thickness.m

Syntax:

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:

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

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