NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. Differences in the isotopic composition of Gd and Sm among lunar samples collected during the Apollo 11, 12, 14, 15, and 16 and Luna 16 missions have been measured by high precision mass spectrometry. These differences (up to 1.9% in [...]Gd/[...]Gd and 2.0% in [...]Sm/[...]Sm) can be attributed unambiguously to low energy neutron capture reactions and correspond to neutron fluences as high as 10[...] n/cm[...] (E 3 x 10[...] yr. In terms of a uniform mixing model the measured neutron fluences imply that the depth of the regolith is between 10 and 14 m at all of the Apollo sites studied. These are greater than the depths implied from cratering theory. The [...]Xe/[...] ratios for the soils indicate that they have been well mixed to a depth of > 200 g/cm[...]. Detailed fluence studies in the Apollo 12 double core show that these materials could not have been undisturbed for > 10[...] yr. The upper layers of the Apollo 15 and 16 drill stems also imply mixing on this time scale. However, the Apollo 15 drill stem has a smooth peak in the fluence at a depth of ~ 190 g/cm[...]. From the magnitude of this peak, it can be concluded that below a depth of ~ 75 g/cm[...] these materials have been undisturbed for at least 400 my. The fluence profile in the Apollo 16 drill stem is more complicated but indicates an area where material has been accumulating for several hundred million years. A model is presented for the depth dependence of the ratio of [...]Xe produced by neutron capture on [...]Ba to [...]Xe produced by spallation reactions on Ba. Effective exposure depths are calculated for 24 rocks from Apollo 11 and 12. Detailed irradiation histories are presented for rocks 10017, 14310, and 15595. An erosion rate for Hadley Rille of ~1 cm/my is calculated from the neutron fluence of rock 15595. From Gd and Sm isotopic measurements it is shown that the Norton County meteorite has been exposed to a neutron flux with a spectrum compatible with that predicted by the LCH calculations. The neutron fluence to which our sample of Norton County has been exposed is 1.2 x 10[...] n/cm[...]. No neutron produced effects were observed in the isotopic composition of Gd from a bulk sample of the Allende meteorite.