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Random matrices and chaos in nuclear physics: Nuclear reactions

G. E. Mitchell*, A. Richter†, and H. A. Weidenmüller‡

G. E. Mitchell*

  • North Carolina State University, Raleigh, North Carolina 27695, USA and Triangle Universities Nuclear Laboratory, Durham, North Carolina 27706, USA

A. Richter†

  • Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany and ECT*, Villa Tambosi, I-38123 Villazzano (Trento), Italy

H. A. Weidenmüller‡

  • Max-Planck-Institut für Kernphysik, D-69029 Heidelberg, Germany

  • *mitchell@tunl.duke.edu
  • †richter@ikp.tu-darmstadt.de
  • ‡Hans.Weidenmueller@mpi-hd.mpg.de
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Rev. Mod. Phys. 82, 2845 – Published 5 October, 2010

DOI: https://doi.org/10.1103/RevModPhys.82.2845

Abstract

The application of random-matrix theory (RMT) to compound-nucleus (CN) reactions is reviewed. An introduction into the basic concepts of nuclear scattering theory is followed by a survey of phenomenological approaches to CN scattering. The implementation of a random-matrix approach into scattering theory leads to a statistical theory of CN reactions. Since RMT applies generically to chaotic quantum systems, that theory is, at the same time, a generic theory of quantum chaotic scattering. It uses a minimum of input parameters (average S matrix and mean level spacing of the CN). Predictions of the theory are derived with the help of field-theoretical methods adapted from condensed-matter physics and compared with those of phenomenological approaches. Thorough tests of the theory are reviewed, as are applications in nuclear physics, with special attention given to violation of symmetries (isospin and parity) and time-reversal invariance.

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Rev. Mod. Phys. 82, 2845– Published 5 October, 2010

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