Solutions of the Schrödinger equation for anisotropic dipole-dipole interaction plus van der Waals interaction
By generalizing Gao's approach [Phys. Rev. A 58, 1728 (1998)1050-294710.1103/PhysRevA.58.1728] for solving the Schrödinger equation for an isotropic van der Waals (vdW) potential to the systems with a multiscale anisotropic long-range interaction, we derive the solutions for the Schrödinger equ...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2025-05-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.023162 |
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| Summary: | By generalizing Gao's approach [Phys. Rev. A 58, 1728 (1998)1050-294710.1103/PhysRevA.58.1728] for solving the Schrödinger equation for an isotropic van der Waals (vdW) potential to the systems with a multiscale anisotropic long-range interaction, we derive the solutions for the Schrödinger equation for an anisotropic dipole-dipole interaction plus an isotropic attractive vdW potential, i.e., C_{d}(1−3cos^{2}θ)/r^{3}−C_{6}/r^{6}, which is projected to the subspace with angular momentum l≤l_{cut}, with l_{cut} being an arbitrary angular-momentum cutoff. Here θ is the polar angle of the coordinate r and r=|r|. The asymptotic behaviors of these solutions for r→0 and r→∞ are obtained. The generalization of our approach for the case of an anisotropic vdW potential is also discussed. These results can be used in the research of collisions and chemical reactions between ultracold polar molecules in a static electric field. Our approach to derive the solutions can be applied to the systems with a general long-range potential ∑_{λ=2}^{λ_{max}}V_{λ}(θ,φ)/r^{λ}, with φ being the azimuthal angle of r, and thus can be used in collision problems between various kinds of molecules, ions, or atoms (e.g., the collisions between ultracold dipolar atoms). |
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| ISSN: | 2643-1564 |