scholarly journals Universality of excited three-body bound states in one dimension

2021 ◽  
Author(s):  
Lucas Happ ◽  
Matthias Zimmermann ◽  
Maxim A Efremov
Keyword(s):  
Excited States ◽  
Bound States ◽  
Space Dimension ◽  
Binding Energies ◽  
Wave Functions ◽  
One Dimension ◽  
Strong Indication ◽  
Body System ◽  
Weakly Bound ◽  
Three Body

Abstract We study a heavy-heavy-light three-body system confined to one space dimension in the regime where an excited state in the heavy-light subsystems becomes weakly bound. The associated two-body system is characterized by (i) the structure of the weakly-bound excited heavy-light state and (ii) the presence of deeply-bound heavy-light states. The consequences of these aspects for the behavior of the three-body system are analyzed. We find a strong indication for universal behavior of both three-body binding energies and wave functions for different weakly-bound excited states in the heavy-light subsystems.

scholarly journals Numerical Study of a Model Three-Body System

1972 ◽  
Vol 25 (5) ◽  
pp. 507 ◽  
Author(s):  
LR Dodd
Keyword(s):  
Bound States ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Bound State ◽  
Negative Parity ◽  
Binding Energies ◽  
Body System ◽  
Matrix Formulation ◽  
Wide Range ◽  
Three Body

An investigation is made of the properties of a simple three-body system consisting of three particles moving in one dimension and interacting through d-function potentials. The exact equations of three-particle scattering theory for this system are reduced without approximation to a set of three coupled one-dimensional integral equations which are solved numerically for a wide range of different potential strengths and particle masses. For the special case of identical particles the numerical solutions are compared with the exact solutions found previously by the author. The method of solution for general values of the parameters, which is based on computing the eigenvalue trajectories of the kernel of the scattering equations, allows a. systematic search for three-body bound states. In the case of nuclear or atomic-like configurations, a unique symmetric bound state is found and its binding energy computed. For molecular configurations, where there are two identical heavy particles interacting by the exchange of a third light particle, several excited states of both positive and negative parity are found and a comparison is made of their binding energies with the predictions of the adiabatic approximation. A reaction matrix formulation of the exact equations is used to calculate the probabilities of elastic and rearrangement scattering below the threshold for breakup. When the particles are identical, there is no elastic or rearrangement scattering in the backward direction. However, for particles of different mass or potentials of unequal strength, all kinematically possible scattering processes occur and the scattering properties of the model are quite complex. In particular an interesting feature of the calculations is the appearance of cusps in the elastic cross sections at the rearrangement threshold.

Weakly bound states of a three-body system

1994 ◽  
Vol 49 (3) ◽  
pp. 1281-1284 ◽  
Author(s):  
Zhongzhou Ren
Keyword(s):  
Bound States ◽  
Body System ◽  
Weakly Bound ◽  
Three Body

scholarly journals Electromagnetic transition form factors of baryons in a relativistic Faddeev approach

2018 ◽  
Vol 181 ◽  
pp. 01013 ◽  
Author(s):  
Reinhard Alkofer ◽  
Christian S. Fischer ◽  
Hèlios Sanchis-Alepuz
Keyword(s):  
Ground State ◽  
Bound States ◽  
Body Wave ◽  
Form Factors ◽  
Wave Functions ◽  
Electromagnetic Form Factors ◽  
Transition Form ◽  
Electromagnetic Transition ◽  
Three Body ◽  
Gluon Interaction

The covariant Faddeev approach which describes baryons as relativistic three-quark bound states and is based on the Dyson-Schwinger and Bethe-Salpeter equations of QCD is briefly reviewed. All elements, including especially the baryons’ three-body-wave-functions, the quark propagators and the dressed quark-photon vertex, are calculated from a well-established approximation for the quark-gluon interaction. Selected previous results of this approach for the spectrum and elastic electromagnetic form factors of ground-state baryons and resonances are reported. The main focus of this talk is a presentation and discussion of results from a recent investigation of the electromagnetic transition form factors between ground-state octet and decuplet baryons as well as the octet-only Σ0 to Λ transition.

scholarly journals Numerical Simulations of Encounters of Hard Binaries

1985 ◽  
Vol 113 ◽  
pp. 335-338
Author(s):  
Seppo Mikkola
Keyword(s):  
Cross Sections ◽  
Transfer Rate ◽  
Binding Energies ◽  
Body System ◽  
Energy Transfer Rate ◽  
Orbital Elements ◽  
Numerical Integrations ◽  
Order Of Magnitude ◽  
Three Body ◽  
Theory And Experiments

Results from numerical integrations of random binary-binary encounters have been used to obtain various cross-sections and outcome distributions for the four-body scattering. The initial orbital elements were chosen randomly except the Kepler-energies for which various selected values were used. Rough estimates for mass effects were obtained by simulating encounters of binaries with unequal component masses.We developed a semi-analytical theory for obtaining the types and energies of the outcome configurations. The theory contains some adjustable parameters, the values of which we deduced by comparing the theory and experiments.The energy transfer rate by collisions (=outcome is not two binaries) dominates over that due to fly-by's by an order of magnitude, provided that the binaries are hard. The formation of a hierarchical three-body system is fairly common. In a collision of energetically similar very hard binaries the probability is about 20 percent, while it is greater than 50 percent if the binding energies differ by a factor of more than four.

A two-body method for the bound states of a three-body system

1965 ◽  
Vol 63 (4) ◽  
pp. 625-633 ◽  
Author(s):  
J.W. Murphy ◽  
S. Rosati
Keyword(s):  
Bound States ◽  
Body System ◽  
Three Body ◽  
Body Method

Instability of a three-body system in one dimension

1979 ◽  
Vol 49 (3) ◽  
pp. 381-392 ◽  
Author(s):  
G. M. Obermair
Keyword(s):  
One Dimension ◽  
Body System ◽  
Three Body

Qualitative analysis of the existence of bound states and resonances of dipositronium

2000 ◽  
Vol 78 (2) ◽  
pp. 79-88
Author(s):  
C G Bao ◽  
T Y Shi
Keyword(s):  
Qualitative Analysis ◽  
Internal Wave ◽  
Excited States ◽  
Bound States ◽  
Wave Functions ◽  
Structure And Stability

Symmetry has imposed very strong constraints on the structure and stability of the internal wave functions of dipositronium. Based on symmetry considerations, the existence of a number of bound excited states and resonances has been suggested. More specifically, evidence for the existence of four bound states has been provided.PACS Nos.: 36.10Dr, 02.20-a

FOUR-BODY CONTINUUM-DISCRETIZED COUPLED-CHANNEL CALCULATIONS APPLIED TO 6He REACTIONS AROUND THE COULOMB BARRIER

2011 ◽  
Vol 20 (04) ◽  
pp. 947-952 ◽  
Author(s):  
M. RODRÍGUEZ-GALLARDO ◽  
A. M. MORO
Keyword(s):  
Harmonic Oscillator ◽  
Cross Section ◽  
Coulomb Barrier ◽  
Elastic Cross Section ◽  
Body System ◽  
Weakly Bound ◽  
Discretization Methods ◽  
Coupled Channels ◽  
Three Body ◽  
Coupled Channel

The scattering of a weakly bound three-body system by a target is studied within the four-body continuum-discretized coupled-channels (4b-CDCC) framework. Two different methods, the transformed harmonic oscillator (THO) method and the binning procedure, are used for discretizing the three-body continuum. The formalism is applied to different reactions induced by the Borromean nucleus 6 He at energies around the Coulomb barrier: 6 He +64 Zn at 13.6 MeV, 6 He +120 Sn at 17.4 MeV, and 6 He +208 Pb at 22 MeV. Elastic cross section distributions are presented for these reactions comparing both discretization methods, THO and binning, as the mass of the target increases.

scholarly journals Fermions Meet Two Bosons—the Heteronuclear Efimov Effect Revisited

2020 ◽  
Author(s):  
Binh Tran ◽  
Michael Rautenberg ◽  
Manuel Gerken ◽  
Eleonora Lippi ◽  
Bing Zhu ◽  
...  
Keyword(s):  
Infinite Series ◽  
Bound States ◽  
Scattering Length ◽  
Mass Difference ◽  
Scaling Law ◽  
Scaling Factor ◽  
Binding Energies ◽  
Efimov Effect ◽  
Three Body ◽  
Efimov States

Abstract In this article, we revisit the heteronuclear Efimov effect in a Bose-Fermi mixture with large mass difference in the Born-Oppenheimer picture. As a specific example, we consider the combination of bosonic 133Cs and fermionic 6Li. In a system consisting of two heavy bosons and one light fermion, the fermion-mediated potential between the two heavy bosons gives rise to an infinite series of three-body bound states. The intraspecies scattering length determines the three-body parameter and the scaling factor between consecutive Efimov states. In a second scenario, we replace the single fermion by an entire Fermi Sea at zero temperature. The emerging interaction potential for the two bosons exhibits long-range oscillations leading to a weakening of the binding and a breakup of the infinite series of Efimov states. In this scenario, the binding energies follow a modified Efimov scaling law incorporating the Fermi momentum. The scaling factor between deeply bound states is governed by the intraspecies interaction, analogous to the Efimov states in vacuum.

Sign in / Sign up

Export Citation Format

Share Document