| Recreating Allard-Unger Result | 
| 85% protons : 12% Nitrogen : 3% Iron | 
| Spectrum | 
| Monte Carlo | analytic without &alpha | analytic with &alpha | 
|   |   |   | 
| Xmax | 
| Monte Carlo | analytic without &alpha | analytic with &alpha | 
|   |   |   | 
| RMS | 
| Monte Carlo | analytic without &alpha | analytic with &alpha | 
|   |   |   |