Nonlinear Enhancement of the Multiphonon Coulomb Excitation in Relativistic Heavy Ion Collisions

Physical Review C (Impact Factor: 3.88). 08/1998; DOI: 10.1103/PhysRevC.59.R1242
Source: arXiv

ABSTRACT We propose a soluble model to incorporate the nonlinear effects in the transition probabilities of the multiphonon Giant Dipole Resonances based on the SU(1,1) algebra. Analytical expressions for the multi-phonon transition probabilities are derived. Enhancement of the Double Giant Resonance excitation probabilities in relativistic ion collisions scales as $(2 k +1)(2k)^{-1}$ for the degree of nonlinearity $(2k)^{-1}$ and is able to reach values $1.5-2$ compatible with experimental data. The enhancement factor is found to decrease with increasing bombarding energy. [KEYWORDS: Relativistic Heavy Ion Collisions,Double Giant Resonance] Comment: 12 pages, 2 figures

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Moving highly-charged ions carry strong electromagnetic fields that act as a beam of photons. In collisions at large impact parameters, hadronic interac-tions are not possible, and the ions interact through photon-ion and photon-photon collisions known as ultra-peripheral collisions (UPCs). Hadron colliders like the Rel-ativistic Heavy Ion Collider (RHIC), the Tevatron, and the Large Hadron Collider (LHC) produce photonuclear and two-photon interactions at luminosities and energies beyond that accessible elsewhere; the LHC will reach a γ p energy ten times that of the Hadron-Electron Ring Accelerator (HERA). Reactions as diverse as the production of anti-hydrogen, photoproduction of the ρ 0 , transmutation of lead into bismuth, and excitation of collective nuclear resonances have already been studied. At the LHC, UPCs can study many types of new physics processes.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We construct a three-dimensional analytically soluble model of the nonlinear effects in Coulomb excitation of multiphonon Giant Dipole Resonances (GDR) based on the SU(2,1) algebra^1. Analytical expressions for the multi-phonon transition probabilities are derived. For reasonably small magnitude of nonlinearity x~= 0.15-0.3, the enhancement factor for the Double Giant Resonance excitation probabilities and the cross sections reaches values 1.3-2 compatible^1,2 with experimental data from relativistic ion collision experiments^3. The full 3-dimensional model predicts enhancement of the multiple GDR cross sections at low and high bombarding energies (with the minimum at ~= 1.3 GeV for the Pb+Pb colliding system). Enhancement factors for Double GDR measured in thirteen different processes with various projectiles and targets at different bombarding energies are well reproduced with the same value of the nonlinearity parameter with the exception of the anomalous case of ^136Xe which requires a larger value. The work has been supported by the FAPESP and by the CNPq. References ^1 M. S. Hussein, A. F. R. de Toledo Piza and O. K.Vorov, Ann. Phys. (N.Y.), 2000, to appear. ^2 M. S. Hussein, A. F. R. de Toledo Piza and O. K.Vorov, Phys. Rev. C59,R1242 (1999). ^3 T. Aumann, P.F. Bortignon, and H. Emling, Annu. Rev. Nucl. Part. Sci. 48, 351 (1998).
    Annals of Physics 08/2000; 284(1). DOI:10.1006/aphy.2000.6066 · 3.07 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We implement the Brink–Axel hypothesis for the excitation of the double giant dipole resonance (DGDR): the background states which couple to the one-phonon giant dipole resonance are themselves capable of dipole absorption. These states (and the ones which couple to the two-phonon resonance) are described in terms of the gaussian orthogonal ensemble of random matrices. We use second-order time-dependent perturbation theory and calculate analytically the ensemble-averaged cross section for excitation of the DGDR. Numerical calculations illuminate the mechanism and the dependence of the cross section on the various parameters of the theory, and are specifically performed for the reaction 208Pb+208Pb at a projectile energy of 640 MeV/nucleon. We show that the contribution of the background states to the excitation of the DGDR is significant. We find that the width of the DGDR, the energy-integrated cross section and the ratio of this quantity over the energy-integrated cross section for the single giant dipole resonance, all agree with experiment within experimental errors. We compare our approach with that of Carlson et al. who have used a similar physical picture.
    10/2000; 690(4-690):382-408. DOI:10.1016/S0375-9474(01)00356-6


Available from