Article

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

University of São Paulo, San Paulo, São Paulo, Brazil
Physical Review C (Impact Factor: 3.88). 08/1998; 59(3). 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

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    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).
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    10/2000; 690(4-690):382-408. DOI:10.1016/S0375-9474(01)00356-6
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