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Sthick = thickness(zmax, Lambdasp, rho)

Calculates the thickness correction factor for nuclide production by spallation. The arguments are zmax, the sample thickness in cm; Lambdasp, the effective attenuation length for production by neutron spallation in atoms $ \cdot$ g $ ^{-1} \cdot$ yr$ ^{-1}$; and rho, the sample density in g $ \cdot$ cm$ ^{-3}$. Accepts vector inputs.

Calculating the thickness correction factor $ S_{thick}$ begins by assuming that the production rate decreases with depth according to a single exponential function:

$\displaystyle P(z) = P(0)\exp(\frac{\rho z}{\Lambda_{sp}})$ (81)

where $ P(0)$ is the surface production rate and $ z$ is depth below the surface (cm). The thickness scaling factor $ S_{thick}$ is then:

$\displaystyle S_{thick} = \frac{1}{z_{max}} \int^{z_{max}}_{0}P(z) dz = \frac{\...
...{sp}}{\rho z_{max}} \left[ 1 - \exp(\frac{-\rho z_{max}}{\Lambda_{sp}}) \right]$ (82)

where $ \Lambda_{sp}$ is the effective attenuation length for production by spallation (input argument Lambdasp) and $ \rho$ is the sample density (input argument rho).