Reaction imaging in uniform electric and magnetic fields

Abstract

We extend our recent analysis (Briggs and Feagin 2013 J. Phys. B: At. Mol. Opt. Phys. 46 025202) of the imaging theorem relating the asymptotic coordinate and momentum wavefunctions describing a fragmentation reaction to the classical time-of-flight trajectory of the scattered fragments extracted by uniform and parallel electric and magnetic fields onto a position-sensitive detector.

Autonomous quantum to classical transitions and the generalized imaging theorem

“…The extent of the emergence of classical motion described by the IT is seen by direct comparison of equation (6) and the exact equation (1). In the latter the relation between the non-commuting variables r and p is nondeterministic in that the spatial wave function at position r f and time t f is given by a transform at time t i of the momentum wave function involving integration over all possible values of p. By contrast, the IT of equation (6) expresses the result that the asymptotic wave function at r f and t f is given simply by the semiclassical wavefunction for the system emerging at time t i from the point r i but weighted by the exact momentum wave function at time t i of particles with momentum p i , where r p , i i and r f are classical variables connected deterministically by the classical trajectory.…”

“…Besides the familiar spreading of the wavefunction with time, one sees that for z 10 f > and t 200 > there is convergence to the IT result. It is instructive to generalize this example to include accelerated motion due to a constant force F acting along the positive z axis, an example relevant to electric-field extraction and detection (F qE = ) [6] as well as atom interferometry in a gravitational field (F=mg) [9]. The classical action is given by [1] (7) is unchanged, p z m t d d i f = .…”

“…This constant-force action S F  is essentially a coordinate-translated version of the free-particle action S 0 . Hence, the accelerated state evolves as a Galilean-like boost of the free propagation description and takes on the exact form [6] z t z Ft m t , e 2 , . 17…”

“…In practice, rather than measure p f , one can also measure of course r f and the time of flight for each detector hit to determine r p , i i . See[6].…”

Scattering theory, multiparticle detection, and time

“…The use of the IT in connection with modern multi-particle detection by electric and magnetic field extraction is discussed in detail in Ref. [7].…”