Semiclassical calculation of heavyion scattering in the chaotic regime
Abstract
The semiclassical approach has proven to be a most valuable tool for the construction of the scattering matrix and accurate evaluation of cross sections in a large variety of heavyion collision problems. In its familiar implementation, however, its use is restricted to what is now known as the 'regular regime', as it makes use of classical reaction functions that must be continuous and interpolable. In this paper we identify what version of the semiclassical formalisms may be especially suitable for extension into the chaotic regime that develops at energies close to the Coulomb barrier. We also show the crucial role of the absorptive part of the ionion potential to retain the usefulness of the semiclassical methods under conditions of irregularity.
 Authors:
 Departamento de Fisica Atomica, Molecular y Nuclear, Universidad de Sevilla, Apdo. 1065, E41080 Sevilla (Spain)
 Departamento de Fisica, Comision Nacional de Energia Atomica, Av. del Libertador 8250, Buenos Aires (Argentina)
 (B1653HIM), Villa Ballester (Argentina)
 Publication Date:
 OSTI Identifier:
 20995297
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. C, Nuclear Physics; Journal Volume: 75; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevC.75.054611; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; CHAOS THEORY; COULOMB FIELD; HEAVY ION REACTIONS; HEAVY IONS; IONION COLLISIONS; SCATTERING; SEMICLASSICAL APPROXIMATION
Citation Formats
Dasso, C. H., Gallardo, M. I., Saraceno, M., and Escuela de Ciencia y Tecnologia, Universidad Nacional de San Martin, Alem 3901. Semiclassical calculation of heavyion scattering in the chaotic regime. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVC.75.054611.
Dasso, C. H., Gallardo, M. I., Saraceno, M., & Escuela de Ciencia y Tecnologia, Universidad Nacional de San Martin, Alem 3901. Semiclassical calculation of heavyion scattering in the chaotic regime. United States. doi:10.1103/PHYSREVC.75.054611.
Dasso, C. H., Gallardo, M. I., Saraceno, M., and Escuela de Ciencia y Tecnologia, Universidad Nacional de San Martin, Alem 3901. Tue .
"Semiclassical calculation of heavyion scattering in the chaotic regime". United States.
doi:10.1103/PHYSREVC.75.054611.
@article{osti_20995297,
title = {Semiclassical calculation of heavyion scattering in the chaotic regime},
author = {Dasso, C. H. and Gallardo, M. I. and Saraceno, M. and Escuela de Ciencia y Tecnologia, Universidad Nacional de San Martin, Alem 3901},
abstractNote = {The semiclassical approach has proven to be a most valuable tool for the construction of the scattering matrix and accurate evaluation of cross sections in a large variety of heavyion collision problems. In its familiar implementation, however, its use is restricted to what is now known as the 'regular regime', as it makes use of classical reaction functions that must be continuous and interpolable. In this paper we identify what version of the semiclassical formalisms may be especially suitable for extension into the chaotic regime that develops at energies close to the Coulomb barrier. We also show the crucial role of the absorptive part of the ionion potential to retain the usefulness of the semiclassical methods under conditions of irregularity.},
doi = {10.1103/PHYSREVC.75.054611},
journal = {Physical Review. C, Nuclear Physics},
number = 5,
volume = 75,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}

Classical dynamics of heavyion scattering is investigated in the case of a collision between a supposed spherical nucleus, {sup 28}Si, and a deformed one, {sup 24}Mg, at energies above the Coulomb barrier. Evidence of regular and irregular motion is found. The chaotic behavior justifies the presence of Ericson's fluctuations observed for this reaction, while the presence of regular motion embedded in the chaotic region could be the crucial point to explain the nature of the observed isolated resonances, once the semiclassical theory is applied.

Semiclassical treatment of heavy ion elastic scattering
A generalized semiclassical treatment for the elastic scattering of heavy ions is developed in the presence of a complex optical potential. The scattering phase shift and its derivatives with respect to the impact parameter are calculated after extending the JWKBL approximation. The results are compared with experimental data for the elastic scattering of 160 from medium and heavy target nuclei and, a relation between the present treatment and that of the optical model and Regge pole analysis is established. (orig.) (GE) 
Accuracy of the semiclassical approximation for chaotic scattering
The semiclassical approximation for scattering probabilities is tested for a simple chaotic system consisting of a particle in one dimension scattering from a localized potential that varies periodically in time. Good agreement between semiclassical and exact quantum mechanical results is found even for relatively large de Broglie wavelengths. 
Stochastic versus semiclassical approach to quantum chaotic scattering
The authors explore the universal features of quantum scattering system for which the classical scattering is chaotic. They do so by comparing the semiclassical approach and the stochastic approach, exhibiting their mutual overlap and their individual limits of applicability. They investigate in particular predictions of both approaches for the average cross section, for the autocorrelation function of a pair of Smatrix elements, its Fourier transform, the Wigner time delay, and the distribution of the poles of the Smatrix in the complex energy plane. The relationship of both approaches with Dyson's circular ensemble of Smatrices is also exhibited. 
Statistics of time delay and scattering correlation functions in chaotic systems. II. Semiclassical approximation
We consider Smatrix correlation functions for a chaotic cavity having M open channels, in the absence of timereversal invariance. Relying on a semiclassical approximation, we compute the average over E of the quantities Tr[S{sup †}(E − ϵ) S(E + ϵ)]{sup n}, for general positive integer n. Our result is an infinite series in ϵ, whose coefficients are rational functions of M. From this, we extract moments of the time delay matrix Q = − iħS{sup †}dS/dE and check that the first 8 of them agree with the random matrix theory prediction from our previous paper [M. Novaes, J. Math. Phys.more »