Title: Symmetry and the Geometric Phase in Ultracold Hydrogen-Exchange Reactions,
Abstract: Quantum reactive scattering calculations are reported for the ultracold
hydrogen-exchange reaction and its non-reactive atom-exchange isotopic
counterparts, proceeding from excited rotational states. It is shown that while
the geometric phase (GP) does not necessarily control the reaction to all final
states one can always find final states where it does. For the isotopic
counterpart reactions these states can be used to make a measurement of the GP
effect by separately measuring the even and odd symmetry contributions, which
experimentally requires nuclear-spin final-state resolution. This follows from
symmetry considerations that make the even and odd identical-particle exchange
symmetry wavefunctions which include the GP locally equivalent to the opposite
symmetry wavefunctions which do not. This equivalence reflects the important
role discrete symmetries play in ultracold chemistry generally and highlights
the key role ultracold reactions can play in understanding fundamental aspects
of chemical reactivity.