Subatomic Physics

9.3. Conservation and Breakdown of Parity 247
As stated above, the alpha particle has
spin 0 and positive parity. If it is
emitted with orbital angular momentum
L, it carries a parity (−1) L .Since
the initial state of the decay has spin
0, an alpha emitted with angular momentum
L can only reach states with
spin J = L. The parities of these
states then must be (−1) L =(−1) J or
0 + , 1 − , 2 + , 3 − , 4 + ,.... Such states indeed
are seen to be populated by the
alpha decay in Fig. 9.2.
228
Th
0 +
0 +
27%
72%
0.4%
0.2%
224
Ra
4 +
1 -
0 +
2 +
Figure 9.2: Alpha decay of 228 Th. The intensities
of the various alpha branches are given in %.
The examples given so far are simple. In the actual assignment of parities to
particles and excited nuclear states, more complex methods are often necessary,
but the basic ideas remain the same. The various methods used in nuclear and in
particle physics are described in the references listed in Section 5.14.
9.3 Conservation and Breakdown of Parity
In the previous section we have discussed the experimental determination of the
intrinsic parities of some subatomic particles. Implied in all arguments was conservation
of parity in the processes used to find ηP . How good is the evidence for parity
conservation in the various interactions? To answer this question in a quantitative
way, a measure for the degree of parity conservation must be introduced. If |α〉 is
a nondegenerate state of a system with, for instance, even parity, it is written as
|α〉 = |even〉.
If parity is not conserved, |α〉 canbewrittenasasuperpositionofanevenandan
odd part,
|α〉 = c|even〉 + d|odd〉, |c| 2 + |d| 2 =1. (9.26)
A state of this form, with c �= 0andd �= 0, is no longer an eigenstate of the parity
operator P because
P |α〉 = c|even〉−d|odd〉 �= ηP |α〉.
FP = d/c is a measure for the degree of parity nonconservation (d ≤ c). Parity
violation is maximal if the state contains equal amplitudes of |even〉 and |odd〉, or
if |FP | =1.