Theory of multiphonon excitation in heavy-ion collisions.

Abstract

We study the effects of channel coupling in the excitation dynamics of giant resonances in relativistic heavy ions collisions. For this purpose, we use a semiclassical approximation to the coupled-channels problem and separate the Coulomb and the nuclear parts of the coupling into their main multipole components. In order to assess the importance of multistep processes, we neglect the resonance widths and solve the set of coupled equations exactly. Finite widths are then considered. In this case, we handle the coupling of the ground state with the dominant giant dipole resonance exactly and study the excitation of the remaining resonances within the coupled-channels Born approximation. A comparison with recent experimental data is made. Relativistic Coulomb excitation ~RCE! is a well established tool to unravel interesting aspects of nuclear structure @1#. Examples are the studies of multiphonon resonances in the SIS accelerator at the GSI facility, in Darmstadt, Germany @2,3#. Important properties of nuclei far from stability @4# have also been studied with this method. The RCE induced by large-Z projectiles and/or targets, often yields large cross sections in grazing colisions. This results from the large nuclear response ~in the region of the giant resonances! to the acting electromagnetic fields. As a consequence, a strong coupling between the excited states is expected This coupling might be responsible for the large discrepancies between experimental data of RCE and the calculations based on first-order perturbation theory @1‐3#, or the harmonic oscillator model. In the present paper, we apply a semiclassical method @5# to the coupled-channels ~CC! problem and study RCE in several collisions between heavy ions. In this method, the projectile-target relative motion is approximated by a classical trajectory and the excitation of the giant resonances is treated quantum mechanically @6,7#. The use of this method is justified due to the small wavelengths associated with the relative motion. In Sec. II, we neglect the resonance widths and introduce the semiclassical CC equations for relativistic Coulomb excitation. The time-dependent matrix elements of the main multipole components of the Coulomb ~Sec. II A! and nuclear ~Sec. II B! parts of the coupling interaction are calculated. The CC equations are then solved in some limiting cases. Section III is devoted to the excitation of resonances of finite widths. Generalizing the schematic treatment of Ref. @6#, we present an ‘‘exact’’ solution for the coupling between the ground state ~g.s.! and the dominant GDR. The excitation of the weaker resonances are then evaluated through the coupled-channels Born approximation ~CCBA!, from the g.s. and GDR amplitudes. In Sec. IV we apply the results of the previous sections to specific cases and make a comparison with recent experimental data. Finally, in Sec. V, we summarize our results and present the conclusions of this work.