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42313-G6
Three-Body Processes in Degenerate Quantum Gases: Role and Lifetimes of Three-Body Resonances

Viatcheslav Kokoouline, University of Central Florida

Resonances in the three-body collisions,
quantum molecular dynamics with a conical intersection. We have developed a generic method to obtain lifetimes of three-body resonances. The method uses 
hyper-spherical coordinates and a complex absorbing potential placed at a large hyper-radius. Large values of the 
hyper-radius correspond to the system dissociated either into 3 free particles (channel 1+1+1) or a dimer+particle
configuration (channel 2+1). The present method allowed us to analyze the branching ratio for different 2+1 
(different rovibrational states of the dime) and 1+1+1 channels because the wave-functions of the resonances are
available. We have applied the developed method to the following problems. (1) We have tested the method on a model system of three bosons interacting through a potential with a 
barrier. (2) We have also calculated lifetimes of very-long range Efimov quasi-states. Such states have recently been 
created in the ultra- cold gas of cesium atoms. Positions and lifetimes of the obtained Efimov quasi-states are in very 
good agreement with available results obtained using the R-matrix approach. The method is quite general and can be 
applied for a number of applications in chemical and atomic physics, where the dissociation involves several coordinates.  (3) We have applied the above method to obtain lifetimes and positions of resonances of predissociated
vibrational levels of the 22A' electronic state of the H3 molecule. The three-body recombination rate coefficient for the 
H+H+H -> H2+H process has also been estimated. For these calculations, we had to take into account the two lowest, 
12A' and 22A', coupled potential surfaces of the H3 molecule. The two surfaces are degenerate at the equilateral
geometry (conical intersection). To deal with the conical intersection, we have developed a diabatization procedure that
represents accurately two surfaces coupled by the non-Born-Oppenheimer vibronic coupling. The non-diagonal as well
as diagonal matrix elements of the diabatic potential are extracted from the ab initio adiabatic potential surfaces of the
molecule. There is no need to use ab initio non-adiabatic couplings between the potential surfaces to construct the
diabatic potential. The diabatization procedure is general enough and can be used to represent the quantum molecular
dynamics on coupled potential surfaces of other molecules, where a conical intersection is expected to play an important
role. (4) We have also considered the problem of the H-+H2(v,j) -> H-+H2(v',j') scattering, its isotopic variants, and also such related processes as H-+HD(v,j) -> D-+H2(v',j'). These processes are important for current experiments in
ionic traps.  Now we use the method on a regular basis in our study of electron-molecule scattering (dissociative
recombination of molecular ions). A time-dependent implementation is planned. The time-dependent approach can be
used to study for example such processes as two-photon ionization of an atom or dissociative ionization in the presence
of a strong time-dependent laser field. We have developed an R-matrix method for three-body scattering that also uses the slow variable
discretization. The method has been tested on a model three-body system and will be applied in the coming months to
one of the reactions of the “clean coal” technology, C+O2 -> CO+O at a relatively high temperature (>1000K) .
Three- and four-body selection rules We have derived selection rules for ultracold three- and four-body collisions. One aspect of the interaction in
the three- (or four-) body system of identical particles is the selection rules determining allowed and forbidden final
states of the system after a scattering event. Based on the selection rules, we construct correlation diagrams between
different configurations before and after the event. In particular, we describe a possible fragmentation of the system into
one free particle (or a dimer) and a dimer, which can be used, for example, to identify possible decay products of 
quasi-stationary three-(or four-) body states or three- (or four-) body recombination.
Overview and participation of students Two graduate students have been actively participated in the project. One of them Juan Blandon, has
coauthored two publications and another is in preparation. His continues to receive a financial support from the
McKnight Doctoral fellowship by the Florida Education Fund. The second student, Nicolas Douguet, has participated 
in the study of selection rules for three-body scattering. In addition to the graduate students, during the 2007-2008
academic year, I was supervising a high-school student, Kristen Zych (Lake Brantley High School in Seminole county),
who was involved in the current project: She has prepared a research project for the Florida State Science Fair and was
awarded with the second prize for the project.

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