Elastic Scattering Data

• First describe needed data ...
• Given differential cross section ,
  , define total cross section:

  

• And diffusion cross section:

  

• Using semi-classical calculations for
  (cf. Schultz), is finite.
• Still expect many small angle scatterings.
• Devise procedure to ensure efficiency.
  • Note: even more efficient procedures
    are being considered.

• First, write

  

• , ,
• N chosen large enough to satisfy accuracy.
• Must minimize error in
  accurate momentum transfer.
  • Integrate directly,
  • Equate with corresponding approx. form,
  • and C(E_r).
• Then, know RHS of

  

• Divide -space into K equal probability bins:

  

• Find the , such that

  

• To sample , interpolate a uniform
  random number into these bins.

• Essential data required for elastic scattering are:
  1. ,
  2. ,
  3. I^(1,0)(T_i,E₀) used to find and

     

  4. I^(1,1)(T_i,E₀) (ditto),
  5. I^(1,2)(T_i,E₀) (ditto),
  6. C(E_r), for k=1,n.
  • I^(l,n) are integrations over Maxwellian
    ion distribution (Reiter 1993):

    

  • where and .

• Storage and implementation
  • Same format as for all other reactions
    (netCDF files),
  • Note self-describing aspects
    1. Name of reaction,
    2. Number of dependent variables,
    3. Organization of data for each dep. var.
       (``table'' or ``fit''),
    4. Rank of each dep. var. (number
       of independent variables),
    5. Character name for each dependent
       and independent variable,
    6. Number of values of each
       independent variable (for tabular data),
    7. Data tables
       • Separate multidimensional array
         for each dep. var. (see below, however).

• At run time, read in reaction data files
  needed (and only those),
• All and data stored in one large array,
  • For computing 's,
  • And selecting collision partners
    (heavy particle reactions),
  • See flowchart.
  • Stored as 1-D;
  • Multi-dimensionality through explicit macros.
• Other data lumped into ``misc. data'' array,
  • Used to ``process'' a given collision,
  • Types of data required vary with process,
  • And even with model for a given process.
  • retain dep. var. labels from input file.
  • For each variation is a subroutine
    which knows how to use those data,
    • Ideally, would be encoded alongside data in file (a ``method'' for that ``class'').
• Indexing into arrays is by ``problem
  reaction number'' and dep. var. number.