We investigate systems of three identical bosons in the context of current experimental efforts to achieve Bose - Einstein condensation. Calculated adiabatic hyperspherical potential curves permit us to draw some general conclusions about the dependence of the three-body physics on the two-body scattering length. In particular, we find that the long-range three-body interaction is effectively repulsive for either sign of the scattering length. This also hints that a stable Bose - Einstein condensate might be formed for either sign.

I h e hyperspherical close-coupling method is applied to calculate both the elastic and positronium formation cross sections for positron collisions with atomic hydrogen at low energies. By treating the hyperradius as a slow variable, the S c m i n g e r equation in the body fram at each fixed hyperradius is solved using the higher-order finiteelement method and the resulting hyprradial equations are solved using the diabatic-bysector method. The coupled h m d i a l equations are integrated to a large hyperradius where the wavefunctions are matched to the known asymptotic solutions to extract the scattering matrix. Both Le elastic and Le wsihnnium fomtion cross sections are calculated at energies below the H(n = 2) excitation threshold for I = 0. I, 2 and 3. It is shown lhat the present hyperspherical close couplinE method gives results comparable to those obtained by elaborate variaciooal methods.

The nonthermal effects on the doubly excited resonance states of the hydrogen negative ion and helium atom are investigated in Lorentzian astrophysical plasma environments using highly correlated Hylleraas-type wave functions in the framework of the stabilization method. Resonance parameters (resonance position and width) are reported for the first time as functions of the spectral index and plasma parameter. The screening effects are more pronounced in the stronger screening region. V C 2013 American Institute of Physics. [http://dx.

The authors adopted mass-weighted hyperspherical coordinates to study the properties of Coulombic three-body systems where all three particles are different. Using an adiabatic approximation, they applied the finite-element method to the two-dimensional eigenvalue problems at fixed hyperradius. The authors have calculated the adiabatic hyperspherical potential curves, and examined the wavefunctions (in terms of density plots) and the non-adiabatic coupling terms for a number of three-body systems. By fixing the masses of two of the particles, they examined how these properties vary with the mass of the third particle. The existence of stable bound states versus the masses of the systems is also investigated.

Three meshless methods, including incompressible smooth particle hydrodynamic (ISPH), moving particle semi-implicit (MPS) and meshless local Petrov-Galerkin method based on Rankine source solution (MLPG_R) methods, are often employed to model nonlinear or violent water waves and their interaction with marine structures. They are all based on the projection procedure, in which solving Poisson's equation about pressure at each time step is a major task. There are three different approaches to solving Poisson's equation, i.e. (1) discretizing Laplacian directly by approximating the second-order derivatives, (2) transferring Poisson's equation into a weak form containing only gradient of pressure and (3) transferring Poisson's equation into a weak form that does not contain any derivatives of functions to be solved. The first approach is often adopted in ISPH and MPS, while the third one is implemented by the MLPG_R method. This paper attempts to review the most popular, though not all, approaches available in literature for solving the equation.