# 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:

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)

- OSTI Identifier:
- 1575841

- Alternate Identifier(s):
- OSTI ID: 1499272

- Grant/Contract Number:
- FG02-97ER-41014; FG02-97ER41014

- Resource Type:
- Published Article

- Journal Name:
- Physics Letters B

- Additional Journal Information:
- Journal Name: Physics Letters B Journal Volume: 777 Journal Issue: C; Journal ID: ISSN 0370-2693

- Publisher:
- Elsevier

- Country of Publication:
- Netherlands

- 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. Netherlands: N. p., 2018.
Web. https://doi.org/10.1016/j.physletb.2017.12.063.
```

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

```
Miller, Gerald A. Thu .
"Non-universal and universal aspects of the large scattering length limit". Netherlands. https://doi.org/10.1016/j.physletb.2017.12.063.
```

```
@article{osti_1575841,
```

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 B},

number = C,

volume = 777,

place = {Netherlands},

year = {2018},

month = {2}

}

https://doi.org/10.1016/j.physletb.2017.12.063

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

_{S}(r) (red) solid, r$\phi$

_{H}(r) (blue) dashed, and r$\phi$

_{0}(r) (black) dot-dashed, r$\phi$

_{S}D (r) (black) solid, and r$\phi$

_{E}(r) (black) dashed for $a/R$ = 10, 000. Dimensionless units are used (see text).

Works referencing / citing this record:

##
Universal short-range correlations in bosonic helium clusters

journal, January 2020

- Bazak, B.; Valiente, M.; Barnea, N.
- Physical Review A, Vol. 101, Issue 1

Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*