12

H₀+H₁ and the thermal radiation field. Every nucleus, however,
also experiences the field produced by the magnetic moments
of its neighbors. If this dipole-dipole interaction is taken
into account, the Hamiltonian [f-an] assembly of spins
becomes

The sum over j in the right hand term represents
the internal or local field at the ith nucleus;
is the radius vector connecting the ith &
the jth spin. The problem connected with (2.24) is
[she?] of an extreme complexity. It is the equation of motion
for N particles, where N is of the order of Avogadro number.
The local field will, at any time, be of the order of
few [aersted?]. It is mainly determined by the nearest
neighbors, since the magnitude of a dipole field decreases
as the inverse cube of the distance: where a
is the internuclear distance. For two protons, me Å apart,
we find H_loc ≈ [lo ousted?].

The energy levels of the unputurbed system, without
dipole-diple interaction are