Discussion

Simple dimensional considerations indicate that single uranium-rich inclusions less than a few percent of the length, width and height of the host apatite are unlikely to contribute substantial radiogenic helium. For larger inclusions or multiple small inclusions, the parentless helium problem can be partially solved by more aggressive acid dissolution procedures. Under the assumption of uniformly distributed mineral inclusions, the average (U-Th)/He age of many inclusion-rich apatites that have undergone such a treatment is accurate. Please note that the assumption of a random distribution can more easily be verified in the presence of large inclusions (e.g., Figure 10) than for micro-inclusions or a compositionally zoned apatite. Grain-selection is significantly faster and easier without the restriction to inclusion-free grains. For some samples, it is nearly impossible to find inclusion-free grains. Further, by broadening the search to include inclusion-bearing grains, it is much easier to find large, euhedral apatites, requiring relatively small $\alpha$-ejection corrections. Additionally, the presence of U-Th rich inclusions may be an advantage for dating young rapidly cooled rocks. Multi-grain measurements of inclusion-bearing apatites combine the best of two worlds. They have the high U, Th and He content of zircon, but the diffusive behavior and uniquely low closure temperature of apatite. This is similar to the idea behind the work of Min et al. (2006), who dated volcanic olivine and pyroxene using the He produced by the $\alpha$-emitting inclusions contained within them. On the other hand, dissolving U-Th rich inclusions also causes some complications, particularly for single-grain dating. The probability distribution of single grain ages has heavy tails.

The revised methodology has applications to all rock-types which have inclusion-bearing apatites. However, in most studies, only a few grains are usually dated and it is often possible to find two or three suitable clear crystals. For detrital source studies however, this is not the case because in such studies many more grains are necessary to characterize the population. The difficulty of finding enough inclusion-free grains that represent a realistic and representative cross section of the populations can only be made by also including some of the inclusion-bearing apatites. Although the precision of single grain (U-Th)/He ages on inclusion-bearing apatites is worse than the precision of inclusion-free apatite (U-Th)/He ages, it is comparable to or better than the precision of detrital apatite fission track ages. Thus we recommend that for detrital studies using apatite analysis the more aggressive dissolution method is used routinely.

Acknowledgments This manuscript benefited from input from Rainer Wieler and comments from Peter Reiners and two anonymous reviewers. Pieter Vermeesch is financially supported by a Marie Curie Fellowship of the European Union (CRONUS-EU network).