On-shell three-body multiple scattering equations

On-shell T-matrices in multiple scattering

The transition operator T for the scattering of a particle from N potentials Vj(x) can be expanded into a series featuring the transition operators tj associated with the individual potentials. For Vj(x) both absolutely and square integrable in x, we show, using an analytic continuation argument, that if T is on-shell, i.e. in < k|T (σ2 ± i0)|k′ >, |k| = |k′| = σ, then each tj is also on-shell....

Faddeev-type equations for three-body symmetry violating scattering amplitudes

Relativistic three-particle scattering equations.

We derive a set of relativistic three-particle scattering equations in the three-particle c.m. frame employing a relativistic three-particle propagator suggested long ago by Ahmadzadeh and Tjon in the c.m. frame of a two-particle subsystem. We make the coordinate transformation of this propagator from the c.m. frame of the two-particle subsystem to the three-particle c.m. frame. We also point o...

Scattering Amplitudes from Three-Particle Equations

We here use our non-perturbative, cluster decomposable relativistic scattering formalism to calculate photon-spinor scattering, including the related particle-antiparticle annihilation amplitude. We start from a three-body system in which the unitary pair interactions contain the kinematic possibility of single quantum exchange and the symmetry properties needed to identify and substitute antip...

The Effects of Three-Body Scattering on Differential Reflectivity Signatures

Effects of three-body scattering on reflectivity signatures at S and C bands can be seen on the back side of large reflectivity storm cores that contain hail. The fingerlike protrusions of elevated reflectivity have been termed flare echoes or ‘‘hail spikes.’’ Three-body scattering occurs when radiation from the radar scattered toward the ground is scattered back to hydrometeors, which then sca...