Isospin mixing in three-body systems

In this work the structure of three-body resonances is investigated focusing on the mixing of components with different isospin. The presence of the Coulomb interaction makes this mixing possible. This is illustrated by the 2⁺ resonance in ⁶Li, for which a relevant contribution of the components with isospin 0 is found.     

三体问题的受力分析--兼谈失重

分析了三体问题的受力规律,给出了失重的条件．     

Scattering theory of three-body systems

The Faddeev amplitude is expressed in the N/D form in terms of the real reciprocal matrix K. The S-matrix is written in the unitary form (1 + iπK)S = 1 ?iπK. The Breit-Wigner formula for the three-body system including the break-up channel is derived. In the present method, the three-body problem is reduced to solve the eigenvalue problem for the real symmetric kernel.     

Approaching universality in weakly bound three-body systems

Atom-dimer scattering below the three-body breakup threshold is studied for a system of three identical bosons. The atom-dimer scattering length and the energy of the most weakly bound three-body state are shown to be strongly correlated. An appropriate rescaling of the observables reveals the subtlety of the correlation and serves to identify universal trends in the unitary limit of divergent two-body scattering length. The correlation provides a new quantitative measure of the degree of universality in three-body systems with short-ranged interactions, as well as a consistency check of effective field theories and other theoretical models.     

Non-perturbative theory of the polarization interaction in three-body systems

A new approach is developed for treating the polarization interaction in the three-particle system based on Faddeev's equations without using perturbation theory methods or adiabatic approximation. The exact analytical expression for the electric dipole polarizability of the two-particle bound system with a separable interaction of arbitrary form is obtained.     

Importance of the three-body Pauli potential in three-cluster systems

The ground state energies of the 3α system and of theA-α-α system are calculated in the three-cluster fish bone optical model [1], It is found that the three-cluster Pauli potential is very strong in theM-version of the model and weak in the (off-shell transformed)¯M-version. Its influence on theΛ-α-α binding energy and ground state wave function is almost negligible in the¯M-version. The present results indicate that phenomenological three-cluster models with energy-independent two-cluster interactions are not necessarily in contradiction with more microscopic models. It seems to be important, however, to use potentials which contain in their off-shell behaviour both Pauli-principle and saturation character of the nuclear forces.     

Integrable three-body systems with distinct two-body forces

Translationally invariant one-dimensional three-body systems with mutually different pair potentials are derived that possess a third constant of motion, both classically and quantum-mechanically; a Lax pair is given, and all (even) regular solutions of the corresponding functional equation are obtained.     

Exact triple-avoided-crossing resolution for three-body molecular systems

The hyperradial-adiabatic approach is used to study a region of localized triple-avoided crossing. A three-by-three orthogonal transformation involving a system of strongly coupled hyperradial Schrödinger equations is developed, leading to an exact coherent compensation of all peaks in the matrix elements of adiabatic corrections. In other words, the closure relation between adiabatic corrections matricesH+Q ²=0, which formally holds for a complete basis set, is nicely saturated by three strongly interacting states. One may suggest this to be a property of the hyperradial-adiabatic basis.     

On the motion of classical three-body system with consideration of quantum fluctuations

We obtained the systemof stochastic differential equations which describes the classicalmotion of the three-body system under influence of quantum fluctuations. Using SDEs, for the joint probability distribution of the total momentum of bodies system were obtained the partial differential equation of the second order. It is shown, that the equation for the probability distribution is solved jointly by classical equations, which in turn are responsible for the topological peculiarities of tubes of quantum currents, transitions between asymptotic channels and, respectively for arising of quantum chaos.     

A generalized adiabatic approach to exotic three-body systems

A generalized adiabatic approach providing the asymptotic separation of the fast and slow variables for the three-body muonic scattering problem is considered. A uniform classification scheme of the different adiabatic bases for some typical three-body Coulomb systems is discussed. The estimations of the cross section of the elastic scattering process (t¯p) _n=1+d(t¯p)_n=1+d are presented.     

Variational calculation of some S-states of Coulomb three-body systems

A generalized Hylleraas-type basis set with three nonlinear parameters is proposed to study three-body systems interacting via coulomb forces within the framework of non-relativistic quantum mechanics. This basis set improves the rate of convergence with respect to previous ones, specially for non-symmetric systems and excited states of two electron atoms. Accurate binding energies and other properties for S-states of helium-like ions, muonic molecules and the positronium negative ion are reported. Received 21 July 2000 and Received in final form 4 October 2000     

Accurate ground state wavefunctions for several three-body systems

The angularly correlated basis functions proposed by Gasaneo and Ancarani (Phys Rev, A 77:012705, 2008) are used to construct approximated wavefunctions, satisfying all two-body cusp conditions, for several three-body systems. The focus here is on the study of the following negatively charged hydrogen-like ions: ^?∞?H^???, ¹H^???, D^???, T^??? and Mu^???, the negative positronium ion Ps^???, and the exotic systems $e^{-}e^{-}(nm_{e})^{+}$ in which one of the particles is heavier than the other two. Accurate results for the mean of the ground state energy and of other radial quantities are compared with those given in the literature, when available.     

On the motion of a three-body system on hypersurface of proper energy

Based on the fact that for hamiltonian system there exists equivalence between phase trajectories and geodesic trajectories on the Riemannian manifold, the classical three-body problem is formulated in the framework of six ordinary differential equations (ODEs) of the second order on the energy hypersurface of body system. It is shown that in the case when the total interaction potential of the body system depends on the relative distances between particles, the three of six geodesic equations describing rotations of formed by three bodies triangle are solved exactly. Using this fact, it is shown that the three-body problem can be described in the limits of three nonlinear ODEs of canonical form, which in phase space is equivalent to the autonomous sixth-order system. The equations of geodesic deviations on the manifold (the space of relative distances between particles) are derived in an explicit form. A system of algebraic equations for finding the homographic solutions of restricted three-body problem is obtained. The initial and asymptotic conditions for solution of the classical scattering problem are found.     

Quantum propagator for some classes of three-dimensional three-body systems

In this work we solve exactly a class of three-body propagators for the most general quadratic interactions in the coordinates, for arbitrary masses and couplings. This is done both for the constant as the time-dependent couplings and masses, by using the Feynman path integral formalism. Finally, the energy spectrum and the eigenfunctions are recovered from the propagators.