Positronium formation from hydrogen negative Ion, H<FONT FACE=Symbol>-</FONT>

$\bar {\sf {H}}^{+}$ ion production from collisions between antiprotons and excited positronium: cross sections calculations in the framework of the GBAR experiment

“…The binding energy is then E H − = −0.5259. Note that a misprint turned the sign of D into negative in several papers (in [17], for instance) whereas it is positive in the original Chandrasekhar paper, as it should be. The last wave function chosen to describe H − is the Le Sech wave function (labelled LS in the following) [30].…”

“…Straton and Drachman used the Coulomb Born approximation (CBA) with two wave functions for H − to compute the cross sections of equation (3) at four different positron energies (0.1, 0.5, 1 and 100 eV) when Ps and H are in their ground states [16]. Chaudhuri [17] highlighted the importance of the choice of the H − wave function and demonstrated the influence of the correlation description on the total cross section above 50 eV positron energy. Biswas [18] used the two-channel exchange coupled-channel theory to compute the cross section of the reverse process studied in [16], but took a plane wave for the exit channel and thus did not take into account the long range Coulomb interaction between e + and H − .…”

Formation of negative hydrogen ion in positronium-hydrogen collisions

“…In fact , the choice of this simpler wave function is mainly dictated by the feasibility of the present calculation which is already quite involved for a four body problem. Even in the simple first Born approximation ( FBA ) , the mathematical expression for the scattering amplitude becomes quite complex with the correlated wave function [12].…”

“…The ground state energy of the − H ion for this wave function [ 4 ] is E = -0.513 a. u. Although the present work uses the simpler wave function ( − H ion ) of Chandrasekhar [ 4 ] that was widely used successfully [ 9, 12 -15 ] , more sophisticated wave functions are available in the literature [ 12,16 ] involving explicit correlation ( e -e ) terms and producing more accurate binding energy of the − H ion. However, the correlated wave function is expected to be more suitable and in fact unavoidable for the two electron transition processes that are mainly governed by the e -e correlation [ 17,18 ] .…”