Environmental Engineering Reference
In-Depth Information
quantum theory permits us to view light as being made up of particles (the study of
the photoelectric effect famously providing the first direct evidence) and since these
particles must necessarily travel at the speed of light then Special Relativity predicts
that they should also be massless. Such massless particles are called 'photons'.
Example 7.2.4
Aneutralπ meson (pion) is an elementary particle which can decay
into two photons, i.e. π
γγ.
6
If the pion is moving with a kinetic energy equal
to 1 GeV what angle is formed between the two photons if they are emitted at equal
angles relative to the original direction of the pion? [The neutral pion has a mass
of 135 MeV/c
2
.]
→
Solution 7.2.4
It is usually a very good idea to draw a sketch in problems like this;
something like that illustrated in Figure 7.4. Our goal is to compute the angle α.We
have the equations for energy and momentum at our disposal, along with the laws
of conservation of energy and momentum, and we must use them carefully. Let us
first collect together what we know before the decay:
m
π
c
2
Before:
E
=
+
K,
(E
2
m
π
c
4
)
1
/
2
/c,
p
x
=
−
p
y
=
0
and we have made use of Eq. (7.36) to fix the momentum of the pion given its total
energy. After the decay we have that
After:
E
1
=
cp
1
,
E
2
=
cp
2
,
p
1
x
=
p
1
cos
α,
p
2
x
=
p
2
cos
α,
p
1
y
=
p
1
sin
α,
p
2
y
=−
p
2
sin
α
and we have used E
cp for the massless photons. We can obtain the angle α using
momentum conservation in the x direction. However before that we need to figure
=
p
1
g
p
a
a
g
K
= 1 GeV
p
2
m
p
= 135 MeV/
c
2
Before
After
Figure 7.4
Neutral pion decay to two photons
6
The symbol
γ
is often used to denote a photon.
