Volume dependence of N-body bound states

Journal Article · Sun Apr 01 00:00:00 EDT 2018 · Physics Letters B

DOI:https://doi.org/10.1016/j.physletb.2018.01.060· OSTI ID:1437814

König, Sebastian; Lee, Dean

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.

• Research Organization: North Carolina State University, Raleigh, NC (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: FG02-03ER41260
• OSTI ID: 1437814
• Alternate ID(s): OSTI ID: 1499280
• Journal Information: Physics Letters B, Journal Name: Physics Letters B Vol. 779 Journal Issue: C; ISSN 0370-2693
• Publisher: Elsevier
• Country of Publication: Netherlands
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS