Universal lowenergy behavior in threebody systems
Abstract
We consider a pairwise interacting quantum 3body system in 3dimensional space with finite masses and the interaction term V{sub 12} + λ(V{sub 13} + V{sub 23}), where all pair potentials are assumed to be nonpositive. The pair interaction of the particles (1, 2) is tuned to make them have a zero energy resonance and no negative energy bound states. The coupling constant λ > 0 is allowed to take the values for which the particle pairs (1, 3) and (2, 3) have no bound states with negative energy. Let λ{sub cr} denote the critical value of the coupling constant such that E(λ) → −0 for λ → λ{sub cr}, where E(λ) is the ground state energy of the 3body system. We prove the theorem, which states that near λ{sub cr}, one has E(λ) = C(λ − λ{sub cr})[ln(λ − λ{sub cr})]{sup −1} + h.t., where C is a constant and h.t. stands for “higher terms.” This behavior of the ground state energy is universal (up to the value of the constant C), meaning that it is independent of the form of pair interactions.
 Authors:
 FIAS, RuthMoufangStraße 1, D–60438 Frankfurt am Main (Germany)
 Publication Date:
 OSTI Identifier:
 22403098
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUND STATE; COUPLING CONSTANTS; GROUND STATES; PAIRING INTERACTIONS; PARTICLES; THREEBODY PROBLEM; THREEDIMENSIONAL CALCULATIONS
Citation Formats
Gridnev, Dmitry K. Universal lowenergy behavior in threebody systems. United States: N. p., 2015.
Web. doi:10.1063/1.4907983.
Gridnev, Dmitry K. Universal lowenergy behavior in threebody systems. United States. doi:10.1063/1.4907983.
Gridnev, Dmitry K. 2015.
"Universal lowenergy behavior in threebody systems". United States.
doi:10.1063/1.4907983.
@article{osti_22403098,
title = {Universal lowenergy behavior in threebody systems},
author = {Gridnev, Dmitry K.},
abstractNote = {We consider a pairwise interacting quantum 3body system in 3dimensional space with finite masses and the interaction term V{sub 12} + λ(V{sub 13} + V{sub 23}), where all pair potentials are assumed to be nonpositive. The pair interaction of the particles (1, 2) is tuned to make them have a zero energy resonance and no negative energy bound states. The coupling constant λ > 0 is allowed to take the values for which the particle pairs (1, 3) and (2, 3) have no bound states with negative energy. Let λ{sub cr} denote the critical value of the coupling constant such that E(λ) → −0 for λ → λ{sub cr}, where E(λ) is the ground state energy of the 3body system. We prove the theorem, which states that near λ{sub cr}, one has E(λ) = C(λ − λ{sub cr})[ln(λ − λ{sub cr})]{sup −1} + h.t., where C is a constant and h.t. stands for “higher terms.” This behavior of the ground state energy is universal (up to the value of the constant C), meaning that it is independent of the form of pair interactions.},
doi = {10.1063/1.4907983},
journal = {Journal of Mathematical Physics},
number = 2,
volume = 56,
place = {United States},
year = 2015,
month = 2
}

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