## Non-universal and universal aspects of the large scattering length limit

## Abstract

The momentum density, of interacting many-body Fermionic systems is studied (for ) using examples of several well-known two-body interaction models. It is shown that can be approximated by a zero-range model for momenta k less than about , where the effective range. If the scattering length is large and one includes the effects of a fixed value of , is almost universal for momenta k up to about . However, can not be approximated by a zero-range model for momenta k greater than about , where a is the scattering length, and if one wishes to maintain a sum rule that relates the energy of a two component Fermi-gas to an integral involving the density. We also show that the short separation distance, s, behavior of the pair density varies as .

- Authors:

- Univ. of Washington, Seattle, WA (United States)

- Publication Date:

- Research Org.:
- Univ. of Washington, Seattle, WA (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1499272

- Grant/Contract Number:
- FG02-97ER41014

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics Letters. Section B

- Additional Journal Information:
- Journal Volume: 777; Journal Issue: C; Journal ID: ISSN 0370-2693

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Miller, Gerald A. Non-universal and universal aspects of the large scattering length limit. United States: N. p., 2018.
Web. doi:10.1016/j.physletb.2017.12.063.
```

```
Miller, Gerald A. Non-universal and universal aspects of the large scattering length limit. United States. doi:10.1016/j.physletb.2017.12.063.
```

```
Miller, Gerald A. Wed .
"Non-universal and universal aspects of the large scattering length limit". United States. doi:10.1016/j.physletb.2017.12.063. https://www.osti.gov/servlets/purl/1499272.
```

```
@article{osti_1499272,
```

title = {Non-universal and universal aspects of the large scattering length limit},

author = {Miller, Gerald A.},

abstractNote = {The momentum density, of interacting many-body Fermionic systems is studied (for ) using examples of several well-known two-body interaction models. It is shown that can be approximated by a zero-range model for momenta k less than about , where the effective range. If the scattering length is large and one includes the effects of a fixed value of , is almost universal for momenta k up to about . However, can not be approximated by a zero-range model for momenta k greater than about , where a is the scattering length, and if one wishes to maintain a sum rule that relates the energy of a two component Fermi-gas to an integral involving the density. We also show that the short separation distance, s, behavior of the pair density varies as .},

doi = {10.1016/j.physletb.2017.12.063},

journal = {Physics Letters. Section B},

number = C,

volume = 777,

place = {United States},

year = {2018},

month = {1}

}