Positronium-Proton Scattering at Low Energies

Abstract

Calculations of low energy positronium-proton scattering using the close coupling approach are reported at energies below the three-body breakup energy of 0·5 Rydberg. The channel space includes nine physical hydrogen and positronium states and in addition twelve hydrogen and positronium pseudo-states. Total elastic and electron-transfer cross sections are reported at incident energies below the ionisation threshold. Cross sections for electron transfer to the H(n=2) and H(n=3) levels are also reported.

Positron-Hydrogen Scattering, Annihilation, and Positronium Formation

“…We also compare the present phase shifts with those obtained by Schwartz (1961) [14] obtained by using the Kohn variational principle, Houston and Drachman (1971) [18], by using the Harris method, Kohn variational calculation of Humberston and Wallace (1972) [19], and Gien (1997) [20], by using the Harris-Nesbet method in Table 2. The 21-state close-coupling approximation phase shifts obtained by Mitroy and Ratnavelu (1995) [21][22][23] are lower than the present results. [21][22][23] has reported a large basis close-coupling calculation of scattering at low energies.…”

“…The 21-state close-coupling approximation phase shifts obtained by Mitroy and Ratnavelu (1995) [21][22][23] are lower than the present results. [21][22][23] has reported a large basis close-coupling calculation of scattering at low energies. The phase shifts of these calculations are lower than the present results given in Table 2.…”

Formation of antihydrogen in excited states

“…The problem ofH formation has been tackled using several approaches. Most widely used approach is based on close coupling approximation (CCA) method (see [11][12][13][14][15]). SinceH formation is a three particle charge-exchange collision problem so Faddeev's equation which in principle should be used for such problems, were also used [16,17].…”

Application of the hidden-crossing method to positronium formation

“…The D-wave cross section ͓12,14,15͔ for Ps formation computed using the Kohn variational method converges more slowly with respect to the number of linear parameters than the S and P waves and is believed to be within 10% of the exact value. Extensive two-center close-coupling calculations have been performed, for instance, an 18-state calculation by McAlinden et al ͓16͔ and Kernoghan et al ͓17͔, a 33-state calculation by Kernoghan et al ͓18͔,and 20,21, and 28-state calculations by Mitroy and collaborators ͓19-21͔. Gien ͓22͔ has employed the Harris-Nesbet method using a wave function that is comprised of the 1s, 2s, 2p, and 3p state of hydrogen and positronium together with al-gebraic Hylleraas correlation functions.…”