Effects of long a-stopping distances

Phosphate specimens for dating are usually only -3 to 30 times larger than these stopping distances, and as a result the skin effecf of ejection or implantation can have a significant influence on He ages computed from Equation (2). U and Th tend to be concentrated in phosphates compared to surrounding minerals, so the net consequence of 

Quantitative modeling of a ejection is an alternative approach (Farley et al. 1996). The object of the modeling is to calculate what fraction (Ft) of the U and Th in a crystal is capable of yielding a particles that stop within the crystal. The importance of this quantity is that the measured U and Th must be reduced by this fraction when calculating a He age. Equivalently, an a ejection corrected age tcorr) can be computed by increasing the age from Equation (2) by a factor of 1/Ft  

Ft depends on the stopping distances of the a particles (hence on both the mineral of interest and its relative Th and U abundance), the size and geometry of the crystal, and how the parent nuclides are distributed. For homogeneously distributed parent nuclides in a sphere of radius r with stopping distance s it has been shown (Farley et al. 1996) that  

Correction equations similar to (4) but valid for cylinders, hexagonal prisms, and cubes have been published (Farley et al. 1996). These equations are appropriate for some phosphates (especially apatite), but may not apply to others, e g., to commonly low-symmetry crystals of monazite. An approximation that may be useful for low symmetry minerals relates Ft to surface to volume ratio (P), specifically  

For P 0.07, this approximation generally underestimates the true Ft value (Fig. 2a). Meesters and Dunai (2002b) present alternative means for assessing the effects of a ejection for various geometries. 

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Figure 5. The effects of long a-stopping distances on He retention. The upper figure illustrates the three relevant possibilities within a schematic crystal a retention, possible a ejection, and possible a implantation. The center of the circle denotes the site of the parent U or Th nuclide, and the edge of the white circle labeled He indicates the locus of points where the a particle may come to rest the arrow indicates one possible trajectory. The lower plot shows schematically how a retention changes from rim to core to rim along the path A-A exact equations defining the shape of this curve as a function of grain size were given by Farley et al. (1996).

As an alternative, Farley et al. (1996) developed a quantitative model for correcting He ages for the effects of long a stopping distances based on measured grain geometry and size. Several assumptions are required ... 

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