Pion correlations as a function of atomic mass in heavy ion collisions Page: 65 of 130
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CHAPTER 6. BACKGROUND GENERATION AND FUNCTION FITTING
events there are two momenta, so 1'0 will be used for the aih event's first pion momentum
and 02 for the 1th event's second pion momentum.
With this notation, the two pion experiment consists of measuring a set of N two pion
events, which can be written
{{(T01.. )}Q , where N = the number of events.
Central to the analysis is making a histogram, so the definition of a function that
corresponds to making a histogram is needed. Therefore, define a 6 function by
( 1 for fe ith momentum bin
0 for fy ith momentum bin
then making a histogram of the momentum distribution for the first pion in the events
corresponds to finding the ni that are the number of counts per bin by
N
ni= (orE i).
ant
Before starting into the details of the calculations, it is best to reveal the plan of
attack. What is wanted is, of course, the Cij in terms of known quantities. The known
quantities in this experiment are the momentum distributions of the pions, the 6(103 E i),
for the data set of two pion events. The functions q;, wi and p;i are unknown (or, in
the case of pij, known approximately). Therefore, the calculation will express the ;,
wi and Ci; in terms of the momentum distributions and other known quantities. This
:equires that some normalizations be assumed for the probabilities and for the momentum
distributions. In many cases the value assumed for the normalization is unimportant, so
long as a normalization is assumed.
Assume the following normalizations
M
wi = 1 , Probability of emission somewhere = 1, and (6.2)
ri = n , The efficiency of the spectrometer. (6.3)
Since f is unknown, this can be used to define f. Also, the normalization of wi implies
that w; ~ O(N), where M = the number of bins.55
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Chacon, A.D. Pion correlations as a function of atomic mass in heavy ion collisions, report, November 26, 1989; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc1055804/m1/65/: accessed July 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.