Subatomic Physics

14.2. The Pion–Nucleon Interaction—Survey 427
The total cross sections for the
scattering of positive and negative
pions have been displayed in
Fig. 5.34. The cross sections for
the elastic processes, Eqs. (14.2)
and (14.3), and for charge exchange,
Eq. (14.4), are sketched
in Fig. 14.5 up to a pion kinetic
energy of about 500 MeV. (5)
The best-known photoproduction
processes are
γp −→ π 0 p (14.5)
γp −→ π + n. (14.6)
The reaction γn can be studied
by using deuterium targets
and subtracting the contribution
of the proton. The
cross sections for the processes
in Eqs. (14.5) and (14.6) are
shown in Fig. 14.6. The feature
that dominates Eqs. (14.2)–
(14.6) is the appearance of a resonance.
In pion scattering, it
occurs at a pion kinetic energy
of about 170 MeV; in photoproduction,
the photon energy at
the peak is about 300 MeV. Despite
this difference in kinetic energies,
the peaks in pion scattering
and pion photoproduction
can be interpreted by one phenomenon,
the formation of an excited
nucleon state, ∆, as indicated
in Fig. 14.7.
Figure 14.5: Cross sections for the low-energy elastic
and charge-exchange pion–proton reactions.
Figure 14.6: Total cross sections for the photoproduction
of neutral and charged pions
from hydrogen, as a function of the incident
photon energy.
The mass of this resonance particle is approximately given by mN ∗ ≈ mN +mπ+
Ekin/c 2 = 1260 MeV/c 2 in pion scattering, and by mN ∗ ≈ mN +Eγ = 1240 MeV/c 2
in photoproduction. Proper computation, taking into account the recoil of the N ∗ ,