Introduction

The (U-Th)/He thermochronometer is based on the $\alpha$-decay of $^{238}$U, $^{235}$U, $^{232}$Th and the often neglected $^{147}$Sm in accessory minerals such as apatite, sphene and zircon. Of these minerals, apatite is by far the most used, because of its relatively well-understood diffusive behavior and uniquely low closure temperature ($\sim$70$^o$C; Wolf et al., 1996). The radioactive parent (U and Th) and radiogenic daughter ($^4$He) are measured separately on different types of mass spectrometer, and accurate ages are only possible if all parent and daughter nuclides are accounted for. Fitzgerald et al. (2006) provide an excellent discussion of factors that might violate this requirement, such as $\alpha$-ejection, mineral and fluid inclusions or He implantation by a U-Th rich matrix. The present paper focuses on arguably the most important complication, which is associated with mineral inclusions rich in U and/or Th. The most common $\alpha$-emitting mineral inclusions in apatite are monazite and zircon (Farley and Stockli, 2002). Zircon contains up to 5000 ppm U and Th, while Th-concentrations of monazite can be up to 30% (Deer et al, 1992). These inclusions eject He into the surrounding apatite that is measured following degassing by heating with a laser or in a resistance furnace. However, zircon inclusions in particular will not dissolve in the concentrated HNO$_3$ commonly used to digest apatites prior to U-Th analysis. Hence, a substantial fraction of the measured He may be ``parentless''.

In the following sections, we will first assess the severity of this problem through some simple order-of-magnitude considerations. As a solution to the ``parentless He problem'', we propose the dissolution of apatite and inclusions in more aggressive acids, such as hot HF (Carter et al., 2004). However, this does not solve a second complication associated with $\alpha$-emitting mineral inclusions, namely the way they complicate the $\alpha$-ejection correction. Typically, $\alpha$-ejection corrections are made under the assumption of uniform U-Th concentration, but this assumption is clearly violated in the presence of U-Th rich mineral inclusions. A mathematical study of this effect is given in Section 3. Besides complicating the $\alpha$-ejection correction, inhomogeneous U-Th distributions also have an effect on the diffusive behavior (closure temperature) of the radiogenic helium. Section 4 will illustrate that this is a relatively minor effect. Therefore, the HF-dissolution technique might also be applicable to slowly cooled rocks (e.g., 1 $^o$C/Ma). However, several studies have reported unresolved problems with slowly cooled rocks, including large data scatter (Fitzgerald, 2006) and (U-Th)/He ages older than fission track ages (Soderlund et al, 2005; Green and Duddy, 2006). To avoid these problems, Section 5 illustrates the effectiveness of the HF-dissolution technique on inclusion-rich apatites from rapidly cooled rocks of Naxos (Greece).

<