RxnRate-expPolyCrossSection

Exponential Polynomial Cross-Section

This is a fitting formula presented by [Kim92] for electron-impact excitation and ionization interactions which fits well from threshold to high energies (<10 keV). For relativistic energies a relativistic formula should be used. Resonant structures are smoothed out. See [Kim92] for more details, including suggested values for the fitting constants, A, B, C, D, and I for some species. In the html version of the paper (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4909190/) there is a typo in table 1: C should be positive, which can be seen in the original pdf of the paper.

The cross-sections will take the functional from of the equation:

\[\sigma (y) = \frac{1}{y} \left( A \ln (y) + \frac{B \ln (y) + C*(y-"toZero")}{y + D} \right)\]

where

\[y = x/I\]

The vanishAtThreshold attribute (see below), sets whether the cross-section goes to a zero or non-zero value at the reaction threshold energy/velocity.

expPolyCrossSection Attributes

A (float, required): The value for the fitting constant A in the formula above.

B (float, required): The value for the fitting constant B in the formula above.

C (float, required): The value for the fitting constant C in the formula above.

D (float, required): The value for the fitting constant D in the formula above.

I (float, required): The value for the fitting constant I in the formula above. A scaling factor for the independent variable, x, so must have the same units [m/s or eV]. For reactions with energy/velocity thresholds, this should be that threshold.

toZero (int, required): Sets the value for the toZero parameter in the formula above. Enter either “1” to have the cross-section go to zero at threshold energy/velocity, or “0” to have the cross-section go to a non-zero value at this threshold.

variable (string, required)

Set the independent variable, x, in the equation above. Options are:

velocity [m/s]
energy [eV]

This sets whether vorpal uses the velocity or energy of the reactant particles to calculate the probability of an interaction.

Example expPolyCrossSection Block

<RxnRate rxnRate>
  kind = expPolyCrossSection
  A = 0.7576
  B = -5.521
  C = 5.867
  D = 2.948
  I = 13.61
  toZero = 1
  variable = energy
</RxnRate>