REFIT-2009: Multilevel Resonance Parameter Least Square Fit of Neutron Transmission, Capture, Fission & Self Indication Data.

**RELATED AND AUXILIARY PROGRAMS:**

A modified version of the Harwell computer library minimizing routine VA02A is used to obtain the best fit to the data by varying the required parameters and outputs the parameters at the minimum value of chi-squared. The modified library routine SV01AS outputs the uncertainties (one standard deviation) together with the correlation coefficients matrix. The source of these routines is present with the main source code.

RESCON-2009 converts ENDF format into REFIT format.

National Physical Laboratory, Middlesex United Kingdom, and Serco Dorset, United Kingdom, through the NEA Data Bank, Issy-les-Moulineaux, France.

Fortran 90 and Visual Basic 6.6a. IBM compatible computers under Windows XP (C775PCX8600).

REFIT carries out fits to measured neutron cross-section data by adjusting the nuclear parameters used in the multilevel R-matrix formalism as well as experimental parameters. The adjustment of the parameters is continued until the calculated transmission and/or reaction yields from neutron time of flight (TOF) measurements agree with the observed data within the limits of the measured uncertainties. In its present form it can perform simultaneous fits on up to 30 sets of measured data. The data sets can be of different types, refer to different target sample thickness, and refer to different sample isotopic composition. The types of measurement include transmission and the reaction types: capture, fission, scattering, and self-indication. The output gives details of the analysis and all the fitted parameters with their uncertainties. The code also outputs a new list of resonance parameters in ENDF6 format suitable for putting in an evaluation file.

The nuclear cross section for each nucleus is calculated from initial parameters using an R-matrix multilevel formalism. The cross section is then Doppler broadened using either an ideal gas model or Moxon’s simple Phonon Model, Meister’s Einstein Crystal Model, or Naberejnev’s Harmonic Crystal Model. Some of the parameters associated with the Doppler broadening can be adjusted in the fit, e.g. in the gas model the effective temperature. The transmission or reaction yield for a given sample is then calculated from the Doppler broadened cross sections, given abundances of the nuclei and the thickness of the sample in the neutron beam. In the case of reaction data, the calculated reaction yield includes the effects of a multiple collision of the neutrons in the sample and the detection of scattered neutrons. The theoretical curves are then folded with the resolution function which can be calculated from parameters that include the initial pulse width, the decay of neutrons leaving the source and moderator, etc. or from tabulated values. The nuclear parameters are the resonance energies, neutron widths, radiation widths, and effective nuclear interaction radii. Provision has also been made to fit experimental parameters such as zero delay, flight path length, background, normalization, resolution parameters etc. as well as the nuclear parameters.

The program in its present form is set up for a maximum of 30 different samples, 40 different isotopes with a total of only 8000 resonance parameters, 185 variables and a total of 10000 data points.

The running time is variable and case dependent. The test cases were run with the following elapsed time on the PC: copper test2 takes a few seconds; resium theoretical tests 1 and 2 take a few seconds and stop when measurement data are required; and the U238 test takes 2.5 hours.

IBM compatible personal computers, Windows OS.

Windows OS.

M. C. Moxon, T. C. Ware, and C. J. Dean, *REFIT-2009 A
Least-Square Fitting Program for Resonance Analysis of Neutron Transmission,
Capture, Fission and Scattering Data Users’ Guide for REFIT-2009-10*,
UKNSF(2010)P243 (April 2010).

The code package includes the Fortran source, PC executables, sample case input and output, and the referenced document.

September 2011.

**KEYWORDS**: NEUTRON; NEUTRON CROSS SECTION, R-MATRIX
THEORY, TRANSMISSION DATA, TRANSMISSION MATRIX