Search results for "three-body problem"
showing 10 items of 32 documents
A non-relativistic model for the $[cc][\bar{c}\bar{c}]$ tetraquark
2017
We use a non-relativistic model to study the spectroscopy of a tetraquark composed of $[cc][\bar{c}\bar{c}]$ in a diquark-antidiquark configuration. By numerically solving the Schr\"{o}dinger equation with a Cornell-inspired potential, we separate the four-body problem into three two-body problems. Spin-dependent terms (spin-spin, spin-orbit and tensor) are used to describe the splitting structure of the $c\bar{c}$ spectrum and are also extended to the interaction between diquarks. Recent experimental data on charmonium states are used to fix the parameters of the model and a satisfactory description of the spectrum is obtained. We find that the spin-dependent interaction is sizable in the …
A Heavy Quark Symmetry Approach to Baryons
2005
We evaluate different properties of baryons with a heavy c or b quark. The use of Heavy Quark Symmetry (HQS) provides with an important simplification of the non relativistic three body problem which can be solved by means of a simple variational approach. This scheme is able to reproduce previous results obtained with more involved Faddeev calculations. The resulting wave functions are parametrized in a simple manner, and can be used to calculate further observables.
The Three-Body Problem
1972
The quantum mechanical three-body problem has been studied with increasing interest in the last decade. The main progress was achieved by deriving integral equations which are not only theoretically correct, but also practically applicable. Such equations allow us in particular to investigate, besides three-body bound states, the scattering of an elementary particle from a bound two-particle system.
Minimum fuel control of the planar circular restricted three-body problem
2012
The circular restricted three-body problem is considered to model the dynamics of an artificial body submitted to the attraction of two planets. Minimization of the fuel consumption of the spacecraft during the transfer, e.g. from the Earth to the Moon, is considered. In the light of the controllability results of Caillau and Daoud (SIAM J Control Optim, 2012), existence for this optimal control problem is discussed under simplifying assumptions. Thanks to Pontryagin maximum principle, the properties of fuel minimizing controls is detailed, revealing a bang-bang structure which is typical of L1-minimization problems. Because of the resulting non-smoothness of the Hamiltonian two-point bound…
Periodic Orbits in the Isosceles Three-Body Problem
1991
The Saturn’s satellites Janus and Epimetheus are the first known bodies in the Solar System that has horseshoe orbits in a frame that rotates with uniform angular velocity. Both satellites have similar masses and orbital elements when they are far from one another. Moreover, their orbits are nearly symmetric. In fact, in the past, they have been identify as a unique satellite and afterwards, some mathematical theories about their orbits has been necessaries to understand why they do not collide. In particular, the interest in planar three-body problem with two small masses has increased6. We assume that the two small masses have similar symmetric initial conditions. The aim of this paper is…
Spheroidal and hyperspheroidal coordinates in the adiabatic representation of scattering states for the Coulomb three-body problem
2009
Recently, an involved approach has been used by Abramov (2008 J. Phys. B: At. Mol. Opt. Phys. 41 175201) to introduce a separable adiabatic basis into the hyperradial adiabatic (HA) approximation. The aim was to combine the separability of the Born–Oppenheimer (BO) adiabatic basis and the better asymptotic properties of the HA approach. Generalizing these results we present here three more different separable bases of the same type by making use of a previously introduced adiabatic Hamiltonian expressed in hyperspheroidal coordinates (Matveenko 1983 Phys. Lett. B 129 11). In addition, we propose a robust procedure which accounts in a stepwise procedure for the unphysical couplings that are …
Minimum Time Control of the Restricted Three-Body Problem
2012
The minimum time control of the circular restricted three-body problem is considered. Controllability is proved on an adequate submanifold. Singularities of the extremal flow are studied by means of a stratification of the switching surface. Properties of homotopy maps in optimal control are framed in a simple case. The analysis is used to perform continuations on the two parameters of the problem: The ratio of the masses, and the magnitude of the control.
Results of Three-Nucleon Calculations
1972
The motivation for studying the nonrelativistic three-body problem originates in the fact that three-particle collisions occur very frequently in many areas of physics a) atomic physics: the scattering of electrons, positrons and protons off hydrogen atoms b) nuclear physics: three-nucleon problem c) statistical mechanics: 3rd virial coefficient d) low-energy elementary particle physics: final-state interactions in three-body decays of hadrons.
States Of Rho D*(D)Over-Bar* With J=3 Within The Fixed Center Approximation To The Faddeev Equations
2015
We study the interaction of ρ, D * and $$\bar D^*$$ with spins aligned using the fixed center approximation to the Faddeev equations. We select a cluster of $$D^* \bar D^*$$ , which is found to be bound in I = 0 and can be associated to the X(3915), and let the ρ meson orbit around the D * and $$\bar D^*$$ . In this case we find an I = 1 state with mass around 4340 MeV and narrow width of about 50 MeV. We also investigate the case with a cluster of ρD * and let the $$\bar D^*$$ orbit around the system of the two states. The ρD * cluster is also found to bind and leads to the D 2 * state. The addition of the extra $$\bar D^*$$ produces further binding and we find, with admitted uncertainties…
Causality, non-locality and three-body Casimir–Polder energy between three ground-state atoms
2006
The problem of relativistic causality in the time-dependent three-body Casimir–Polder interaction energy between three atoms, initially in their bare ground-state, is discussed. It is shown that the non-locality of the spatial correlations of the electromagnetic field emitted by the atoms during their dynamical self-dressing may become manifest in the dynamical three-body Casimir–Polder interaction energy between the three atoms.