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Chinese Physics Letters

Hyperspherical Calculations on Electron Affinity and Geometry for Li − and Na −

Han Hui-Li, Xianzhou Zhang, Ting-Yun Shi

Published Dec 1, 2007• 2 citations
Publisher

Abstract

Using a model potential to describe the interaction between the core and the valence electron, we perform hyperspherical calculations for electron affinity and geometry of the weakly bound Li − and Na − systems. In our calculation, channel functions are expanded in terms of B-splines. Using the special properties of B-splines, we make the knot distributions more precisely, characterizing the behaviour of channel functions. This improves the convergence greatly. Our results are in good agreement with the other theoretical and experimental values.

DOI
10.1088/0256-307x/24/12/029

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Using a model potential to describe the interaction between the core and the valence electron, we perform hyperspherical calculations for electron affinity and geometry of the weakly bound Li − and Na − systems. In our calculation, channel functions are expanded in terms of B-splines. Using the special properties of B-splines, we make the knot distributions more precisely, characterizing the behaviour of channel functions. This improves the convergence greatly. Our results are in good agreement with the other theoretical and experimental values.
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The three-body Schrdinger equation is approximately solved in the hyperspherical coordinates and the binding energies of the three-body weakly bound systems are calculated with the purpose to find if He-He-Ba trimers could exist. Using the special feature of the B-spline function like the flexible and highly localized properties, hypersphercial potentials are obtained by modifying the knots distribution of the B-spline basis of different weakly bound three-atom systems. Employing the best empirical interaction potentials between each pair of particles, we obtain that in the ground state binding energies of the weakly bound typical three-atom systems, the bindings of the molecules, 4He-4He-138Ba, 4He-3He-138Ba and 3He-3He-138Ba are possible. The binding energies of these systems are shown in the order of 1 Kelvin, each system could support only one bound state. These weakly bound molecules can exist only in a very cold environment. To get insight into the geometry of the molecules, the features of the channel functions associated with the hyperspherical potential curves of each system are investigated.
We discuss the bound states of weakly bound van der Waals trimers within the framework of hyperspherical coordinates. The wave function is expanded in terms of hyperspherical harmonics, which form a complete basis set in the angular variables. The resulting set of coupled second-order differential equations in the hyperradius is solved exactly. Our method gives a value for the zero-point energy of H+3 which is in excellent agreement with previous calculations. For (H2)3 and Ne3, however, our results show some discrepancy with earlier work.
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The parametric model potential developed by Peach for describing the electron interaction with the alkali-metal ion core yields energy levels that are in excellent agreement with the measurements of the spectra. Because of its relative simplicity, the lll-independent model potential is an attractive choice for studying positron--alkali-metal collisions. In order to test how well the model potential can be used to describe an effective three-body system, we use the Peach model potential to calculate the energy and geometry of the weakly bound e+Li{e}^{+}\mathrm{Li}e+Li and ${e}^{\ensuremath{-}}\mathrm{Li}$ systems. The binding energy is in good agreement with calculations using the exact Hamiltonian.