This preview shows pages 1–3. Sign up to view the full content.
Ph1b (analytic track): Solution to Homework 4
Chefung Chan (cchan@caltech.edu), Winter 2008
Problem 814
(a) (1 point)
In the centerofmass frame, the system has zero total momentum.
Since producing one photon would give a nonzero momentum, there must be at
least two photons produced. (See page 238 and Fig. 811 in particular).
(b) (2 points)
From the conservation of energy,
E
A
+
E
B
=
E
C
+
E
D
(
m
+
K
)+
m
=
E
C
+
E
D
(
∗
)
From conservation of momentum,
p
A
+
p
B
=
p
C
+
p
D
p
(
m
+
K
)
2
−
m
2
=
E
C
−
E
D
,
(
∗∗
)
where in the last step we have used the fact that, for photons,
E
=

p

.So
lv
ing
(
∗
)and(
∗∗
) for the unknowns
E
C
and
E
D
gives:
E
C
=
m
+
K
2
+
1
2
p
K
(2
m
+
K
)
E
D
=
m
+
K
2
−
1
2
p
K
(2
m
+
K
)
.
(c) (2 points)
(1)
When
K
±
m
(or equivalently,
K/m
±
1) we have
E
C
=
E
D
≈
m
.
(2)
When
K/m
²
1, we write the square root term as:
1
2
p
K
(2
m
+
K
)=
K
2
r
2
m
K
+1
≈
K
2
±
1+
1
2
2
m
K
²
=
K
2
+
m
2
.
Therefore,
E
C
≈
K
,
and
E
D
≈
m
2
.
Problem 817
(a) (2 points)
We are told that the protons and antiprotons are accelerated up
to 0.9 TeV and collide head on. Since this is the centerofmass frame, all the
energy is available for the interaction, that is:
E
T
=
E
p
+
+
E
p
−
=1
.
8TeV
.
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document(b) (3 points)
Now we consider the the lab frame, in which an (even faster) an
tiproton collides with a proton at rest.
lab:
p
+
→←
p
−
rest:
p
+
←←
p
−
Since this frame moves at the speed of the proton (corresponding to 0.9 TeV)
with respect to the centerofmass frame, we Fnd that
E
p
+
=
m
p
+
γ
p
+
⇒
γ
p
+
=
900 GeV
938 MeV
≈
959
v
p
+
=
s
1
−
1
γ
2
p
+
≈
0
.
999 999 5
.
Comparing the proton’s energy and momentum
E
=
mγ
and
p
=
mγv
we Fnd
that these are almost identical if
v
is very close to one. The proton is highly
relativistic.
This is the end of the preview. Sign up
to
access the rest of the document.
 Winter '08
 McKewn
 Mass, Momentum, Work, Photon

Click to edit the document details