Application of the hidden-crossing method to positronium formation

Abstract

We have applied the hidden-crossing method to compute S-, P-, and D-wave cross sections for Ps formation in positron-hydrogen collisions in the Ore gap. The hidden-crossing method has provided a physical explanation of why the S-wave cross section is so small and why the D wave is significant. The one-Sturmian theory is used to correct the hidden-crossing theory to take into account the factor (͉͗d 2 /dR 2 ͘ϩ(1/4)/R 2 ). We have considered this correction term in computing the P-and D-wave cross sections. The hidden-crossing results are compared with accurate results from other methods. This comparison helps assess the accuracy of the hidden-crossing method in describing three-body collisions.

Hyperspherical hidden crossing method applied to Ps(1s)-formation in low energy e+− H, e+− Li and e+− Na collisions

“…The HHCM theory [1] and its application to e + − H scattering [2] is described in detail elsewhere. For e + − H collisions, the position vector of the electron and positron with respect to the proton are r − and r + , respectively.…”

“…The hyperadius is R = r 2 − + r 2 + , and the two hyperangles are α = tan −1 (r − /r + ) and θ = cos −1 (r − ·r + ) [23]. The hyperspherical adiabatic energy eigenvalues ε µ (R) are obtained by solving 2…”

“…In order to improve the accuracy of the cross sections obtained with the HHCM, a correction term was derived from the one-Sturmian theory [2]. The potentials with the correction term agree asymptotically with the close coupling potentials through order 1/R 2 [3][4][5].…”

“…The correction term can be included in a consistent way by following the prescription for the paths given in [6]; we refer to these calculations as HHCM +cor .The HHCM has previously been applied with success to three-body collisions, including electron excitation [1] and impact ionization [1,[7][8][9][10][11][12]. Earlier HHCM calculations for Ps(1s) formation in e + − H collisions included an asymptotic approximation to the correction term (for the P-and D-waves) and provided an explanation for the small S-wave Ps(1s)-formation cross section in terms of the Stückelberg phase [2]. The HHCM was also used to treat near-threshold positron impact ionization of hydrogen [13].…”

Positronium Formation From Valence and Inner Shells in Noble Gas Atoms

“…This is true for all the noble gases. The exceptionally small s-wave contribution to Ps formation was noticed earlier for hydrogen and helium (see, e.g., [8,9,10]) and explained by the hidden-crossing method [11]. Figure 2 shows the Ps-formation cross sections for the valence np and subvalence ns orbitals together with their sum, for Ne, Ar, Kr and Xe.…”