Subatomic Physics

300 The Electromagnetic Interaction
In the nuclear example, the nuclide 170 Tm decays with a half-life of 129 d to
an excited state of 170 Yb, which then decays to its ground state with emission of a
gamma ray of 0.084 MeV. The second example is the decay of the neutral sigma;
in the transition Σ 0 γ → Λ 0 , a 77-MeV gamma ray is emitted.
The lifetime of the neutral sigma is 7 ×
10 −20 sec; the half-life of the 84 keV state in 170 Yb,
on the other hand, has been determined as 1.61
nsec. (It is customary to quote mean lives in particle
physics and half-lives in nuclear physics; see
Eq. (5.33) for the relationship.) The basic idea
underlying the half-life measurement is shown in
Fig. 10.8. (8) The radioactive source, in the example
170 Tm, is placed between two counters. The
beta counter detects the beta ray that populates
the 2 + state in 170 Yb. After some delay, the excited
state decays with the emission of a 0.084
MeV photon. This photon has a certain probability
of being delayed by a time D, and the coincidence
rate between the delayed beta pulse and
the gamma pulse is detected with an AND circuit
(Section 4.9). The coincidence count rate N(D)
is recorded on a semilogarithmic plot against D,
and the slope of the resulting curve gives the desired
half-life. The corresponding ideas have already
been discussed in Section 5.7, and the plot
shown in Fig. 10.8 is a specific example of an exponential
decay as sketched in Fig. 5.15.
Figure 10.7: Two examples
of subatomic gamma decays.
Note that the energy scales
differ by about a factor 100.
The method shown here, in which the decay curve is measured point by point, is
only one possible approach. Many other techniques for investigating decay lifetimes
have been evolved (8) and at present the half-lives of more than 1500 states are
known.
After this brief excursion into the experimental aspects of electromagnetic transitions
of subatomic particles, we return to theory and ask: can the decays shown
as examples in Fig. 10.8 be explained by the treatment given in Section 10.4? It
can be seen immediately that the transition Σ 0 → Λ 0 cannot be caused by electric
dipole transitions: The matrix element that appears in the electric dipole transition
rate, Eq. (10.77), has the form
〈β|x|α〉 ≡〈Λ 0 |x|Σ 0 〉≡
�
d 3 xψ ∗ Λ xψΣ.
8 The measurement of short mean lives is discussed by R. E. Bell, in Alpha-, Beta- and Gamma-
Ray Spectroscopy, Vol. 2 (K. Siegbahn, ed.), North-Holland, Amsterdam, 1965; T.K. Alexander
and J.S. Foster, Adv. Nucl. Phys. 10, 197 (1979); G. Bellini et al., Phys. Rept. 83, 1 (1982).