Subatomic Physics

14.1. Range and Strength of the Low-Energy Strong Interactions 423
on strong forces was gleaned from studying nuclei, and the force between nucleons
therefore enters heavily into the discussion here. It also serves as an introduction
of how dynamical information can be deduced from experiments.
Range The early alpha-particle scattering experiments by Rutherford indicated
that the nuclear force must have a range of at most a few fm. In 1933, Wigner
pointed out that a comparison of the binding energies of the deuteron, the triton,
and the alpha particle leads to the conclusion that nuclear forces must have a range
of about 1 fm and be very strong. (2) The argument goes as follows. The binding
energies of the three nuclides are given in Table 14.2. Also listed are the binding
energies per particle and per “bond.” The increase in binding energy cannot be
due only to the increased number of bonds. However, if the force has a very short
range, the increase can be explained: The larger number of bonds pulls the nucleons
together, and they experience a deeper potential; the binding energies per particle
and per bond increase correspondingly.
Strength The strength of a strong force is best described by a coupling constant.
However, to extract a coupling constant from experimental data, a definite form of
the strong Hamiltonian must be assumed. We shall do this in later sections.
Figure 14.1: Total cross sections for various strong collisions.
Here we compare the strength
of the strong forces to that
of the electromagnetic and
the weak ones from scattering
total cross sections. This
comparison is somewhat arbitrary
because the energy dependence
of the cross sections
are different. The total
cross section for the scattering
of neutrinos from nucleons
at high energies increases linearly
with laboratory energy
as shown in Fig. 11.14; it is
of the order of 5 × 10 −39 ELab(GeV)cm 2 . The cross section for electron scattering
from protons is of the order of magnitude of the Mott cross section, Eq. (6.11), at
high energies, as discussed in Section 6.8. We take the total cross section to be
approximately 90µb/(Ecmin GeV) 2 . In Fig. 14.1, we compare various strong cross
sections as a function of laboratory momentum; in all cases, the cross section is of
the order of several times 10 −26 cm 2 , or approximately geometric. In Fig. 14.2 we
compare the total cross sections for the strong, electromagnetic, and weak processes.
2 E. P. Wigner, Phys. Rev. 43, 252 (1933).