Scattering Theory: The Quantum Theory of Nonrelativistic Collisions

Local projections of low-momentum potentials

“…We start by considering phase shifts, using the distorted wave born approximation (DWBA) [31] to expand [11]. Even though the initial interaction is generally non-local, it is a nearly local potential at very low momentum.…”

Study of the Electroweak Symmetry Breaking Sector for the LHC

“…To see the full proofs, including those of the analytical properties of the S-matrix elements, see Refs. [139,140]. Note that, because of the presence of a left cut due to the terms E log(−s/µ 2 ) on the amplitudes 3 , the so-called forward dispersion relations cannot be used.…”

Atom scattering from disordered surfaces in the sudden approximation: double collisions effects and quantum liquids

“…Here |k is the incident state (t = −∞) and Ω + is the Møller operator, which propagates |k to the state at the time of collision at t = 0. In the Born approximation it is assumed that |k+ ≈ |k [36], which yields…”

“…(31) is fully diagonal, the n th surface particle kinetic energy operator F n on the second line is diagonal in q, and the interaction operator H n on the third line is not diagonal. In the Born approximation one essentially retains only the fully diagonal (kinetic) term [36]. Ideally one would like to diagonalize the complete operator acting on |Φ n , which would solve the scattering problem.…”

“…Starting from the first principles of non-relativistic scattering theory, the exact expression for the T-matrix element is [36]:…”