Related papers: Alternative sets of hyperspherical harmonics: Sati…
The hyperspherical harmonic basis is used to describe bound states in an $A$--body system. The approach presented here is based on the representation of the potential energy in terms of hyperspherical harmonic functions. Using this…
A new formulation is presented for a variational calculation of $N$-body systems on a correlated Gaussian basis with arbitrary angular momenta. The rotational motion of the system is described with a single spherical harmonic of the total…
Energies of the low-lying bound S-states (L=0) of exotic three-body systems, consisting a nuclear core of charge +Ze (Z being atomic number of the core) and two negatively charged valence muons, have been calculated by hyperspherical…
The complex scaling method permits calculations of few-body resonances with the correct asymptotic behaviour using a simple box boundary condition at a sufficiently large distance. This is also valid for systems involving more than one…
Lowest bound S-state energy of Coulomb three-body systems ($N^{Z+}\mu^-e^-$) having a positively charged nucleus of charge number Z ($N^{Z+}$), a negatively charged muon ($\mu^-$) and an electron ($e^-$), is investigated in the framework of…
The solution of the hyperangular Schr\"odinger equation for few-body systems using a basis of explicitly correlated Gaussians remains numerically challenging. This is in part due to the number of basis functions needed as the system size…
A powerful approach to solve the Coulombic quantum three-body problem is proposed. The approach is exponentially convergent and more efficient than the Hyperspherical Coordinate(HC) method and the Correlation Function Hyperspherical…
The coordinate asymptotics of the wave function for the problem of scattering of three particles with Coulomb interaction is constructed. Representation of hyperspherical functions is used to reduce the Schr\"odinger equation to a system of…
Recent advances in the treatment of scattering of charged composite particles are reviewed. In a first part I report on developments of the theory. Specifically I describe the recent completion of the derivation of the co-ordinate space…
We show that the bound states in a three-body system display a Coulomb series with a Gaussian cut-off provided: (i) the system consists of a light particle and two heavy bosonic ones, (ii) the heavy-light short-range potential has a…
A one-dimensional system of bosons interacting with contact and single-Gaussian forces is studied with an expansion in hyperspherical harmonics. The hyperradial potentials are calculated using the link between the hyperspherical harmonics…
Quantum mechanical few-body systems in reduced dimensionalities can exhibit many interesting properties such as scale-invariance and universality. Analytical descriptions are often available for integer dimensionality, however, numerical…
We present a method for treatment of three charged particles. The proposed method has universal character and is applicable both for bound and continuum states. A finite rank approximation is used for Coulomb potential in three-body system…
We propose a new treatment for the quantum three-body problem. It is based on an expansion of the wave function on harmonic oscillator functions with different sizes in the Jacobi coordinates. The matrix elements of the Hamiltonian can be…
We present a method for solving trapped few-body problems and apply it to three equal-mass particles in a one-dimensional harmonic trap, interacting via a contact potential. By expressing the relative Hamiltonian in Jacobi cylindrical…
The two-body Coulomb scattering problem is solved using the standard complex scaling method. The explicit enforcement of the scattering boundary condition is avoided. Splitting of the scattering wave function based on the Coulomb modified…
The analytic structure and asymptotic behavior of channel-coupling potentials in three-body systems are investigated within the framework of the hyperspherical harmonics expansion method. The coupling between different Jacobi partitions is…
We present a general approach for the solution of the three-body problem for a general interaction, and apply it to the case of the Coulomb interaction. This approach is exact, simple and fast. It makes use of integral equations derived…
We outline a rigorous method which can be used to solve the many-body Schroedinger equation for a Coulomb interacting electronic system in an external classical magnetic field as well as a quantized electromagnetic field. Effects of the…
We construct a tridiagonal matrix representation for the three dimensions Dirac-Coulomb Hamiltonian that provides for a simple and straightforward relativistic extension of the complex scaling method. Besides the Coulomb interaction,…