Three-body quantum Coulomb problem: Analytic continuation

Hyperspherical Coulomb spheroidal representation in the Coulomb three-body problem

The new representation of the Coulomb three-body wave function via the well-known solutions of the separable Coulomb two-centre problem φj(ξ, η) = Xj(ξ)Yj(η) is obtained, where Xj(ξ) and Yj(η) are the Coulomb spheroidal functions. Its distinguishing characteristic is the coordination with the boundary conditions of the scattering problem below the three-particle breakup. That is, the wave funct...

Three-potential formalism for the three-body Coulomb scattering problem

We propose a three-potential formalism for the three-body Coulomb scattering problem. The corresponding integral equations are mathematically well-behaved and can succesfully be solved by the Coulomb-Sturmian separable expansion method. The results show perfect agreements with existing low-energy n− d and p− d scattering calculations. PACS number(s): 21.45.+v, 03.65.Nk, 02.30.Rz, 02.60.Nm Types...

Quantum criticality and stability of three-body Coulomb systems

We present quantum phase transitions and critical phenomena of three-body Coulomb systems with charges (Q , q, Q) and masses (M , m, M ). Full numerical results, using the finite-size scaling method, for an arbitrary mass ratio 0<k5(11m/M )<1 over the range 1<l5uQ/qu<1.25, show that there exists a transition curve lc(k) through which all systems undergo a first-order phase transition from stabl...

Contemporary Status of the Three-Body Problem with Coulomb Interactions

Classical Coulomb three-body problem in collinear eZe configuration

Classical dynamics of two-electron atom and ions H−, He, Li, Be, ... in collinear eZe configuration is investigated. It is revealed that the mass ratio ξ between nucleus and electron plays an important role for dynamical behaviour of these systems. With the aid of analytical tool and numerical computation, it is shown that thanks to large mass ratio ξ, classical dynamics of these systems is ful...