Pion correlations as a function of atomic mass in heavy ion collisions Page: 28 of 130
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CHAPTER 3. MOTIVATION AND THEORY
Although photons are used here, any particle could be used. In particular, for a two pion
correlation experiment one would replace "photon" with "pion".
An example of a second order coherent source is a laser. The important feature of the
laser for second order coherence is the amplification technique, not the monochromatic
nature of the light. Amplification by stimulated emission results in many photons leaving
the laser in the same state.! Therefore, if there is a photon in a given state it is
extremely likely that there is a second photon in the same state, and this state is the only
state populated by photons. Taking extremely likely to be 100%, the probabilities (as a
function of the photon momentum) are
P(Pi,P2) _ P(Pt)
' P(P2)
and the laser is second order coherent. Further, C2(Pt,P2) X 1 and At.1. = 0.
So if "pion lasers" are the sole source of pions in the nuclear collision then Atn.. = 0. If
there are coherent and incoherent sources in the collision then arne < 1. Simple arguments
show that if the single-particle momentum spectra are the same for the coherent and
incoherent sources then
1
Atr..= 1+f(3.16)
where f is the ratio of the number of coherent pion pairs to the number of incoherent
pion pairs.
The effect of pion lasers on A'I. depends strongly on the event-mixing technique,
and underlines the assumption (often not stated) that all events must have the same
momentum distribution for the technique to appiy. Imagine the simple case where a pion
laser is the sole source of pions in all of the nuclear collisions in the experiment. If the pion
laser always has the same orientation, then event mixing produces the true background
and A b, = 0. If the pion laser changes orientation randomly from one event to the next
(for example, the first A(1236) to decay triggers the laser and determines the direction)
then the real spectrum will be a 6-function. The background calculation will mix pions
of random orientation, and hence the spectrum will be flat. The ratio of the two will be
a 6-function and A"a. will be arbitrarily large.
'Note that all photons leading the laser in the same state is symmetric under interchange of particle
labels and the symmetrization imposed in Section 3.2 does not apply.18
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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/m1/28/: accessed July 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.