Anisotropic pseudo-potential for polarized dilute quantum gases

Details Anisotropic pseudo-potential for polarized dilute quantum gases Anisotropic pseudo-potential for polarized dilute quantum gases

2002-12-26

arxiv.org/abs/cond-mat/0212597v1

Phys. Rev. A 67, 033607 (2003)

Physics

Condensed Matter

Soft Condensed Matter

1 Fig, submitted to Phys. Rev. A

Scientific paper

10.1103/PhysRevA.67.033607

Anisotropic pseudopotential relevant to collisions of two particles polarized by external field is rigorously derived and its properties are investigated. Such low-energy pseudopotential may be useful in describing collective properties of dilute quantum gases, such as molecules polarized by electric field or metastable $^3P_2$ atoms polarized by magnetic field. The pseudopotential is expressed in terms of reactance (K--) matrix and derivatives of Dirac delta-function. In most applications it may be represented as a sum of traditional spherically-symmetric contact term and anisotropic part. The former contribution may be parameterized by a generalized scattering length. The anisotropic part of pseudopotential may be characterized by off-diagonal scattering length for dipolar interactions and off-diagonal scattering volume for quadrupolar interactions. Two-body matrix element of the pseudopotential in a basis of plane waves is also derived.

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