Topological angular momentum in electron exchange excitation of a single atom

Abstract

In a single free two-valence-electron atom, the motion of the electron spin is a consequence of quantum statistics and the Pauli exclusion principle. Subsequently, during an electron impact exchange excitation from a 1 S 0 M S = 0 to a 3 S 1 M S = 0 state, the electron spin is "parallel transported" around a closed path with a geometrical Berry phase of π radians creating an aligned exchange spin angular momentum. This alignment is observed via the Stokes parameter P 2 of the photon decay into a 3 P state. The geometric phase is in addition to the dynamic phase. Measurements from zinc and mercury atoms in different laboratories show the effect close to the excitation threshold where there are no competing excitation processes. Similar effects are expected in other atomic and molecular quantum scattering processes where comparable geometrical or topological paths exist. Electron quantum scattering theories use antisymmetrized wave functions but none include this geometrical exchange angular momentum.

Comment II on “Topological angular momentum in electron exchange excitation of a single atom”

“…We have no doubt that tremendous experimental effort and attention to detail was exercised in generating the experimental e-Zn results. As elaborated in [1] and [3], the data appear to be consistent against all cross checks performed to date and hence remain a mystery that we cannot explain at the present time. Figure 1, however, shows that the experimental data obtained in Münster for the e-Hg collision system nearly 30 years ago [6], which were used in [3] as further supporting evidence for the need to include a Berry-type phase, can at least be qualitatively reproduced by the DBSR model described in [7], without making any further changes to the method or the accompanying computer code.…”

“…After discussing the P 2 /P e discrepancy between theory and experiment once again for e-Zn excitation in their subsequent paper [3], to which this Comment is directed, Williams et al conclude with the firm recommendation: "The task remains for theory to include a topological nondynamical phase." No suggestion, however, is made how this might or should be done.…”

Alignment of the (3d104s5s)3S1

“…The fact that P 2 is non-zero below the first cascade threshold for the analogous 6 3 P 2 -7 3 S 1 transition in Hg should not be taken as support for the Perth results [17,18,23,33]; Hg is much heavier, the 7 3 S 1 state is intermediately coupled, and some level of Mott scattering is very likely.…”

“…The Perth experiment has been carefully checked and redone with different components and reassembled apparatuses thrice [9,23]. One possible explanation for the discrepancy is that there might be a strong negative ion resonance in the energy region between 6.7 and 7.6 eV that decays into the 5 3 S 1 state and that is not well-LS coupled.…”

Relativistic calculations for spin-polarization of elastic electron—mercury scattering

“…To date, there are considerable attempts to study, both theoretically and experimentally, the elastic electron scattering by the Hg atoms using various formulas, methods and models. But, the agreement between theoretical calculations and experimental data of electron spin-polarization parameters resulting from this collision is not quite satisfactory, specially at lower incident energies [14,15]. Many earlier investigations on the e − -Hg scattering can be traced in the review articles [3,16].…”