# Precise determination of lattice phase shifts and mixing angles

## Abstract

Here, we introduce a general and accurate method for determining lattice phase shifts and mixing angles, which is applicable to arbitrary, non-cubic lattices. Our method combines angular momentum projection, spherical wall boundaries and an adjustable auxiliary potential. This allows us to construct radial lattice wave functions and to determine phase shifts at arbitrary energies. For coupled partial waves, we use a complex-valued auxiliary potential that breaks time-reversal invariance. We benchmark our method using a system of two spin-1/2 particles interacting through a finite-range potential with a strong tensor component. We are able to extract phase shifts and mixing angles for all angular momenta and energies, with precision greater than that of extant methods. We discuss a wide range of applications from nuclear lattice simulations to optical lattice experiments.

- Authors:

- Publication Date:

- Research Org.:
- North Carolina State Univ., Raleigh, NC (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1261215

- Alternate Identifier(s):
- OSTI ID: 1361209

- Grant/Contract Number:
- FG02-03ER41260

- Resource Type:
- Published Article

- Journal Name:
- Physics Letters B

- Additional Journal Information:
- Journal Name: Physics Letters B Journal Volume: 760 Journal Issue: C; Journal ID: ISSN 0370-2693

- Publisher:
- Elsevier

- Country of Publication:
- Netherlands

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; nuclear structure; scattering phase shifts; angular momentum projection

### Citation Formats

```
Lu, Bing-Nan, Lähde, Timo A., Lee, Dean, and Meißner, Ulf-G. Precise determination of lattice phase shifts and mixing angles. Netherlands: N. p., 2016.
Web. doi:10.1016/j.physletb.2016.06.081.
```

```
Lu, Bing-Nan, Lähde, Timo A., Lee, Dean, & Meißner, Ulf-G. Precise determination of lattice phase shifts and mixing angles. Netherlands. doi:10.1016/j.physletb.2016.06.081.
```

```
Lu, Bing-Nan, Lähde, Timo A., Lee, Dean, and Meißner, Ulf-G. Thu .
"Precise determination of lattice phase shifts and mixing angles". Netherlands. doi:10.1016/j.physletb.2016.06.081.
```

```
@article{osti_1261215,
```

title = {Precise determination of lattice phase shifts and mixing angles},

author = {Lu, Bing-Nan and Lähde, Timo A. and Lee, Dean and Meißner, Ulf-G.},

abstractNote = {Here, we introduce a general and accurate method for determining lattice phase shifts and mixing angles, which is applicable to arbitrary, non-cubic lattices. Our method combines angular momentum projection, spherical wall boundaries and an adjustable auxiliary potential. This allows us to construct radial lattice wave functions and to determine phase shifts at arbitrary energies. For coupled partial waves, we use a complex-valued auxiliary potential that breaks time-reversal invariance. We benchmark our method using a system of two spin-1/2 particles interacting through a finite-range potential with a strong tensor component. We are able to extract phase shifts and mixing angles for all angular momenta and energies, with precision greater than that of extant methods. We discuss a wide range of applications from nuclear lattice simulations to optical lattice experiments.},

doi = {10.1016/j.physletb.2016.06.081},

journal = {Physics Letters B},

number = C,

volume = 760,

place = {Netherlands},

year = {2016},

month = {9}

}

DOI: 10.1016/j.physletb.2016.06.081

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