Spectral Resolution of Resonant Positron-Molecule Annihilation due to Multimodes.

The annihilation spectra of positrons on molecules, as a function of incident positron energy, are typically dominated by relatively sharp features that have been identified as vibrational Feshbach resonances (VFR) mediated by fundamental vibrations.\footnote{\small G. F. Gribakin, J. A. Young, C. M. Surko, {\it Rev. Mod. Phys.} {\bf 82}, 2557 (2010).} The theory of Gribakin and Lee is successful in describing the annihilation spectra for selected small molecules where the annihilation is dominated by a small number of dipole-allowed modes.\footnote{\small G. F. Gribakin, C. M. R. Lee, {\it Phys. Rev. Lett.} {\bf 97}, 193201 (2006).} However, in most molecules, these sharp peaks ride on a broad background of enhanced annihilation. There is indirect evidence that this effect is due to a dense set of combination and overtone resonances.\footnote{\small A. C. L. Jones, {\it et al.}, {\it Phys. Rev. Lett.} {\bf 108}, 093201 (2012).} An extension of the Gribakin-Lee theory can be used to describe VFR's due to these multimodes, where the important effect of multiple decay channels is also included. Prospects for resolving these features using a new high-resolution positron beam will be discussed.