Missing level corrections using neutron-resonance spacings

Gary E. Mitchell

North Carolina State University and Triangle Universities Nuclear Laboratory

John F. Shriner, Jr.

Tennessee Technological University

Overview

Neutron, and to a lesser extent proton, resonance data play an important role in the determination of nuclear level densities. Nuclear level densities are very important for a wide variety of pure and applied neutron physics. Most of the relevant information is obtained from neutron resonance data. A key factor to consider when using resonance data to determine level densities is the possibility of missing levels. All of the standard correction methods assume that the neutron resonances obey the predictions of the Gaussian Orthogonal Ensemble version of Random Matrix Theory (RMT) and utilize comparison with the Porter-Thomas distribution of reduced widths in order to determine the fraction of missing levels. Here we adopt an alternate approach, comparing the neutron data with the predictions of RMT for eigenvalue statistics. Since in RMT the widths and eigenvalues are independent, analysis of the eigenvalues provides an independent analysis of the same data set. We summarize recent work in this area using the nearest neighbour spacing distribution, and we also develop tests based on four different eigenvalue statistics (the nearest-neighbor spacing distribution, the Dyson-Mehta Delta 3 measure of long-range order, the internal energy, and a statistic related to the Q statistic originally proposed by Dyson and Mehta).

For those cases where one uses identified energy levels to determine an average spacing, any missing levels or spurious (i.e., misassigned) levels will cause an error in the measured value of the average spacing. Our previous report INDC(NDS)-0561 discussed methods to estimate the number of missing levels among a sequence of levels which share the same quantum numbers. The prototypical case to which these techniques can be applied is a set of L = 0 resonances of neutrons (or protons) on a target with spin zero. The compound nuclear states all then have angular momentum and parity Jpi = 1/2+. However, what is often true in studying neutron resonances is that while the orbital angular momentum L can be determined with reasonable certainly, to determine the angular momentum J is much more difficult and/or timeconsuming. For the case discussed above, s-wave resonances on spin-zero targets, there is no ambiguity. However, considering either resonances with a different value of Jpi or targets with spin greater than zero leads to more than one possible value of angular momentum for the compound nuclear states, and it is the general issue of estimating the number of missing levels in cases where J is less well determined than is L that we begin to examine here. Specifically we consider the case where two different J values are possible for a given value of L: this occurs for s-wave resonances on targets with spin greater than zero or for resonances with L not equal 0 on targets with spin zero. If the experimental values of J are well-determined, then one can apply our earlier techniques to each sequence of levels. (We use the term sequence to indicate a group of levels which share a complete set of quantum numbers). However, if J is not consistently determined with confidence, the techniques developed can be applied to the combined data (all levels without separation by J) to estimate the overall number of missing levels. Fortran codes implementing these tests are available for one and two spin sequences.

Developed RMT tests were applied to the s-wave neutron resonances in n + 238U and n + 232Th. The results for 238U are consistent with each other and raise some issues concerning data purity. For the 232Th all of the tests are in excellent agreement. The techniques were also applied to the known resonances in the n + 235U reaction; results from the new analysis (using the two spin code MF2) were consistent with the single-sequence analysis (using MF code) and produced an average spacing consistent with the value listed in the RIPL-3 database.

Implemented statistics are documented in published IAEA technical reports INDC(NDS)-0561 and INDC(NDS)-0598

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