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Three-body correlations in three-body exotic atoms are studied with simple models that consist of three bosons interacting through a superposition of long- and short-range potentials. We discuss the correlations among particles by comparing…

Nuclear Theory · Physics 2019-11-15 H. Moriya , W. Horiuchi , J. -M. Richard

The article formulates the classical three-body problem in conformal-Euclidean space (Riemannian manifold), and its equivalence to the Newton three-body problem is mathematically rigorously proved. It is shown that a curved space with a…

Mathematical Physics · Physics 2020-08-04 Ashot Gevorkyan

In this work it is shown that there are symmetries beyond the Euclidean group $E\left(3\right)$ in 3-body problem, and by extension in many-body problem, with inverse squared distance inter particle force. The symmetries in 3-body problem…

General Physics · Physics 2025-01-24 Siddhesh C. Ambhire

The restricted three body problem is well-known and very important for dynamics of binary, multiple stars and also planetary systems. We extend the classical version of this problem to the situation that there are some external forces from…

Astrophysics · Physics 2007-05-23 Ing-Guey Jiang , Li-Chin Yeh

We study the influence of relativity on the chaotic properties and dynamical outcomes of an unstable triple system; the Pythagorean three-body problem. To this end, we extend the Brutus N-body code to include Post-Newtonian pairwise terms…

Instrumentation and Methods for Astrophysics · Physics 2021-10-27 Tjarda C. N. Boekholt , Arend Moerman , Simon F. Portegies Zwart

We perform an analytical study of the bifurcation of the halo orbits around the collinear points $L_1$, $L_2$, $L_3$ for the circular, spatial, restricted three--body problem. Following a standard procedure, we reduce to the center manifold…

Mathematical Physics · Physics 2016-01-20 Marta Ceccaroni , Alessandra Celletti , Giuseppe Pucacco

In previous papers, we developed a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular. We considered systems with well separated components and different initial…

Earth and Planetary Astrophysics · Physics 2014-08-28 Nikolaos Georgakarakos

The use of leading order effective field theory (EFT) to describe neutron-deuteron scattering leads to integral equations that have unusual behaviour: when only two-body interactions are included, the scattering amplitude does not approach…

Nuclear Theory · Physics 2007-05-23 B. Blankleider , J. Gegelia

We discuss the three-body properties of identical bosons exhibiting large scattering length in two spatial dimensions. Within an effective field theory for resonant interactions, we calculate the leading non-universal corrections from the…

Quantum Gases · Physics 2015-03-17 K. Helfrich , H. -W. Hammer

We consider the classical three-body problem with an arbitrary pair potential which depends on the inter-body distance. A general three-body configuration is set by three "radial" and three angular variables, which determine the shape and…

Classical Physics · Physics 2019-07-16 Michele Castellana

The oscillator bases expansion stands as an efficient approximation method for the time-independent Schr\"odinger equation. The method, originally formulated with one non-linear variational parameter, can be extended to incorporate two such…

Quantum Physics · Physics 2024-09-24 Cyrille Chevalier , Selma Youcef Khodja

This is a natural continuation of our first paper \cite{pre}, where we develop a new geometrical technique which allow us to study relative equilibria on the two sphere. We consider a system of three positive masses on $\mathbb{S}^2$ moving…

Classical Analysis and ODEs · Mathematics 2022-02-28 Toshiaki Fujiwara , Ernesto Perez-Chavela

The three-body problem is a fundamental long-standing open problem, with applications in all branches of physics, including astrophysics, nuclear physics and particle physics. In general, conserved quantities allow to reduce the formulation…

Earth and Planetary Astrophysics · Physics 2024-05-28 Barak Kol

In this paper, we give a summary of stability criteria that have been derived for hierarchical triple systems over the past few decades. We give a brief description and we discuss the criteria that are based on the generalisation of the…

Earth and Planetary Astrophysics · Physics 2014-08-26 Nikolaos Georgakarakos

We consider three-body systems in two dimensions with zero-range interactions for general masses and interaction strengths. The momentum-space Schr\"odinger equation is solved numerically and in the Born-Oppenheimer (BO) approximation. The…

Quantum Gases · Physics 2013-02-13 F. F. Bellotti , T. Frederico , M. T. Yamashita , D. V. Fedorov , A. S. Jensen , N. T. Zinner

The problem of nonintegrability of the circular restricted three-body problem is very classical and important in the theory of dynamical systems. It was partially solved by Poincare in the nineteenth century: He showed that there exists no…

Dynamical Systems · Mathematics 2024-03-05 Kazuyuki Yagasaki

In this paper, an approach is developed to solve the three body problem involving masses which posses spherical symmetry. The problem dates back to the times of Poincare, and is undoubtedly one of the oldest of unsolved problems of…

Mathematical Physics · Physics 2007-05-23 A. B. Mehmood , U. A. Shah , G. Shabbir

We study the dynamics of the 3-D three-body problem of a small body moving under the attractions of a star and a giant planet which orbits the star on a much wider and elliptic orbit. In particular, we focus on the influence of an eccentric…

Earth and Planetary Astrophysics · Physics 2015-06-04 A. -S. Libert , N. Delsate

Higher order normalizations are performed in the generalized photogravitational restricted three body problem with Poynting-Robertson drag. In this problem we have taken bigger primary as a source of radiation and smaller primary as an…

Dynamical Systems · Mathematics 2007-10-31 B. S. Kushvah , J. P. Sharma , B. Ishwar

We discuss renormalization of the non-relativistic three-body problem with short-range forces. The problem becomes non-perturbative at momenta of the order of the inverse of the two-body scattering length, and an infinite number of graphs…

Nuclear Theory · Physics 2007-05-23 H. -W. Hammer