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Counting Statistics and Ion Interval Density in AMS
John S. Vogel, Ted Ognibene, Magnus Palmblad, Paula Reimer
Center for Accelerator Mass Spectrometry
Lawrence Livermore National Laboratory
Livermore CA 94551
Abstract
Confidence in the precisions of AMS and decay measurements must be comparable for the
application of the 14C calibration to age determinations using both technologies. We confirmed
the random nature of the temporal distribution of 14C ions in an AMS spectrometer for a number
of sample counting rates and properties of the sputtering process. The temporal distribution of
ion counts was also measured to confirm the applicability of traditional counting statistics.
Introduction
AMS counts 14C and other long-lived isotopes with an efficiency that is many orders of magnitude
greater than decay counting. This efficiency leads to precise AMS quantifications of low levels
of 14C from small (< 1 mg C) and/or old samples. AMS quantification of highly defined (i.e.
small) samples of macrofossils (Kitigawa et al 1998), sediments (Hughen et al 1998, 2004),
corals (Bard et al 1990), foraminifera (Bard et al 2004), and stalagmites (Beck et al 2001) is
central to the extension of the radiocarbon calibration beyond the dendrochronology of larger
tree ring samples that were quantified by decay counting in establishing Holocene and late
glacial calibrations (Stuiver et al 1998). Confidence in the precisions of AMS and decay
measurements must therefore be comparable for the application of the 14C calibration to age
determinations using both technologies. The processes giving rise to individual decay events and
mass-separated ion counts are very different, however.
Radioactive decay is known to be a random process whose decays per counting interval are
described by the Poisson distribution (Rutherford & Geiger, 1910). The independent nature of
each event and the temporal distribution of the decay process are readily understood from the
fundamental quantum mechanics of radioactive decay. The randomness of ion arrivals at an
AMS counting detector are not as fundamentally obvious, given the complexity of the multiple
processes involved in delivery of a specific isotope to the ion counter of an AMS spectrometer.
AMS measurements of 14C concentrations arise from negatively ionizing carbon atoms (usually
in a sputtering process) from an isolated and chemically prepared sample, followed by mass
analysis, acceleration, charge changing by collision electron loss, and identification with counting
in an energetic ion detector after mass per charge separation elements. These procedures are not
expected to produce temporal correlations within a stream of rare isotopes, and AMS counts
should arrive randomly, but their temporal distribution need not mimic that of radioactive decay.
The precision of a random counting measurement is well known to be the square root of the
number of independent counts in the measurement. The simple derivation of this concept is in
many standard texts and is summarized again by Ogborn, Collins, & Brown (2003). We once
more confirmed the random nature of the temporal distribution of 14C ions in an AMS spectrometer
for a number of sample counting rates, various sputter energies, and different sample materials.
The temporal distribution of ion counts was also inspected to confirm the applicability of traditional
counting statistics.Uncertainties in AMS
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Vogel, J S; Ognibene, T; Palmblad, M & Reimer, P. Counting Statistics and Ion Interval Density in AMS, article, August 3, 2004; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc1413913/m1/3/: accessed May 31, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.