We study the structure-constant (polarizability) coefficients of the spin-dependent terms of the nucleon Compton scattering amplitude which are third order in the frequency of the incoming photon. It is shown that these spin-polarizability coefficients can be related to sums of products of electromagnetic transition moments of the nucleon, involving the electric and magnetic dipoles, the electric and magnetic quadrupoles, and the charge electric and magnetic dipole mean-square radii. Three sum rules involving products of the electric dipole transition moments emerge from the calculation. PACS numberk): 13.60.F~

We calculate the gravitational deflection of massive particles moving with relativistic velocity in the solar system to second post-Newtonian order. For a particle passing close to the Sun with impact parameter b, the deflection in classical general relativity is ΦC = 2GM/v20b[1 + v20/c2 + 3π/2 MG/bc2 + 3π/8 MG/bc2 v20/c2 + 9(MG/bc2)2], where v0 is the particle speed at infinity and M is the Sun's mass. We compute afterwards the gravitational deflection of a spinless neutral particle of mass m in the same static gravitational field as above, treated now as an external field. For a scalar boson with energy E, the deflection in semiclassical general relativity (SGR) is ΦSC = 4GM/b(1 + m2/2E2). This result shows that the propagation of the spinless massive boson produces inexorably dispersive effects. It also shows that the semiclassical prediction is always greater than the geometrical one, no matter what the boson mass is. In addition, it is found that SGR predicts a deflection angle of ∼2.6 arcsec for a nonrelativistic spinless massive boson passing at the Sun's limb.

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Zero-rest-mass particles in a gravitational field are considered to have energy-momentum tensors T " satisfying T";, = 0 and also T ' , = 0. The latter is satisfied by a massless electromagnetic pulse, and also by a neutrino. In analogy with the theory of material spinning particles in general relativity, moments of these equations are taken and cut off at the dipole level. The moments of the first equation yield the usual poledipole equations. The moments of the second equation yield the auxiliary conditions, which turn out to be p,v' = 0 and v,Sk' = 0, where v ' is the velocity, p ' is the momentum, and S k' is the spin. The special cases of arbitrary spin in flat space, zero spin in curved spaces, and the eikonal approximation are treated and shown to give null geodesic trajectories. However, such trajectories ilo not seem to be a necessary consequence in the general case.

The pole-dipole equations derived in a previous paper for massless particles (whose defining relation is that the energy-momentum tensor has zero trace) are examined. If the reference point X' describing the motion is not somewhere on the disk perpendicular to the three-velocity through the energy center, then X' describes a null geodesic with no assumptions. The property that X' is the particle's energy center in some local reference frame (called a C-frame) is shown to be a constant of the motion. If the energy of the particle in the C-frames is not zero, then the trajectory is again a null geodesic. The conditions on the curvature needed to have the momentum parallel to the four-velocity are determ~ned. Helicity properties are also discussed.

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