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.

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 Double heavy tri-hadron bound state with strange flavor

2019 ◽  
Vol 202 ◽  
pp. 06007
Author(s):  
Li Ma
Keyword(s):  
Bound States ◽  
Bound State ◽  
Molecular State ◽  
Body System ◽  
Comprehensive Investigation ◽  
Channel Effects ◽  
Oppenheimer Approximation ◽  
Three Body ◽  
Coupled Channel ◽  
Estimated Error

Through the Born-Oppenheimer Approximation, we have performed a comprehensive investigation of the DD∗K, D$ \overline D $*K, BB∗$ \overline K $ and B$ \overline B $*$ \overline K $ molecular states. In the framework of One-Pion Exchange model as well as the treatments of the coupled-channel effects and S-D wave mixing, we find a loosely bound tri-meson molecular state these systems with the isospin configuration |0,$ {1 \over 2} $, ±$ {1 \over 2} $> and quantum number I(JP) = 1/2(1−), where the, $ {1 \over 2} $ is the total isospin of the three-body system, the 0 is the isospin of the D∗K, $ \overline D $*K, B∗$ \overline K $ and $ \overline B $∗$ \overline K $. With the estimated error, the mass of the DD∗K or D$ \overline D $∗K molecule is $ 4317.92_{ - 4.32}^{ + 3.66} $ MeV or $ 4317.92_{ - 6.55}^{ + 6.13} $MeV. We also extend our calculations to the bottom sector and find tri-meson bound states for the BB∗$ \overline K $ and B$ \overline B $*$ \overline K $ with the mass $ 11013.65_{ - 8.84}^{ + 8.49} $ MeV and $ 11013.65_{ - 9.02}^{ + 8.68} $MeV respectively.

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.

The charge form factor of the model triton for two-particle interactions with continuum bound states

1981 ◽  
Vol 59 (2) ◽  
pp. 225-230 ◽  
Author(s):  
G. Pantis ◽  
H. Fiedeldey ◽  
D. W. L. Sprung
Keyword(s):  
Form Factor ◽  
Bound States ◽  
Bound State ◽  
Interesting Case ◽  
Charge Form Factor ◽  
Particle Interactions ◽  
Charge Form ◽  
Nonlocal Interactions ◽  
Asymptotic Shape ◽  
Three Body

The charge form factor of the model triton clearly exhibits the collapse which occurs in the triton for purely nonlocal two-body interactions with continuum bound states and approaches an asymptotic shape with increasing binding energy. However, partly nonlocal interactions with continuum bound states, which previously have been shown not to produce such a collapse, also show no evidence whatsoever of the presence of the two-particle continuum bound state in the triton charge form factor. In the physically interesting case of partly nonlocal interactions the occurrence of a continuum bound state in the two-body interactions therefore can be completely harmless in the three-body system.

Fluid Flow and Lateral Fluid Dispersion in Bounded Granular Beds

2002 ◽  
Author(s):  
Azita Soleymani ◽  
Eveliina Takasuo ◽  
Piroz Zamankhan ◽  
William Polashenski
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Results ◽  
Transition To Turbulence ◽  
Wide Range

Results are presented from a numerical study examining the flow of a viscous, incompressible fluid through random packing of nonoverlapping spheres at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), spanning a wide range of flow conditions for porous media. By using a laminar model including inertial terms and assuming rough walls, numerical solutions of the Navier-Stokes equations in three-dimensional porous packed beds resulted in dimensionless pressure drops in excellent agreement with those reported in a previous study (Fand et al., 1987). This observation suggests that no transition to turbulence could occur in the range of Reynolds number studied. For flows in the Forchheimer regime, numerical results are presented of the lateral dispersivity of solute continuously injected into a three-dimensional bounded granular bed at moderate Peclet numbers. Lateral fluid dispersion coefficients are calculated by comparing the concentration profiles obtained from numerical and analytical methods. Comparing the present numerical results with data available in the literature, no evidence has been found to support the speculations by others for a transition from laminar to turbulent regimes in porous media at a critical Reynolds number.

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

BOUND STATE ENERGIES IN THE 1/N EXPANSION

1993 ◽  
Vol 08 (09) ◽  
pp. 1613-1628
Author(s):  
T. JAROSZEWICZ ◽  
P.S. KURZEPA
Keyword(s):  
Bound States ◽  
Symmetric Tensor ◽  
Bound State ◽  
Binding Energies ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Leading Order ◽  
3 Dimensional ◽  
Weakly Coupled

We derive and solve — in an arbitrary number of dimensions — Omnès-type equations for bound-state energies in weakly coupled quantum field theories. We show that, for theories defined in the 1/N expansion, these equations are exact to leading order in 1/N. We derive and discuss the weak coupling and nonrelativistic limits of the Omnès equations. We then calculate the binding energies and effective bound-state couplings in (1+1), (1+2) and (1+3)-dimensional O(N)-invariant ϕ4 theory. We consider both the scalar and symmetric tensor bound states.

scholarly journals Quantum halo states in two-dimensional dipolar clusters

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
G. Guijarro ◽  
G. E. Astrakharchik ◽  
J. Boronat
Keyword(s):  
Bound States ◽  
Pair Correlation ◽  
Bound State ◽  
Binding Energies ◽  
Ultracold Gases ◽  
Quantum Object ◽  
Experimental Realization ◽  
Halo Structure ◽  
Forbidden Region ◽  
Spatial Size

AbstractA halo is an intrinsically quantum object defined as a bound state of a spatial size which extends deeply into the classically forbidden region. Previously, halos have been observed in bound states of two and less frequently of three atoms. Here, we propose a realization of halo states containing as many as six atoms. We report the binding energies, pair correlation functions, spatial distributions, and sizes of few-body clusters composed by bosonic dipolar atoms in a bilayer geometry. We find two very distinct halo structures, for large interlayer separation the halo structure is roughly symmetric and we discover an unusual highly anisotropic shape of halo states close to the unbinding threshold. Our results open avenues of using ultracold gases for the experimental realization of halos composed by atoms with dipolar interactions and containing as many as six atoms.

scholarly journals Studies on bound-state spectra of Manning–Rosen potential

2014 ◽  
Vol 29 (09) ◽  
pp. 1450042 ◽  
Author(s):  
Amlan K. Roy
Keyword(s):  
Bound States ◽  
Bound State ◽  
Wide Range ◽  
New States ◽  
Efficient Scheme ◽  
Molecular Potentials ◽  
Vibrational Energies ◽  
Rosen Potential ◽  
First Time ◽  
Potential Parameters

Accurate ro-vibrational energies, eigenfunctions, radial densities, expectation values are presented for the exponential-type Manning–Rosen (MR) potential. Bound states, accurate up to ten significant figure are obtained by employing a simple, reliable generalized pseudospectral (GPS) method. All 55 eigenstates with n ≤10 are treated for arbitrary values of potential parameters, covering a wide range of interaction, through a non-uniform, optimal spatial radial discretization. A detailed investigation has been made on energy changes with respect to screening and other potential parameters. A systematic estimation of critical screening parameters is given for these eigenstates. Special emphasis has been given to higher states and in the vicinity of critical screening region. A thorough comparison with literature results is made wherever possible. This surpasses the accuracy of all other existing methods currently available. Several new states are reported for the first time. In short, a simple, efficient scheme for accurate calculation of this and other molecular potentials is offered.

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