We measured concentrations of Ne isotopes in quartz in a 27.6-meter sandstone core from a low-erosion-rate site at 2183 m elevation at Beacon Heights in the Antarctic Dry Valleys. Surface concentrations of cosmogenic 21 Ne indicate a surface exposure age of at least 4.1 Ma and an erosion rate no higher than ca. 14 cm Myr 1. 21 Ne concentrations in the upper few centimeters of the core show evidence for secondary spallogenic neutron escape e↵ects at the rock surface, which is predicted by first-principles models of cosmogenic-nuclide production but is not commonly observed in natural examples. We used a model for 21 Ne production by various mechanisms fit to the observations to distinguish cosmic-ray-produced 21 Ne from nucleogenic 21 Ne produced by decay of trace U and Th present in quartz, and also constrain rates of subsurface 21 Ne production by cosmic-ray muons. Core samples have a quartz (U-Th)/Ne closure age, reflecting cooling below ⇠95°C, near 160 Ma, which is consistent with existing apatite fission-track data and the 183 Ma emplacement of nearby Ferrar dolerite intrusions. Constraints on 21 Ne production by muons derived from model fitting are consistent with a previously proposed value of 0.79 mb at 190 GeV for the cross-section for 21 Ne production by fast muon interactions, but indicate that 21 Ne production by negative muon capture is likely negligible.