Scattering theory, multiparticle detection, and time

Abstract

We consider the theory of multiple-particle fragmentation processes in the light of modern multihit position-sensitive detection. First we give a new formulation of time-independent many-body scattering theory as a direct generalisation of standard text-book two-body potential scattering but in such a way as to emphasise position rather than momentum detection. Noteworthy is that classical asymptotic motion of fragments is shown to emerge from this quantum-mechanical timeindependent theory and enables the definition of a classical time parameter. This in turn allows a transition to be made to a time-dependent scattering theory, even in the case where all Hamiltonians are time-independent. Such a time-dependent description is the basis of the imaging theorem, which connects position detection to momentum detection.

Autonomous quantum to classical transitions and the generalized imaging theorem

“…The wave function is simply an 'information field' whose squared modulus of the amplitude gives, via Born's rule, the probability to detect a particle at a certain position or momentum. Recently we have emphasized [10] that this simple interpretation of the measurement process gives all standard results of many-body scattering theory used successfully to reproduce the results of countless experiments on fragmentation processes in atomic, molecular, and nuclear physics. From the IT, the results of detection of different particles at different phase space points will be compatible with their classical motion, even though describable by a quantum wave function.…”

Quantum scattering with semiclassical asymptotic motion

“…Our development follows the derivation of timeindependent many-particle scattering theory presented in Ref. [4]. For simplicity, and to connect with Ref.…”

“…Although in Ref. [4] and in the preceding section, the emphasis is on particle detection at fixed positions, the theory is seemingly at variance with modern coincident detection of differing particles at different times. Indeed the timing of each particle is necessary to define the classical momenta.…”

“…Fig. (4) shows the E = 0.37 eV coincidence data from [38] as a function of ∆T from a pair of detectors arranged for back-to-back ejection r1 = −r 2 at equal distances r 1 = r 2 = 2 cm from the reaction volume. The fit is the macroscopic coordinate distribution from Eq.…”

“…This restores the fixed energy such that the resulting elements of the theory, for example the transition matrix, the scattering ma-trix and Møller operators, are all time independent and expressed in terms of the time-independent interaction potentials. Recently [4], following Gerjuoy [5], we have given a derivation of time-independent scattering theory which avoids the redundant introduction and elimination of time. This theory follows the text-book derivation of time-independent potential scattering but generalized to multi-particle, multi-channel collisions.…”