Upper limit on a time reversal noninvariant part of Wigner's random matrix model

Abstract

The results of a Monte Carlo investigation and comparison with experimental data of Wigner's random matrix model with differing amounts of a time reversal noninvariant part are presented. With Hij=Rij+iyIij, calculations were performed with y=0.00,0.05,0.10,0.20,0.50,and1.00 using 40×40 matrices and y=0.00,0.05,and0.10 with 80×80 matrices. After unfolding the density variation of the eigenvalues the behavior of the Dyson-Mehta Δ3 statistic was examined for different values of y. The behavior of the reduced widths, which has also been examined in a previous calculation by Rosenzweig, Monahan, and Mehta, was found to be considerably more sensitive to small y values than the Δ3 statistic. Thus the reduced width data can place a much lower limit on y than the level spacing information. A comparison of the calculations performed here with recently collected high quality neutron resonance data gives y<0.05 at the 99.7% confidence level. It is also shown that the same value of the Dyson-Mehta Δ3 statistic results when the matrix elements of Wigner's model are chosen from a Gaussian or flat distribution.