Single-Level Breit-Wigner Resonances


Earlier versions of the various evaluated data libraries made very heavy use of the Single-Level Breit-Wigner (SLBW) approach for the following reasons:
  • it is easy to implement,
  • it can use published resonance parameters,
  • it can be Doppler broadened analytically, and
  • it can be used analytically in reactor physics calculations.
However, it doesn't provide the best representation of the cross sections because of the neglect of multi-level and multi-channel effects--it can even produce unphysical negative cross sections for elastic scattering. Thus, some of the older files had corrections given as "File 3 backgrounds."

Here is an shortened example of the SLBW resonance parameters for Pu-238 from ENDF/B-VI: 

      9.423800+4 2.360045+2          0          0          1          09434 2151
      9.423800+4 1.000000+0          0          1          2          09434 2151
      1.000000-5 2.000000+2          1          1          0          09434 2151
      0.000000+0 9.309000-1          0          0          1          09434 2151
      2.360045+2 0.000000+0          0          0         96         169434 2151
     -1.000000+1 5.000000-1 6.217000-2 1.581000-2 4.500000-2 1.360000-39434 2151
     -4.000000-1 5.000000-1 4.670000-2 3.400000-4 4.500000-2 1.360000-39434 2151
      2.855000+0 5.000000-1 3.808600-2 7.470000-5 3.680000-2 1.211000-39434 2151
      9.975000+0 5.000000-1 3.721300-2 2.084000-4 3.024000-2 6.765000-39434 2151
      1.856000+1 5.000000-1 4.249000-2 3.490000-3 3.739000-2 1.610000-39434 2151
      5.980000+1 5.000000-1 3.930000-2 1.550000-3 3.480000-2 2.950000-39434 2151
      ...

The third line says that the resonance range extends from 1e-5 to 200 eV. The fourth line says that the target spin is 0 and the scattering length is .9309. This translates into a potential scattering cross section of 4πa2=10.89 barns. The parameters for 16 different resonances start on the sixth line: there is a negative-energy resonance at -10 eV with J=1/2, a total width of .06217 eV, a scattering width of .01581 eV, a capture width of .045 eV, and a fission width of .00136 eV. When these parameters are given to the RECONR module of the NJOY and Doppler broadened to 300K, the resulting cross sections are shown below:

Pu238

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12 December 2012 T-2 Nuclear Information Service ryxm@lanl.gov