Hyperspherical close-coupling calculation of positronium formation cross sections in positron-hydrogen scattering at low energies

Abstract

I h e hyperspherical close-coupling method is applied to calculate both the elastic and positronium formation cross sections for positron collisions with atomic hydrogen at low energies. By treating the hyperradius as a slow variable, the S c m i n g e r equation in the body fram at each fixed hyperradius is solved using the higher-order finiteelement method and the resulting hyprradial equations are solved using the diabatic-bysector method. The coupled h m d i a l equations are integrated to a large hyperradius where the wavefunctions are matched to the known asymptotic solutions to extract the scattering matrix. Both Le elastic and Le wsihnnium fomtion cross sections are calculated at energies below the H(n = 2) excitation threshold for I = 0. I, 2 and 3. It is shown lhat the present hyperspherical close couplinE method gives results comparable to those obtained by elaborate variaciooal methods.

Large Basis Calculation of Positron?Hydrogen Scattering at Low Energies

“…3, it can be seen that the hyperspherical cross sections for the J == 1 and J == 2 partial waves are almost identical to the present cross sections. The other hyperspherical CC calculation (Zhou and Lin 1994) shows discrepancies with the present cross sections and the cross sections of Igarashi and Toshima (1994) for the higher partial waves. The most likely cause for the discrepancy is the small size of the hyper-radius adopted by Zhou and Lin (1994).…”

“…This is to be expected since the computational difficulties associated with the hyperspherical method increase as the angular momentum increases. On the other hand, the calculations of Zhou and Lin (1994) appear to suffer from a different problem at large angular momentum. They use a hyperspherical radius of 29·3 ao, which is much smaller than adopted by Archer et ale (1990) and Igarashi and Toshima (1994).…”

“…While the cross sections reported for the J == 0 and J == 1 waves are regarded as being close to exact, the calculations for the J == 2 partial wave did not achieve the same degree of precision and the J == 2 cross sections are expected to be accurate to only 10%. The hyperspherical close coupling method has also been applied to this problem (Archer et ale 1990; Igarashi and Toshima 1994;Zhou and Lin 1994). Archer et ale (1990) reported cross sections for the J == 0 partial wave that agree with those of Humberston (1984) to within 0·01 a5.…”

“…Archer et ale (1990) reported cross sections for the J == 0 partial wave that agree with those of Humberston (1984) to within 0·01 a5. The calculations of Zhou and Lin (1994) reported cross sections for the J == 0, 1, 2 and 3 partial waves but were restricted to the Ore gap. Igarashi and Toshima (1994) have reported cross sections over a more extensive energy range and also for the higher partial waves.…”

Weakly bound triatomic 4He23He and 3He24He molecules

“…ithin the past few years, the weakly bound states of the small helium cluster have been studied [1][2][3][4][5][6][7][8][9][10][11], mostly for those states of zero total angular momentum, J ϭ 0. Exploration of the bound rotational excited states is also a fascinating subject.…”