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Journal of Physics B Atomic Molecular and Optical Physics

Structure and resonances of the e+–He(1s2s3Se) system

Zhenzhong Ren, Hui-Li Han, Ting-Yun Shi, J. Mitroy

Published Mar 30, 2012• 7 citations
Publisher

Abstract

We have studied the geometry and resonances of the e(+)He(S-3(e)) 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(1s3s S-3(e)) threshold and one resonance below the Ps(n=2)-He+ threshold are identified.

DOI
10.1088/0953-4075/45/8/085002

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We have studied the geometry and resonances of the e(+)He(S-3(e)) 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(1s3s S-3(e)) threshold and one resonance below the Ps(n=2)-He+ threshold are identified.
Abstract We have investigated the resonances in the e + − He ( 3 S e ) system interacting with screened potentials by using the stabilization method. Two types of screened potential have been considered: static screened Coulomb potential and exponential cosine-screened Coulomb potential. A model potential has been used to describe the interaction between the outer electron and the He + ionic core. We have found two resonances below the Ps ( n = 2 ) − He + threshold. For the unscreened case, our results are in nice agreement with some of the most accurate results available in the literature.
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.
We have calculated SSS-wave resonances in the positron-lithium system using the stabilization method in the framework of hyperspherical coordinates. Resonances below the Li (n=4)(n=4)(n=4) thresholds have been investigated. We have located the previously known SSS-wave resonances by Roy and Ho [J. Phys. B 35, 2149 (2002)] and observed relatively good agreement for the resonance positions. In addition, one Feshbach resonance associated with the Ps (n=2)(n=2)(n=2) threshold is also identified.
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.
In this paper, we investigate small clusters of helium atoms using the hyperspherical harmonic basis. We consider systems with A=2,3,4,5,6A=2,3,4,5,6A=2,3,4,5,6 atoms with an interparticle potential which does not present a strong repulsion at short distances. We use an attractive Gaussian potential that reproduces the values of the dimer binding energy, the atom-atom scattering length, and the effective range obtained with one of the widely used He-He interactions, the Aziz and Slaman potential, called LM2M2. In systems with more than two atoms, we consider a repulsive three-body force that, by construction, reproduces the trimer binding energy of the LM2M2 potential. With this model, consisting of the sum of a two- and three-body potential, we have calculated the spectrum of clusters formed by four, five, and six helium atoms. We have found that these systems present two bound states, one deep and one shallow, close to the threshold fixed by the energy of the $(A\ensuremath{-}1)$-atom system. Universal relations between the energies of the excited state of the AAA-atom system and the ground-state energy of the $(A\ensuremath{-}1)$-atom system are extracted, as well as the ratio between the ground state of the AAA-atom system and the ground-state energy of the trimer.
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.