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Advanced textbooks in physics

Beyond the Born Approximation

Published Aug 4, 2017• 0 citations
Publisher
DOI
10.1142/9781786343031_0011

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•Jan 1, 2020•14 citations
We investigate the condensate wave function and elementary excitations of strongly interacting bosonic polar molecules in a harmonic trap, treating the scattering amplitude beyond the standard first Born approximation (FBA). By using an appropriate trial wave function in the variational method, effects of the leading-order correction beyond the FBA have been investigated and shown to be significantly enhanced when the system is close to the phase boundary of collapse. How such a leading-order effect of going beyond the FBA can be observed in a realistic experiment is also discussed.
The method of many-body Green's functions is developed for arbitrary systems of electrons and nuclei starting from the full (beyond Born-Oppenheimer) Hamiltonian of Coulomb interactions and kinetic energies. The theory presented here resolves the problems arising from the translational and rotational invariance of this Hamiltonian that afflict the existing many-body Green's function theories. We derive a coupled set of exact equations for the electronic and nuclear Green's functions and provide a systematic way to approximately compute the properties of arbitrary many-body systems of electrons and nuclei beyond the Born-Oppenheimer approximation. The case of crystalline solids is discussed in detail.
We report on deviations beyond the Born-Oppenheimer approximation in potassium interatomic potentials. Identifying three previously unknown d-wave Feshbach resonances, we significantly improve the understanding of the K39 interatomic potentials. Combining these observations with the most recent data on known inter- and intraisotope Feshbach resonances, we show that Born-Oppenheimer corrections can be determined from atomic collisional properties alone and that significant differences between the homo- and heteronuclear cases appear.