SAMMY, Multilevel R-Matrix Fits to Neutron and Charged-Particle Cross-Section Data Using Bayes' Equations

1 - Description of problem or function: The purpose of the code is to analyze time-of-flight cross section data in the resolved and unresolved resonance regions, where the incident particle is either a neutron or a charged particle (p, alpha, d,...). Energy-differential cross sections and angular-distribution data are treated, as are certain forms of energy-integrated data. In the resolved resonance region (RRR), theoretical cross sections are generated using the Reich-Moore approximation to R-matrix theory (and extensions thereof). Sophisticated models are used to describe the experimental situation: Data-reduction parameters (e.g. normalization, background, sample thickness) are included. Several options are available for both resolution and Doppler broadening, including a crystal-lattice model for Doppler broadening. Self-shielding and multiple-scattering correction options are available for analysis of capture cross sections. Multiple isotopes and impurities within a sample are handled accurately. Cross sections in the unresolved resonance region (URR) can also be analyzed using SAMMY. The capability was borrowed from Froehner's FITACS code; SAMMY modifications for the URR include more exact calculation of partial derivatives, normalization options for the experimental data, increased flexibility for input of experimental data, introduction of user-friendly input options. In both energy regions, values for resonance parameters and for data-related parameters (such as normalization, sample thickness, effective temperature, resolution parameters) are determined via fits to the experimental data using Bayes' method (see below). Final results may be reported in ENDF format for inclusion in the evaluated nuclear data files. The manner in which SAMMY 7 (released in 2006) differs from the previous version (SAMMY-M6) is itemized in Section I.A of the SAMMY users' manual. Details of the 7.0.1 update are documented in an errata SAMMY 7.0.1 Errata (http://www.ornl.gov/sci/nuclear_science_technology/nuclear_data/sammy/ErrataDetail.html). (See References in Section 10 below.). Please see the home page http://www.ornl.gov/sci/nuclear_science_technology/nuclear_data/ for the ORNL Nuclear Data Group and links from there to the SAMMY home page. 2 - Method of solution: Bayes' Theorem (generalized least squares) is used to find the 'best fit' values of parameters and the associated parameter covariance matrix. In the RRR, different data sets, or different energy ranges of the same data set, may be analyzed either simultaneously (though the implementation is somewhat awkward) or sequentially with results effectively equivalent to those which would be obtained via a simultaneous analysis, provided the output parameter values and covariance matrix from the first analysis are used as input to the second analysis. Also included are expeditious methods (the 'propagated uncertainty parameter' and 'implicit data covariance' procedures) of including the correct data covariance matrix within the fitting procedure. In the RRR, sequential analysis is the default mode though analyses can also be performed simultaneously. In the URR, the default mode is simultaneous analysis, though capability for sequential analyses is also available. 3 - Restrictions on the complexity of the problem: None noted