Statistical tests applied to proton resonances in57Co

Abstract

Statistical tests are applied to a sequence of 1/2 + resonances observed in 56Fe(p,p) and the results are compared with predictions of the random matrix model. The target nucleus and proton energy were chosen to yield favorable level densities, strength functions, and Coulomb penetrabilities. In addition, the TUNL high resolution system provides excellent sensitivity to small resonances. These points combine to yield a fairly pure and complete sequence, as indicated by the Dyson F statistic and the Dyson-Mehta A 3 statistic. Good agreement is found with the orthogonal ensemble predictions for the long and short range spacing correlations, and for the widths of the k-th nearest neighbor spacing distributions for k=0 to 10.

Random matrices and chaos in nuclear physics: Nuclear structure

“…Thus the proton resonance data complement the neutron resonance data; the best results for each set are obtained in quite different mass regions. Almost all of the data used to compare with RMT are for spin-zero targets and from the Triangle Universities Nuclear Laboratory (TUNL) (Wilson et al, 1975;Watson et al, 1981).…”

Statistics of 2+ levels in even–even nuclei

“…The interest in such a study derives from the success of random-matrix theory (RMT) in describing the spectral properties of nuclear levels (actually: resonances) near neutron threshold and proton threshold [2,3]. Careful analysis has shown that the spectral fluctuation properties of these resonances are in very good agreement with the predictions of the Gaussian orthogonal ensemble (GOE) of random matrices.…”

REGULARITY AND CHAOS IN LOW–LYING 2+ STATES OF EVEN–EVEN NUCLEI

“…The evidence derives from the agreement between calculated and measured spectral properties. There is, on the other hand, equally strong evidence for the validity of a random-matrix description, especially from the spectral statistics of slow neutron resonances [1,2]. This success of random-matrix theory negates a dynamical description in terms of simple and (nearly) integrable models and has raised the question: Where in the spectrum of a nucleus with mass number A does the chaotic region start?…”