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Title: 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:
; ORCiD logo
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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1016/j.physletb.2018.01.060

Citation Metrics:
Cited by: 9 works
Citation information provided by
Web of Science

Figures / Tables:

Fig. 1. Fig. 1. : (Color online) Finite-volume energy shift for $N$ = 2, 3, 4, 5 particles interacting via a Gaussian potential ($R$ = 1, $V$ 0 = −1) in one dimension. All quantities are given in units of the particle mass $m$ = 1 (see text).

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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
  • DOI: 10.15120/gsi-2019-00697

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