Subatomic Physics

224 Angular Momentum and Isospin
(If needed, the commutator can be calculated with Eqs. (5.20) and (5.6).) The
component of the angular momentum along the field, however, still remains conserved.
It is customary to select the quantization axis z along the magnetic field.
Equations (5.6) and (5.20) then give
[H0 + Hmag,Jz] =0. (8.12)
The system is still invariant under rotations about the direction of the externally
applied field, namely the z axis. However, the introduction of a preferred direction
through the application of the magnetic field has broken the overall symmetry, and
J is no longer conserved. Before the application of the field, the energy levels
of the system were (2J + 1)-fold degenerate, as shown on the left-hand side of
Fig. 5.5. The introduction of the field results in a removal of the degeneracy, and
the corresponding Zeeman splitting is shown in Fig. 5.5.
8.3 Charge Independence of Hadronic Forces
In 1932, when the neutron was discovered, the nature of the forces holding nuclei
together was still mysterious. By about 1936, crucial features of the nuclear force
had emerged. (2) Particularly revealing was the analysis of pp and np scattering
data. Of course, at that time, such scattering experiments could be performed
only at very low energies, but the outcome was still surprising: After subtracting
the effect of the Coulomb force in pp scattering, it was found that the pp and
the np hadronic force were of about equal strength and had about equal range. (3)
This result was corroborated by studies of the masses of 3 Hand 3 He which gave
approximately equal values for the pp, np, andnn interactions. Strong evidence
for a charge independence of the nuclear forces was also found by Feenberg and
Wigner. (4) Charge independence for nuclear forces can be formulated by stating
that the forces between any two nucleons in the same state are the same, apart from
electromagnetic effects. Today, the experimental evidence for charge independence
is very strong, and it is known that all hadronic forces, not just the one between
nucleons, are charge-independent. (5) We shall not discuss the experimental evidence
for charge independence here but only point out that the concept of isospin, which
will be discussed in the following sections, is a direct consequence of the charge
independence of hadronic forces.
2 In 1936 and 1937, Bethe and collaborators surveyed the state of the art in a series of three
articles, later known as the Bethe bible. These admirable reviews in Rev. Mod Phys. 8, 82 (1936),
9, 69 (1937), and 9, 245 (1937), reprinted in Basic Bethe, Am. Inst. Phys., New York, 1986, can
still be read with profit.
3 G. Breit, E.U. Condon, and R.D. Present, Phys. Rev. 50, 825 (1936).
4 E. Feenberg and E.P. Wigner, Phys. Rev. 51, 95 (1937).
5 The evidence for charge independence of the hadronic forces is discussed by G.A. Miller and
W.T.H. van Oers in Symmetries and Fundamental Interactions, ed. W.C. Haxton and E.M.
Henley, World Sci., Singapore (1995), p. 127.