Subatomic Physics

436 Strong Interactions
The even parity of the deuteron implies that L
must be even. There are then only two possibilities
for forming total angular momentum 1,
namely L = 0 and L = 2. In the first case,
shown in Fig. 14.8(a), the two nucleon spins add
up to the deuteron spin; in the second, shown in
Fig. 14.8(b), orbital and spin contributions are antiparallel.
In the s state, where L =0,theexpected
magnetic moment is the sum of the moments
of the proton and the neutron, or
µ(s state) = 0.879 634µN.
The actual deuteron moment deviates from this
value by a few percent,
µd − µ(s)
= −0.026. (14.29)
µd
Figure 14.8: The two possible
ways in which spin and orbital
contribution can form a
deuteron of spin 1.
The approximate agreement between µd and µ(s) implies that the deuteron is
predominantly in an s state, with the two nucleon spins adding up to the deuteron
spin. If the nuclear force were spin-independent, proton and neutron could also form
a bound state with spin 0. The absence of such a bound state is evidence for the
spin dependence of the nucleon–nucleon force. The deviation of the actual deuteron
moment from the s-state moment can be explained if it is assumed that the deuteron
ground state is a superposition of s and d states. Part of the time, the deuteron has
orbital angular momentum L = 2. Independent evidence for this fact comes from
the observation that the deuteron has a small, but finite, quadrupole moment. The
electric quadrupole moment measures the deviation of a charge distribution from
sphericity. Consider a nucleus with charge Ze to have its spin J point along the z
direction, as shown in Fig. 14.9. The charge density at point r =(x, y, z) isgiven
by Zeρ(r). The classical quadrupole moment is defined by
�
Q = Z
d 3 r(3z 2 − r 2 �
)ρ(r) =Z
d 3 rr 2 (3 cos 2 θ − 1)ρ(r). (14.30)
For a spherically symmetric ρ(r), the quadrupole moment vanishes. For a cigarshaped
(prolate) nucleus, the charge is concentrated along z, andQ is positive. The
quadrupole moment of a disk-shaped (oblate) nucleus is negative. As defined here,
Q has the dimension of an area and is given in cm 2 ,orbarns(10 −24 cm 2 ), or fm 2 .