bei48482_FM

394 Chapter Eleven

Figure 11.4(a) The spin magnetic moment pof the proton is in the same direction as its spin angular

momentum S.(b) In the case of the neutron, nis opposite to S.

(a) b)

S

μp

μn

S

p n

(

As in the case of electrons, magnetic moments are associated with the spins of pro-

tons and neutrons. In nuclear physics, magnetic moments are expressed in nuclear

magnetons(N), where

N5.051 10 ^27 J/ T3.152 10 ^8 eV/T (11.3)

Here mpis the proton mass. The nuclear magneton is smaller than the Bohr magneton

of Eq. (6.42) by the ratio of the proton mass to the electron mass, which is 1836. The

spin magnetic moments of the proton and neutron have components in any direction of

Proton pz2.793 N

Neutron nz

1.913 N

There are two possibilities for the signs of pzand nz depending on whether msis

^12 or ^12 . The sign is used for pzbecause pzis in the same direction as the spin

S, whereas is used for nzbecause nzis opposite to S(Fig. 11.4).

At first glance it seems odd that the neutron, with no net charge, has a spin mag-

netic moment. But if we assume that the neutron contains equal amounts of positive

and negative charge, a spin magnetic moment could arise even with no net charge. As

we shall find in Chap. 13, such a picture has experimental support.

The hydrogen nucleus^11 H consists of a single proton, and its total angular momen-

tum is given by Eq. (11.2). A nucleon in a more complex nucleus may have orbital

angular momentum due to motion inside the nucleus as well as spin angular mo-

mentum. The total angular momentum of such a nucleus is the vector sum of the spin

and orbital angular momenta of its nucleons, as in the analogous case of the electrons

of an atom. This subject will be considered further in Sec. 11.6.

When a nucleus whose magnetic moment has the zcomponent zis in a constant

magnetic field B,the magnetic potential energy of the nucleus is

Magnetic energy UmzB (11.4)

This energy is negative when zis in the same direction as Band positive when zis

opposite to B. In a magnetic field, each angular momentum state of the nucleus is

therefore split into components, just as in the Zeeman effect in atomic electron states.

Figure 11.5 shows the splitting when the angular momentum of the nucleus is due to

the spin of a single proton. The energy difference between the sublevels is

E 2 pzB (11.5)

e



2 mp

Nuclear

magneton

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