Do positrons measure atomic and molecular diameters?

Abstract

Abstract. We report on density functional calculations (DFT) of elastic integral scattering cross-sections for positron collisions with argon, krypton, nitrogen and methane. The long-range asymptotic polarization potential is described using higher-order terms going much beyond an induced dipole potential (−α/r 4 ) while the short-range interaction is modeled by two different forms of electron -positron correlation potential (Boroński-Nieminen and Quantum Monte Carlo potentials). The results of both approaches agree quite well with the recent theoretical and measured values. Based on the present and previous theoretical and experimental data we discuss some systematics observed in integral scattering cross-sections below the positronium formation threshold. In particular we point out on the correlation between the values of scattering cross-sections and atomic dimensions.

A rigid sphere approach to positron elastic scattering by noble gases, molecular hydrogen, nitrogen and methane

“…Figure 7b shows present calculations of elastic crosssections for molecular nitrogen (N 2 ) using three different values of rigid sphere radius: R 0 = 1.2875a 0 , R 0 = 1.3249a 0 and R 0 = 1.4268a 0 . The use of the smallest R 0 yields cross-sections consistent with ab initio calculations of Tenfen et al [69] and DFT results obtained using Boronski-Nieminen functional by Franz et al [10], while intermediate R 0 gives better agreement with experimental data by Zecca et al [77] at low energies (<1 eV) and Karwasz et al [51] at higher energies. On the other hand, the highest value of R 0 provides results that agree with old experimental data by Sueoka and Hamada [76] and with Schwinger multichannel calculation by Carvalho et al [68] reproducing this experimental TCS.…”

“…The agreement is particularly good above 2 eV, at the "flat" part of cross-sections, just below positronium formation threshold. To best [65], Zammit et al [66] and Fedus et al [3]; theories for N2: Elza et al [67], Carvalho et al [68], Tenfen et al [69], Mukherjee and Mukherjee [70] and Franz et al [10]; theories for CH4: Jain and Gianturco [71], Zecca et al [72] and Franz et al [10]. Experiments for H2: Fedus et al [3], Karwasz et al [51], Zecca et al [73] and Machacek et al [74]; experiments for N2: Hoffman et al [75], Sueoka and Hamada [76], Karwasz et al [51] and Zecca et al [77]; experiments for CH4: Floeder et al [78], Sueoka and Mori [79], Dababneh et al [80] and Zecca et al [72].…”

“…This effect is similar to classical elastic scattering on hard sphere. Recently, in more detailed study [10] we showed that the atomic radii dea e-mail: kamil@fizyka.umk.pl termined from positron scattering data using a classical rigid sphere model are comparable to covalent radii of atoms. However this simple picture does not translate directly into the quantum mechanics since pure quantummechanical hard-sphere model is not applicable to lowenergy positron scattering [11].…”

“…The latter is found to be compatible with the position of principal maximum in the radial distribution of outermost orbital (defined here as the atomic radius) for atomic targets. Providing the present model we benefit also from the fact that the de Broglie wavelength of positron with kinetic energy below the positronium formation threshold is usually comparable or much greater than the di- [22] and Franz et al [10] are also presented.…”

Positron-electron correlation-polarization potentials for the calculation of positron collisions with atoms and molecules*

“…Over the past ten years the experimental and calculated scattering cross sections for low-energy collisions of positrons with rare gas atoms, like argon and krypton, have converged within the experimental uncertainties [2][3][4][5][6][7][8][9][10]. For positron collisions with (polar and non-polar) molecules the situation is less favourable.…”