Few-Body Systems

The behavior of the two-electron quantum dot interacting with a uniform magnetic field is not fully understood yet. This lack of clarity arises from the fact that the mixed, spherical and cylindrical, coordinates do not allow the system to be separable. In this paper, we applied an standard variational method, with a physical recipe for choosing compact trial functions. In order to solve the six dimensional integrals necessary to compute the expectation value of the Hamiltonian, we used a Monte Carlo routine. The energy values obtained are in agreement with the ones presented in previous literature.

It is accepted that the shock acceleration mechanism can explain the non-thermal cosmic rays in supernova remnants, active galactic nuclei and gamma ray bursts. Especially, the importance of relativistic shock acceleration of cosmic rays in extragalactic sources is an important subject of study. In this work we will discuss the shock acceleration mechanism and will review the properties of non-relativistic and relativistic shocks, particularly focusing on relativistic Monte Carlo simulation studies.

 The Faddeev equations for the three-body bound state are solved directly as three-dimensional integral equation without employing partial wave decomposition. The numerical stability of the algorithm is demonstrated. The three-body binding energy is calculated for Malfliet-Tjon-type potentials and compared with results obtained from calculations based on partial wave decomposition. The full three-body wave function is calculated as function of the vector Jacobi momenta. It is shown that it satisfies the Schrödinger equation with high accuracy. The properties of the full wave function are displayed and compared to the ones of the corresponding wave functions obtained as finite sum of partial wave components. The agreement between the two approaches is essentially perfect in all respects.

A method proposed to assign the symmetry character of the rovibrational spectrum of trimers has been applied to the case of H $$^+_3$$ . This system, much lighter than previously investigated rare gas three body molecules such as Ar $$_3$$ or Ne $$_3$$ , constitutes a challenging example to test the possible limitations of this approach. Calculation of the corresponding rovibrational spectra for $$J=1$$ and rotational constants and the corresponding comparison with results from hyperspherical coordinates methods reveals that distorsion Coriolis coupling terms, not accounted for in the original method, play a significant role for some specific symmetry representations.

The ASACUSA collaboration of CERN has recently irradiated antiprotonic helium atoms with two counter-propagating laser beams. This excited some non-linear two-photon transitions of the antiproton at the deep UV wavelengths λ = 139.8–197.0 nm. The counterpropagating geometry of the laser beams reduced the thermal Doppler broadening of the observed resonances. Their narrow spectral lines allowed the measurement of three transition frequencies with fractional precisions of 2.3–5 parts in 109. By comparing the results with three-body QED calculations, the antiproton-to-electron mass ratio was derived as 1836.1526736(23).

In this letter, we present the exact solution of the three-dimensional Klein–Gordon oscillator on the (anti)-de Sitter spaces, the energy spectrum and the associated wave functions are extracted and the wave functions are expressed according to the Jacobi polynomial. On the other hand, we have investigated the three-dimensional the Klein–Gordon equation with a Coulomb plus scalar potential, we use the perturbation theory to calculate corrections to the spectrum in this framework of the extended uncertainty principle.