Scattering of wave packets with phases

Abstract

A general problem of 2 → N f scattering is addressed with all the states being wave packets with arbitrary phases. Depending on these phases, one deals with coherent states in (3 + 1) D, vortex particles with orbital angular momentum, the Airy beams, and their generalizations. A method is developed in which a number of events represents a functional of the Wigner functions of such states. Using width of a packet σ p / p as a small parameter, the Wigner functions, the number of events, and a cross section are represented as power series in this parameter, the first non-vanishing corrections to their plane-wave expressions are derived, and generalizations for beams are made. Although in this regime the Wigner functions turn out to be everywhere positive, the cross section develops new specifically quantum features, inaccessible in the plane-wave approximation. Among them is dependence on an impact parameter between the beams, on phases of the incoming states, and on a phase of the scattering amplitude. A model-independent analysis of these effects is made. Two ways of measuring how a Coulomb phase and a hadronic one change with a transferred momentum t are discussed.

Relativistic quantum-mechanical description of twisted paraxial electron and photon beams

“…A frequently encountered inexactness [18][19][20] is the superfluous factor exp (ikz). Other quantummechanical solutions are 3D-localized particle wavepackets [18,[24][25][26][27][28][29]. Quantum numbers of twisted photons have been determined in Ref.…”

Effects of the transverse coherence length in relativistic collisions

“…The general formula (6), in which the incoming states are described with the Wigner functions, is totally equivalent to the standard approach (see, e. g., [36,37]) with the wave functions or the density matrices. The current representation, however, is more illustrative when dealing with the spatially localized wave packets instead of plane waves, and allows one to conveniently describe effects of the finite impact parameters [1] and of the non-Gaussianity of the packets [11].…”

Quantum scattering beyond the plane-wave approximation

“…Note that in a more general case of arbitrary boost, one should deal with a tensor σ ij instead of the scalar σ p . As a result, the small parameter of the problem no longer preserves its simple form (2) [5]. For ultrarelativistic energies, |⟨p⟩| ≫ m, the de Broglie wave length is much smaller than the Compton one, which does not mean, however, that the wave nature of particles does not reveal itself in scattering.…”

“…On the other hand, a proper discussion of its limits of applicability in the scattering problems seems to be absent in literature, which is a bit disturbing, especially when striving for higher-order radiative corrections. There are also important examples from the collider physics, atomic physics, neutrino physics, etc., in which the plane-wave model becomes inapplicable -see, for instance, [1,2,3,4,5,6] and references therein.…”

“…Possible applications of these states to the hadronic physics have been discussed in Refs. [5,15,16].…”