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Quantum reactive scattering calculations are reported for the ultracoldhydrogen-exchange reaction and its non-reactive atom-exchange isotopiccounterparts, proceeding from excited rotational states. It is shown that whilethe geometric phase (GP) does not necessarily control the reaction to all finalstates one can always find final states where it does. For the isotopiccounterpart reactions these states can be used to make a measurement of the GPeffect by separately measuring the even and odd symmetry contributions, whichexperimentally requires nuclear-spin final-state resolution. This follows fromsymmetry considerations that make the even and odd identical-particle exchangesymmetry wavefunctions which include the GP locally equivalent to the oppositesymmetry wavefunctions which do not. This equivalence reflects the importantrole discrete symmetries play in ultracold chemistry generally and highlightsthe key role ultracold reactions can play in understanding fundamental aspectsof chemical reactivity.

Symmetry and the Geometric Phase in Ultracold Hydrogen-Exchange Reactions