Detailed investigation of low-energy positronium-hydrogen scattering

Abstract

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 wavefunctions 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 Sand 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.

Confined variational calculation of o -Ps–He scattering properties

“…3 P-wave phase shift for k = 0.1a −1 0 ) coincides with the CKVM result[36]. In the CKVM calculations, the value of δ 1 D 0.4 is less accurate than that of δ 3 P 0.1 because the mixed-symmetry basis functions are neglected for the D wave.…”

“…In this work, we first develop a strategy to effectively eliminate unphysical confining effects while extending the CVM to nonzero partial-wave scattering and higher collision energies. The advanced CVM is verified by calculating the P-and D-wave phase shifts for Ps-H scattering and comparing them with results of the complex Kohn variational method (CKVM) [36]. We then calculate the properties of o-Ps-He scattering: S-, P-, and D-wave phase shifts, momentum-transfer cross section, and energy dependence of the pickoff annihilation rate for S wave and P wave.…”

Deep Minimum and a Vortex for Positronium Formation in Low-Energy Positron-Helium Collisions

“…In this figure, N denotes the nucleus of the helium atom, He 2+ , which we take to be infinitely massive. The complex Kohn asymptotic form of the two components, Ψ 1 and Ψ 2 , for the th partial wave may be written in the form [13,19,47,48]…”

Confined variational calculation of positronium-hydrogen scattering below the positronium excitation threshold

“…There are many theoretical studies of Ps-H scattering using various approaches, including the Kohn variational method [22][23][24], the inverse Kohn variational method [22,23], the complex Kohn variational method [25,26], the diffusion Monte Carlo method [27], the stochastic variational method (SVM) [28,29], the close-coupling method [30][31][32][33][34][35][36], the static exchange method [37][38][39], the many-body theory [40], and the confined variational method (CVM) [41]. To handle the complicated short-range correlations in Ps-H scattering, correlated basis functions (Hylleraas-type basis [25], explicitly correlated Gaussian (ECG) basis [41], and others [24,27]) have been adopted in previous variational calculations.…”