10], concept of hot phonons [11][12][13].…”

Multiple giant resonances in nuclei: their excitation and decay

“…We first remind the reader of the hybrid direct+fluctuation decay model of DHA [5]. According to this model, which has been extensively used in the analysis of decay data [21,22], the GR decays to a find channel f in the following manner:…”

Microscopic studies of two-phonon giant resonances

“…These works indicate that the Brink-Axel mechanism should play an important role, being able to explain, in part, some discrepancies between theory and experimental cross sections. Further work along these lines were published by, Hussein and collaborators [80,81,82]. In a recent publication [83], the influence of the isospin structure of the double giant resonance was studied in details.…”