# Volume dependence of N-body bound states

## Abstract

We derive the finite-volume correction to the binding energy of an N-particle quantum bound state in a cubic periodic volume. Our results are applicable to bound states with arbitrary composition and total angular momentum, and in any number of spatial dimensions. The only assumptions are that the interactions have finite range. The finite-volume correction is a sum of contributions from all possible breakup channels. In the case where the separation is into two bound clusters, our result gives the leading volume dependence up to exponentially small corrections. If the separation is into three or more clusters, there is a power-law factor that is beyond the scope of this work, however our result again determines the leading exponential dependence. We also present two independent methods that use finite-volume data to determine asymptotic normalization coefficients. The coefficients are useful to determine low-energy capture reactions into weakly bound states relevant for nuclear astrophysics. Using the techniques introduced here, one can even extract the infinite-volume energy limit using data from a single-volume calculation. The derived relations are tested using several exactly solvable systems and numerical examples. We anticipate immediate applications to lattice calculations of hadronic, nuclear, and cold atomic systems.

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1437814

- Alternate Identifier(s):
- OSTI ID: 1499280

- Grant/Contract Number:
- FG02-03ER41260

- Resource Type:
- Published Article

- Journal Name:
- Physics Letters B

- Additional Journal Information:
- Journal Name: Physics Letters B Journal Volume: 779 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

```
König, Sebastian, and Lee, Dean. Volume dependence of N-body bound states. Netherlands: N. p., 2018.
Web. doi:10.1016/j.physletb.2018.01.060.
```

```
König, Sebastian, & Lee, Dean. Volume dependence of N-body bound states. Netherlands. doi:10.1016/j.physletb.2018.01.060.
```

```
König, Sebastian, and Lee, Dean. Sun .
"Volume dependence of N-body bound states". Netherlands. doi:10.1016/j.physletb.2018.01.060.
```

```
@article{osti_1437814,
```

title = {Volume dependence of N-body bound states},

author = {König, Sebastian and Lee, Dean},

abstractNote = {We derive the finite-volume correction to the binding energy of an N-particle quantum bound state in a cubic periodic volume. Our results are applicable to bound states with arbitrary composition and total angular momentum, and in any number of spatial dimensions. The only assumptions are that the interactions have finite range. The finite-volume correction is a sum of contributions from all possible breakup channels. In the case where the separation is into two bound clusters, our result gives the leading volume dependence up to exponentially small corrections. If the separation is into three or more clusters, there is a power-law factor that is beyond the scope of this work, however our result again determines the leading exponential dependence. We also present two independent methods that use finite-volume data to determine asymptotic normalization coefficients. The coefficients are useful to determine low-energy capture reactions into weakly bound states relevant for nuclear astrophysics. Using the techniques introduced here, one can even extract the infinite-volume energy limit using data from a single-volume calculation. The derived relations are tested using several exactly solvable systems and numerical examples. We anticipate immediate applications to lattice calculations of hadronic, nuclear, and cold atomic systems.},

doi = {10.1016/j.physletb.2018.01.060},

journal = {Physics Letters B},

number = C,

volume = 779,

place = {Netherlands},

year = {2018},

month = {4}

}

DOI: 10.1016/j.physletb.2018.01.060

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

_{0}= −1) in one dimension. All quantities are given in units of the particle mass $m$ = 1 (see text).

Works referencing / citing this record:

##
Volume Dependence of N-Body Bound States

text, January 2018

- König, Sebastian; Lee, Dean
- GSI Helmholtzzentrum fuer Schwerionenforschung, GSI, Darmstadt

Figures / Tables found in this record:

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