Missing Levels with Two Superimposed Sequences
J. F. Shriner, Gary E. Mitchell · 2011
Neutron, and to a lesser extent proton, resonance data play an important role in the determination of nuclear level densities.Those densities in turn have a variety of applications in both, pure and applied physics.A key factor to consider when using resonance data to determine level densities is the possibility of missing levels.Previously, we have studied how predictions of the Gaussian Orthogonal Ensemble (GOE) version of Random Matrix Theory (RMT) can be used to estimate the fraction of missing levels for a sequence of levels, a group of levels which share the same quantum numbers.Here we look at a related problem, how to estimate the number of missing levels when the data consist of two superimposed (and perhaps not well separated) sequences.We have developed tests based on four different eigenvalue statistics (the nearest-neighbor spacing distribution, the Dyson-Mehta Δ 3 measure of long-range order, the internal energy, and a statistic related to the Q statistic originally proposed by Dyson and Mehta).Fortran codes implementing these tests are available at http://www- nds.iaea.org/missing-levels/(see MF and MF2 codes).The techniques were applied to the known resonances in the n+ 235 U reaction; results from the new analysis were consistent with the single-sequence analysis and produced an average spacing consistent with the value listed in the RIPL-3 database.