Subatomic Physics

14.5. Low-Energy Nucleon–Nucleon Force 437
In an external inhomogeneous electric field, a nucleus
with quadrupole moment acquires an energy that depends
on the orientation of the nucleus with respect to
the field gradient. (16) This interaction permits the determination
of Q; for the deuteron, a nonvanishing value
was found. (17) The present value is
Qd =0.282 fm 2 . (14.31)
s states are spherically symmetric and have Q =0. The
nonvanishing value of Qd thus verifies the conclusion
drawn from the nonadditivity of the magnetic moments:
The deuteron ground state must possess a d-state admixture.
(See also Section 6.8, in particular Fig. 6.35.) The
presence of a d-state component implies that the nuclear
force cannot be purely central, because the ground state
in a central potential is always an s state; the energies
of states with L �= 0 are pushed higher by the centrifugal
potential. The noncentral force giving rise to the
deuteron quadrupole moment is called the tensor force.
Such a force depends on the angle between the vector
joining the two nucleons and the deuteron spin.
Figure 14.10: The tensor force in the deuteron is attractive
in the cigar-shaped configuration and repulsive in the diskshaped
one. Two bar magnets provide a classical example
of a tensor force.
Figure 14.9: Prolate and
oblate nuclei, with spins
pointing in the z direction.
The nuclei are assumed to be
axially symmetric; z is the
symmetry axis.
Figure 14.10 shows two extreme
positions. Since the
deuteron quadrupole moment
is positive, comparison of
Figs. 14.9 and 14.10 indicates
that the tensor force must be
attractive in the prolate and
repulsive in the oblate configuration.
A simple and well-known example of a classical tensor force is also shown in
Fig. 14.10. Two bar magnets, with dipole moments m1 and m2, attract each
other in the cigar-shaped arrangement but repel each other in the disk-shaped one.
16 Careful discussions of the quadrupole moment are given in E. Segrè, Nuclei and Particles,
Benjamin, Reading, Mass., Section 6.8; and Jackson, Section 4.2.
17 J. M. B. Kellog, I. I. Rabi, and J. R. Zacharias, Phys. Rev. 55, 318 (1939).