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Journal of Physics B Atomic Molecular and Optical Physics

Electron translation phase factors

Derrick S. F. Crothers, R. J. S. Lee

Published Nov 1, 2000• 5 citations
Publisher

Abstract

In `On the quantum mechanics of particles with classically assigned trajectories', Barton and Calogeracos (1996 Proc. R. Soc. A 452 1167) find that the wavefunction surprisingly acquires an overall phase factor of the form exp(+i∫ 0 t E ( t ') d t '), surprising in that the conjugate was expected, with E the relative kinetic energy. It is shown that, with the correct interpretation in terms of electron translation phase factors, there is no surprise and the effect is well known experimentally and theoretically in charge transfer and ionization in ion-atom collisions.

DOI
10.1088/0953-4075/33/22/102

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In `On the quantum mechanics of particles with classically assigned trajectories', Barton and Calogeracos (1996 Proc. R. Soc. A 452 1167) find that the wavefunction surprisingly acquires an overall phase factor of the form exp(+i∫ 0 t E ( t ') d t '), surprising in that the conjugate was expected, with E the relative kinetic energy. It is shown that, with the correct interpretation in terms of electron translation phase factors, there is no surprise and the effect is well known experimentally and theoretically in charge transfer and ionization in ion-atom collisions.
We consider the state vector of a system containing a particle, in the approximation treating the particle (mass = m) as if it followed a classically prescribed trajectory R(t). Since a real particle has position and momentum operators r and p of its own, one must find a way effectively to demote these from dynamical variables to mere time-dependent parameters. The traditional method is to subject the Hamiltonian system to a formal constraint r — R(t) = 0. Here we consider instead the particle trapped in a sufficiently tight-binding potential V(r — R(t)); the conclusions remain the same but the reasoning becomes much more accessible. The state vector acquires an overall phase factor exp{—i ft dt' (-1/2mR2(t'))} surprising in that the integrand features not the enforced kinetic energy, but its negative. We elucidate the physics of this phase factor, sketch a scenario for verifying it experimentally and show that it persists essentially unchanged when the trapped particle is coupled to the Maxwell field. The standard adiabatic approximation routinely applied misses this factor altogether, but a more careful modification recovers the right result.
Abstract The investigation of cold interactions between ions and neutrals has recently emerged as a new scientific frontier at the interface of physics and chemistry. Here, we report a study of charge-transfer (CT) collisions of Rb atoms with N2+{}_{2}^{+}2+​2+ and O2+{}_{2}^{+}2+​2+ ions in the mK regime using a dynamic ion-neutral hybrid trapping experiment. We observe markedly different CT kinetics and dynamics for the different systems and reaction channels studied. While the kinetics in some channels are consistent with classical capture theory, others show distinct non-universal dynamics. The experimental results are interpreted with the help of classical-capture, quasiclassical-trajectory and quantum-scattering calculations using ab-initio potentials for the highly excited molecular states involved. The theoretical analysis reveals an intricate interplay between short- and long-range effects in the different reaction channels which ultimately determines the CT dynamics and rates. Our results illustrate salient mechanisms that determine the efficiency of cold molecular CT reactions.
If a time-dependent Hamiltonian is allowed to evolve adiabatically, and if it returns to its original form, then the ground state wavefunction must have picked up the dynamic or(and) the geometric phase factor(s) due to some interaction during the above evolution. Here, (i) we invoke the Pancharatnam's notion of phase retardation to show that the microscopic origin of Berry's phase is due to a change in the phase velocity (of a wavefunction), and (ii) the dynamic phase factor is shown to have its origin in the group velocity of a wavefunction. We also expose that the emitted photon's polarization during an electronic transition has its origin in the changes of the phase velocity of the electron wavefunction. Here, we prove the above statements, (i) and (ii), such that they are not due to some interpretational issues, hence, an exposeˊ{\rm \acute{e}}eˊ.
The investigation of cold interactions between ions and neutrals has recently emerged as a new scientific frontier at the interface of physics and chemistry. Here, we report a study of charge-transfer (CT) collisions of Rb atoms with N[Formula: see text] and O[Formula: see text] ions in the mK regime using a dynamic ion-neutral hybrid trapping experiment. We observe markedly different CT kinetics and dynamics for the different systems and reaction channels studied. While the kinetics in some channels are consistent with classical capture theory, others show distinct non-universal dynamics. The experimental results are interpreted with the help of classical-capture, quasiclassical-trajectory and quantum-scattering calculations using ab-initio potentials for the highly excited molecular states involved. The theoretical analysis reveals an intricate interplay between short- and long-range effects in the different reaction channels which ultimately determines the CT dynamics and rates. Our results illustrate salient mechanisms that determine the efficiency of cold molecular CT reactions.