Nonuniversal and universal aspects of the large scattering length limit
Abstract
The momentum density, n (k) of interacting manybody Fermionic systems is studied (for k >k_{F}) using examples of several wellknown twobody interaction models. It is shown that n (k) can be approximated by a zerorange model for momenta k less than about 0.1 /r_{e}, where r_{e} the effective range. If the scattering length is large and one includes the effects of a fixed value of r_{e} ≠ 0, n (k) is almost universal for momenta k up to about 2 /r_{e}. However, n (k) can not be approximated by a zerorange model for momenta k greater than about 1 / (a r_{e}^{2})^{1/3}, where a is the scattering length, and if one wishes to maintain a sum rule that relates the energy of a two component Fermigas to an integral involving the density. We also show that the short separation distance, s, behavior of the pair density varies as s^{6}.
 Publication:

Physics Letters B
 Pub Date:
 February 2018
 DOI:
 10.1016/j.physletb.2017.12.063
 arXiv:
 arXiv:1702.03370
 Bibcode:
 2018PhLB..777..442M
 Keywords:

 Nuclear Theory;
 Condensed Matter  Quantum Gases;
 Nuclear Experiment;
 Physics  Atomic and Molecular Clusters;
 Physics  Atomic Physics
 EPrint:
 6 pages 2 figures. This version corrects several errors in the previous version. The analysis is deepened, and one conclusion is changed