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42313-G6
Three-Body Processes in Degenerate Quantum Gases: Role and Lifetimes of Three-Body Resonances
Lifetimes of three-body states
We have developed a generic method of calculation of 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 tested the method on a model system of three bosons interacting through a potential with a barrier. 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 has been already applied for a number of applications in chemical and atomic physics, where the dissociation involves several coordinates.
Now we use the method on a regular basis in our study of electron-molecule scattering (dissociative recombination of molecular ions). 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.
Two-channel three-body states: bound states and resonances
The method described above has been generalized for systems having several channels (i.e. the 3-body potentials with two or more components). We have calculated bound states and resonances for two different two-channel three-body potentials : One potential is a model potential corresponding to the Van der Waals potential at large inter-particle separations. The second potential is the actual two-channel potential of the two lowest electronic states of the H3 molecule. The potential consists of two surfaces, having a conical intersection. The two surfaces interact mainly through the Jahn-Teller coupling, which is the strongest near the intersection. Correspondingly, the vibrational motion of quasi-stationary states of the upper surface are strongly influenced by the Jahn-Teller coupling. The two-channel vibrational wave functions have the geometrical phase associated with the vibration around the conical intersection.
Three-body selection rules
We have derived selection rules for ultracold three-body collisions. One aspect of the interaction in the three-body system of identical particles is the selection rules determining allowed and forbidden final states of the system after a scattering process. Based on the selection rules, we construct correlation diagrams between the different configurations before and after a collision. In particular, we describe a possible fragmentation of the system into one free particle and a dimer, which can be used, for example, to identify possible decay products of quasi-stationary three-body states or three-body recombination.
Overview and participation of students
During the second financial year of the project a substantial progress has been made. 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. Since the beginning of the project in 2005, it was particularly successful in encouraging students to study physics and quantum chemistry and do research. In addition to the graduate students, since September 2007, I am supervising a high-school student, Kristen Zych, who is involved in the current project: She is preparing in my group a project for a regional science fair. Because the students have had an alternative financial support during the 2005-2006 academic year, I could save some money and use it during the year 2007.
