Ting-Yun Shi

Investigation of hydrogenic-donor states confined by spherical quantum dots with B-splines

The energy spectra of an off-centre hydrogenic donor confined in finite spherical quantum dots have been calculated as a function of the donor position for different radii based on the effective-mass approximation using the linear variational method. B-splines have been used as basis functions, which can easily construct the trial wavefunction with appropriate boundary and cusp conditions. Comparison with other results given in the literature is made and good agreement is achieved. The changing feature of energy levels in accord with the nuclear position is analysed.

The long-range non-additive three-body dispersion interactions for the rare gases, alkali, and alkaline-earth atoms.

The long-range non-additive three-body dispersion interaction coefficients Z(111), Z(112), Z(113), and Z(122) are computed for many atomic combinations using standard expressions. The atoms considered include hydrogen, the rare gases, the alkali atoms (up to Rb), and the alkaline-earth atoms (up to Sr). The term Z(111) arising from three mutual dipole interactions is known as the Axilrod-Teller-Muto coefficient or the DDD (dipole-dipole-dipole) coefficient. Similarly, the terms Z(112), Z(113), and Z(122) arise from the mutual combinations of dipole (1), quadrupole (2), and octupole (3) interactions between atoms and they are sometimes known, respectively, as dipole-dipole-quadrupole, dipole-dipole-octupole, and dipole-quadrupole-quadrupole coefficients. Results for the four Z coefficients are given for the homonuclear trimers, for the trimers involving two like-rare-gas atoms, and for the trimers with all combinations of the H, He, and Li atoms. An exhaustive compilation of all coefficients between all possible atomic combinations is presented as supplementary data.

Nonrelativistic ab initio calculations for 2 S-2, 2 P-2, and 3 D-2 lithium isotopes: Applications to polarizabilities and dispersion interactions

The electric dipole polarizabilities and hyperpolarizabilities for the lithium isotopes Li-6 and Li-7 in the ground state 2 S-2 and the excited states 2 P-2 and 3 D-2, as well as the leading resonance and dispersion long-range coefficients for the Li(2 S-2)-Li(2 S-2) and Li(2 S-2)-Li(2 P-2) systems, are calculated nonrelativistically using variational wave functions in Hylleraas basis sets. Comparisons are made with published results, where available. We find that the value of the second hyperpolarizability of the 2 S-2 state is sensitive to the isotopic mass due to a near cancellation between two terms. For the 3 D-2 state polarizability tensor, the calculated components disagree with those measured in the sole experiment and with those calculated semiempirically.

Hyperspherical coupled channel calculations for the spectra and structure parameters of rare gas trimers NeAr2 and Ne2Ar

We calculate the L=0 vibration energies and rotational constants for the van der Waals trimers 20NeAr2, 20Ne2Ar, and their corresponding isotopologues within the framework of hyperspherical coordinates. The Schrodinger equation in hyperangular coordinates is solved at a series of fixed hyper-radii using B-splines and the resulting coupled hyper-radial equation is solved using the slow variable discretization method developed by Tolstikhin et al. [J. Phys. B 29, L389 (1996)]. Using the special properties of B-splines, we make the knot distributions more precisely, characterizing the behavior of channel functions. Our method improves the convergence greatly. It turns out that our numerical tool works quite well in study of rare gas trimers. Calculations are performed on two kinds of pair potentials, the HFD-B and Tang-Toennies (TT) potentials, and the resultant rotational constants and their isotope shifts are compared with the experimental results obtained from high-resolution spectroscopy. The TT pair potentials give much better agreement with the experimental values for 20Ne2Ar and 22Ne2Ar trimers, while the HFD-B pair potentials give much better agreement with the experimental values for 20NeAr2 and 22NeAr2 trimers.

Oscillator strengths between low-lying ro-vibrational states of hydrogen molecular ions

It is important for experimental design to know the transition oscillator strengths in hydrogen molecular ions. In this work, for HD(+), HT(+), and DT(+), we calculate the ro-vibrational energies and oscillator strengths of dipole transitions between two ro-vibrational states with the vibrational quantum number ν = 0-5 and the total angular momentum L = 0-5. The oscillator strengths of HT(+) and DT(+) are presented as supplementary material.

Accurate one-centre method for hydrogen molecular ion calculation using B-spline-type basis sets in strong magnetic fields

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 10(9)G to 4.414 x 10(13) 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 1 sigma(g,u), 1 pi(g,u), 1 delta(g,u) and 2 sigma(g) states of the H-2(+) in strong magnetic fields were found to be accurate to three to four significant digits at least up to 2.35 x 10(12) G, even for the antibonding states 1 sigma(u), 1 pi(g) and 1 delta(u), whose equilibrium distances R-eq are very large.

S-wave resonances in the positron–helium scattering

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.

Dynamic dipole polarizabilities of the Li atom and the Be + ion

The dynamic dipole polarizabilities for Li atoms and Be+ ions in the 2(2)S and 2(2)P states are calculated using the variational method with a Hylleraas basis. The present polarizabilities represent the definitive values in the nonrelativistic limit. Corrections due to relativistic effects are also estimated. Analytic representations of the polarizabilities for frequency ranges encompassing the n = 3 excitations are presented. The recommended polarizabilities for Li-7 and Be-9(+) are 164.11 +/- 0.03 a(0)(3) and 24.489 +/- 0.004 a(0)(3), respectively.

The weakly bound states and resonances of the BeHe2 triatomic system

In the present study, we carry out a full search of the bound states and resonances of the He(2)Be triatomic system, with its isotopic variants (3)He(2)(9)Be, (3)He(4)He(9)Be, and (4)He(2)(9)Be using the hyperspherical method. Three-body long-range effects are also included in the computation by adding to the additive potential the Axilrod-Teller triple-dipole term. In addition, the possibility of the occurrence of Efimov-type states in these systems is discussed. We have found a bound state for each of the (3)He(2)(9)Be and (3)He(4)He(9)Be trimers, while one weakly bound excited state is also found to exist for the (4)He(2)(9)Be system.

Binding energy and geometry of e+A (A=Li,Na) by the hyperspherical approach

We calculate the binding energy and geometry of the weakly bound e(+)Li and e(+)Na systems within the framework of hyperspherical coordinates. The Schrodinger equation in hyperangular coordinates is solved at a series of fixed hyper-radii using B-splines and the resulting coupled hyper-radial equation is solved using the slow variable discretization method developed by Tolstikhin et al. [J. Phys. B 29, L389 (1996)]. Great efforts are made in optimizing the distribution of B-splines to overcome the slow convergence of the binding energy and geometrical quantities. This approach allows us to obtain the results with improved convergence that are in good agreement with the best values reported to date. In addition, an analysis of the structure of the two systems is also made and the e(+)Na system is seen to exhibit quantum halo features.