Pseudopotential of an interaction with a power-law decay in two-dimensional systems
| Autor: | Sheng-Min Shih, Daw-Wei Wang |
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| Rok vydání: | 2009 |
| Předmět: | |
| Zdroj: | Physical Review A. 79 |
| ISSN: | 1094-1622 1050-2947 |
| Popis: | We analytically derive the general pseudopotential operator of an arbitrary isotropic interaction for particles confined in two-dimensional (2D) systems using the frame work developed by Huang and Yang for three-dimensional scattering. We also analytically derive the low-energy dependence of the scattering phase shift for an arbitrary interaction with a power-law decaying tail, ${V}_{2\text{D}}(\ensuremath{\rho})\ensuremath{\propto}{\ensuremath{\rho}}^{\ensuremath{-}\ensuremath{\alpha}}$ (for $\ensuremath{\alpha}g2$). We apply our results to the 2D dipolar gases $(\ensuremath{\alpha}=3)$ as an example, calculating the momentum and dipole moment dependences of the pseudopotential for both $s$- and $p$-wave scattering channels if the two scattering particles are in the same 2D layer. Results for the $s$-wave scattering between particles in two different (parallel) layers are also investigated. Our results can be directly applied to the systems of dipolar atoms and/or polar molecules in a general 2D geometry. |
| Databáze: | OpenAIRE |
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