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 ${H}_{\mathrm{ij}}={R}_{\mathrm{ij}}+iy{I}_{\mathrm{ij}}$, calculations were performed with $y=0.00,0.05,0.10,0.20,0.50,\mathrm{and}1.00$ using 40\ifmmode\times\else\texttimes\fi{}40 matrices and $y=0.00,0.05,\mathrm{and}0.10$ with 80\ifmmode\times\else\texttimes\fi{}80 matrices. After unfolding the density variation of the eigenvalues the behavior of the Dyson-Mehta ${\ensuremath{\Delta}}_{3}$ 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 ${\ensuremath{\Delta}}_{3}$ 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 ${\ensuremath{\Delta}}_{3}$ statistic results when the matrix elements of Wigner's model are chosen from a Gaussian or flat distribution.NUCLEAR STRUCTURE Monte Carlo calculation, Wigner's random matrix model. Effect of time reversal violation on statistical behavior of resonances. Comparison with experimental data.