Elements of Modern Physics
390
Finally, it is noted that the long-lived component
0
2
| K 〉 was found
(Christenson, Cronin, Fitch and Turlay, 1964) to decay to a small extent into
two π-mesons which means that CP is not conserved and that
0
1
| K 〉 and
0
2
| K 〉
are only approximate eigenstates of the Hamiltonian.
PROBLEMS
1. Using the operators in Eq. (4.127), except the factor of , for the isospin
operators for I == 1/2, and the representation in Eq. (4.126) for the P and
N states respectively, obtain the isospin values of the states for the protonneutron system in Eqs. (10.8) to (10.11)
2. If a positron of energy E annihilates an electron at rest, giving out two
photons, e
+
+ e → γ + γ, obtain the angular distribution of energy.
3. Determine the maximum energy of π
–
when the K
+
at rest decays into
π
+
π
+
π
–
.
4. What is the lifetime of Σ
0
so much smaller than that of Σ
+
or Σ
–
?
5. What is the range of weak-interaction forces originating from the exchange
of W-bosons of mass about 80 GeV?
6. Obtain from dimensional arguments, the lifetime of β-decay, given that it
is proportional to
2
2
w
m
Ê
ˆ
Á
˜
a
Ë
¯
and that the remaining factor is a function of
, c and m e .
7. For a particle moving with high velocity, the force-acceleration relation
in Eq. (10.41) changes to evB = mv
2
/r (1 – v
2
/c
2
)
1/2
. What os the field
needed to keep a proton of 5 GeV energy, in a circular orbit of radius
20 m?