Thin/thick target yields

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Universal sigmoid curve
Universal curve of the resonance self-shielding factors against the z-parameter, showing values for wires, foils and sphere geometries. Taken from E. Martinho et al.

FISPACT-II is a point solution code which does not directly consider the geometry of a simulated scenario, but several robust systematics exist for the treatment of geometry effects such as point-source doses and spatial self shielding. The keyword SSFGEOMETRY allows the user to employ the universal sigmoid curve model which has been demonstrated for foils, wires, spheres and cylinders to give good agreement for spatial self shielding effects. These consider one resonance in a pure target, using a universal dimensionless parameter,

[math]z = \Sigma_{tot}(E_{res})L_{eff} \sqrt{\frac{\Gamma_\gamma}{\Gamma}}[/math]

based on macroscopic cross section at the energy of the resonance [math]\Sigma_{tot}(E_{res})[/math], ‘effective length’ [math]L_{eff}[/math], radiative capture width [math]\Gamma_\gamma[/math] and total resonance width [math]\Gamma[/math]. The seld-shielding factor for this resonance is then a function only of [math]z[/math] with empirical constants. The model has been extended to a group of separated resonances by taking a weighted sum of the self-shielding factors with weights

where [math]\Gamma_n[/math] is the neutron scattering width, I and J are the spins of the target and compound resonance states, respectively. FISPACT-II can use these on a group-by-group basis for all nuclides within the target material, providing the self shielding factors for all cross sections using the PRINTLIB 6 keyword.