Subatomic Physics

434 Strong Interactions
into the Klein–Gordon equation,
� 1
c 2
∂ 2
∂t 2 − ∇2 +
�
mc
� �
2
Φ(x) =0. (14.26)
�
For a time-independent field and for ρ(x) = 0, comparison of Eqs. (14.26) and
(14.22) yields
k = mc
. (14.27)
The constant k in the Yukawa potential is just the inverse of the Compton wavelength
of the field quantum. The mass of the field quantum determines the range
of the potential. We have thus regained the result already expressed in Section 5.8.
In addition, we have found the radial dependence of the potential for the case of a
point source. The simple form of the Yukawa theory thus provides a description of
the strong potential produced by a point nucleon in terms of the mass of the field
quantum. It “explains” the short range of the strong forces. Before delving deeper
into meson theory, we shall describe in more detail what is known about the forces
between nucleons.
14.5 Low-Energy Nucleon–Nucleon Force
The properties of the forces between nucleons at energies where its constituent
substructure can be neglected, has been studied directly in collision experiments
or indirectly by extracting them from the properties of bound systems, namely the
nuclei. In the present section, we shall first discuss the properties of the nuclear
force as deduced from nuclear characteristics and then sketch some of the results
obtained in scattering experiments below a few hundred MeV.
From the observed characteristics of nuclei, a number of conclusions about the
nuclear force, that is, the strong force between nucleons, can be drawn. The most
important ones will be summarized here.
Attraction The force is predominantly attractive; otherwise stable nuclei could
not exist.
Range and Strength As explained in Section 14.1, comparison of the binding
energies of 2 H, 3 H, and 4 He indicates that the range of the nuclear force is of the
order of 1 fm. If the force is represented by a potential with such a width, a depth
of about 50 MeV is found (Section 16.2).
Charge Independence As discussed in chapter 8, the strong force is chargeindependent.
After correction for the “electromagnetic interaction,” (13) the pp, nn,
13We have placed “electromagnetic interaction” in quotes because there is an additional effect
of the same order, which is not electromagnetic in origin: the masses of the up and down quarks
are not identical. This mass difference, which is not believed to be primarily electromagnetic in
origin, affects charge independence.
�