Introductory Lab: Poisson Statistics
Experiments in Modern Physics (P451)
In this experiment we will explore the statistics of random events in physical measurements. The random
events used in this study will be pulses from a scintillation detector exposed to a radioactive source. We
will practice generating and fitting histograms and discuss both the
χ
2
and maximum likelihood methods of
estimating fit parameters. This experiment is adapted from a similar one at MIT [1]. Additional information
about scintillation counters and Poisson statistics is available in Refs. [2, 3] and should be reviewed before
beginning work on the lab.
Introduction
A sequence of independent random events is one in which the occurrence of any event has no effect on the
occurrence of any other. One example is simple radioactive decay such as the emission of 663 keV photons
by a sample of
137
Cs. In contrast, the fissions of nuclei in a critical mass of
235
U are correlated events in a
“chain reaction” in which the outcome of each event, the number of neutrons released, affects the outcome
of subsequent events.
A continuous random process is said to be “steady state with mean rate
μ
” if
lim
T
→∞
X
T
=
μ,
(1)
where
X
is the number of events accumulated in time
T
.
How can one judge whether a certain process does, indeed, have a rate that is steady on time scales of
the experiment itself? The only way is to make repeated measurements of the number of counts
x
i
in time
intervals
t
i

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