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An accurate one-centre method is here applied to the calculation of the equilibrium distances and the energies for the hydrogen molecular ion in magnetic fields ranging from 109G to 4.414 × 1013 G. Both the radial and angular wavefunctions were expanded in terms of optimization B-splines. The slow convergence problem in the general one-centre method and singularities at the nuclear positions of the H+2 were solved well. The accuracy of the one-centre method has been improved in this way. We compared our results with those generated by high-precision methods from published studies. Equilibrium distances of the 1σg,u, 1πg,u, 1δg,u and 2σg states of the +2 in strong magnetic fields were found to be accurate to three to four significant digits at least up to 2.35 × 1012 G, even for the antibonding states 1σu, 1πg and 1δu, whose equilibrium distances Req are very large. [ABSTRACT FROM AUTHOR]

We have studied the geometry and resonances of the e+He(3Se) system in the framework of hyperspherical coordinates. A model potential proposed by us is used to describe the interaction between the out electron with the He+ ionic core. The calculated binding energy and expectation distance of the system are in agreement with other calculations. In addition, two resonances below the e+-He(1s2s3Se) threshold and one resonance below the Ps(n=2)-He+ threshold are identified. [ABSTRACT FROM AUTHOR]

We have performed a three-body calculation for investigation of S-wave resonances in the positron-helium scattering in the hyperspherical coordinates. B-splines are used to obtain accurate hyperspherical potential curves and channel functions. An adiabatical hyperspherical approach is used to predict semi-quantitatively the position of the resonances. A multichannel calculation with the stabilization method is also used to extract accurately the positions and widths of resonances. We find four resonances associated with the He+-Ps(n = 2) channel. The resonance parameters for the lowest two resonances are in reasonable agreement with the calculations of Kar and Ho (2004 J. Phys. B: At. Mol. Opt. Phys. 37 3177), and two more new resonances below the Ps(n = 2) threshold are identified. [ABSTRACT FROM AUTHOR]