Low-energy correlations in the positronium–hydrogen-atom system

M. W. J. Bromley, Jim Mitroy, S. A. Novikov +2 more

S Hara, P A Fraser

The total elastic scattering and ortho-para conversion cross sections of low-energy ortho-positronium with hydrogen atoms have been calculated in the static exchange approximation including the l=0, 1 and 2 partial waves with the incident positronium wavenumber k ranging from 0 to 3.0 (in atomic units) for l=0 and from 0 to 1.2 for l=1 and 2. The scattering lengths are a (+) =7.275 a 0 and a (-) =2.476 a 0 for the space-symmetric and anti-symmetric cases respectively. A resonance is found in the anti-symmetric s-wave scattering at k approximately=2.07, but its real existence is of course questionable because of neglected effects.

Denton Woods, Sandra J. Ward, Peter Van Reeth

We investigate the four-body Coulomb process of low-energy elastic positronium-hydrogen (Ps-H) scattering below the Ps($n=2$) excitation threshold using scattering wave functions that include Hylleraas-type correlation terms. Using the complex Kohn variational method, we compute phase shifts through the $^{1,3}H$ wave and obtain highly accurate $^{1,3}S$- and $^{1,3}P$-wave phase shifts. The complex Kohn variational results compare well to a number of other calculations for this system. We present elastic differential, elastic integrated, and momentum transfer cross sections, and for the singlet, resonances through the $^{1}F$ wave. The differential cross section exhibits interesting features, including a change from slightly backward peaked to forward peaked scattering as the energy of the incident positronium increases and rich structure due to multiple resonances near the Ps($n=2$) threshold. We also give a detailed analysis of the scattering lengths and effective ranges using multiple effective range theories.

Allen Paine Mills

Peter Van Reeth, J W Humberston

A detailed investigation is made of low energy positronium–hydrogen s-wave elastic scattering, using the Kohn variational method, with very flexible scattering wavefunctions including all inter-particle correlations. The singlet and triplet scattering lengths are calculated and found to be a + = 4.311 a 0 and a − = 2.126 a 0 respectively. The phase shifts are believed to be within less than 0.5% of the exact values, and they are in good agreement with the results of previous calculations.

Hiroyuki Yabu