Positronium Formation Threshold Research Articles

Positron scattering from structurally related biomolecules.

We report the integral elastic, momentum transfer, and inelastic (positronium formation and ionisation) cross sections for positron scattering from structurally related molecules. The molecules chosen for the current investigation are formamide, formylphosphine, formic acid, N-methylformamide, acetone, acetic acid, and formaldehyde. The cross sections were calculated using the optical potential approach and the complex scattering potential-ionisation contribution method for impact energies between 1 and 5 keV. A sizable repository of data is now available for positron scattering from various atoms and molecules; however, data on the impact of positrons on current targets is still scarce and fragmented. While most cross sections are the first of their kind, we analyze our total cross sections (TCSs) with the previous literature available, which has become attractive to researchers trying to model the tracks of charged particles in matter. TCSs have recently seen a resurgence in popularity thanks to their utility in specifying the mean-free path between the collisions of such simulations. We find good qualitative convergence between experimental and theoretical results below and above the positronium formation threshold. However, around the threshold region, a significant discrepancy is encountered, which can be accounted for due to the experiment's lack of forward angle scattering effect discrimination. This level of agreement evolves to become quantitative at intermediate and higher energies.

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

We find a zero in the positronium formation scattering amplitude and a deep minimum in the logarithm of the corresponding differential cross section for positron–helium collisions for an energy just above the positronium formation threshold. Corresponding to the zero, there is a vortex in the extended velocity field that is associated with this amplitude when one treats both the magnitude of the momentum of the incident positron and the angle of the scattered positronium as independent variables. Using the complex Kohn variational method, we determine accurately two-channel K-matrices for positron–helium collisions in the Ore gap. We fit these K-matrices using both polynomials and the Watanabe and Greene’s multichannel effective range theory taking into account explicitly the polarization potential in the Ps-He+ channel. Using the fitted K-matrices we determine the extended velocity field and show that it rotates anticlockwise around the zero in the positronium formation scattering amplitude. We find that there is a valley in the logarithm of the positronium formation differential cross section that includes the deep minimum and also a minimum in the forward direction.

Close-coupling scattering cross sections and a model for positron cooling in a buffer gas of molecular nitrogen

Cross sections for positron scattering from molecular nitrogen are reported for energies below the positronium formation threshold. The elastic and state-to-state rotational and vibrational cross sections were obtained within the close-coupling formalism, using a three-dimensional potential energy surface for the interaction of the system. The inelastic cross sections was involved in a kinetic model to describe recent experimental results about positron cooling in a buffer gas of molecular nitrogen. Unlike a previous model [M. R. Natisin et al., J. Phys. B 47, 225209 (2014)], our prediction attributes a leading role to the $0\ensuremath{\rightarrow}1$ vibrational excitation of ${\mathrm{N}}_{2}$.

Low-energy positron scattering from gas-phase benzene

In this paper we are presenting calculations of the elastic cross section of positrons with gas-phase benzene for the energy range from 0.25 eV to 9.0 eV. The calculations are done with the molecular R-matrix method for positron-scattering from poly-atomic molecules using a scaling factor to scale the electron-positron interaction. The scaling factor influences the position of the poles of the R-matrix. We adjust the scaling factor is such a way, that the position of the lowest pole is similar to the proposed binding energy of around 150 meV, given by [J.A. Young, C.M. Surko, Phys. Rev. Lett 99, 133201 (2007)]. Below the threshold for positronium formation, we calculate elastic cross section in good agreement with experimental cross sections. Above the threshold for positronium formation we use the difference between the experimental total cross section data and our computed elastic cross section to provide a first estimation of the cross section for positronium formation.Graphical abstract

Theoretical study of positron scattering by group 14 tetra hydrides: A quantum mechanical approach

The present work provides a comprehensive set of positron impact scattering cross sections for group 14 tetrahydrides, namely, SiH4, GeH4, SnH4, and PbH4. The well-established spherical complex optical potential and complex scattering potential-ionization contribution methods are modified to incorporate positron scattering in the present work to calculate various cross sections. The positronium formation channel is adequately included through an improved inelastic threshold. The energy range chosen for the direct ionization cross section is from the respective ionization potential (I) of the molecule to 5 keV. Likewise, positronium formation and total ionization cross sections are reported from the positronium formation threshold to 300 eV and 5 keV, respectively, and the total cross section is computed for an extensive energy range of 1 eV to 5 keV. The positron impact total cross section for stannane molecule is computed for the first time. A characteristic valley is observed in the total cross sections with minima close to the positronium formation threshold. Further increase of cross section signifies the opening of inelastic channels especially positronium formation. In general, a reasonable agreement is found between the present results and other comparisons, wherever available. Furthermore, this is the first report of the inelastic cross sections (direct ionization, positronium formation, and total ionization) for the present set of targets.

Convergent close-coupling approach to positron scattering on He+

A close-coupling method is used to generate electron-loss and total scattering cross sections for the first three partial waves with both a single-centre and two-centre expansion of the scattering wave function for positron scattering on He+. The two expansions are consistent with each other above the ionisation threshold verifying newly-developed positronium-formation matrix elements. Below the positronium-formation threshold both the single- and two-centre results agree with the elastic-scattering cross sections generated from the phase shifts reported in previous calculations.

Positron scattering calculations of elastic, total and momentum transfer cross section for alkaline earth atoms

The family of alkaline earth atoms (group 2 elements) forms an interesting set of targets worth studying due to its low positronium formation threshold. In this article, calculations on several important cross sections such as elastic, total and momentum transfer up on positron impact on alkaline earth atoms have been reported. The present calculation uses a modified form of the well-established spherical complex optical potential (SCOP) method. The incident positron is assumed to have energies over a wide range from 1 eV to 5 keV. In the present endeavour, we have proficiently incorporated the positronium formation channel to derive reliable cross section data. Very few scattering studies were found in literature and mostly are theoretical calculations with the exception of Mg. Momentum transfer cross section for the present set of atoms has been reported for the first time.

Positron scattering studies of different inelastic channels for group IIA elements

This article reports the study of various inelastic channels such as positronium formation and ionization for positron scattering from group IIA elements. Modified spherical complex optical potential method developed by our group is employed for the present calculations for an extensive energy range from positronium formation threshold to 5 keV. Furthermore, a modified absorption threshold is introduced, which is utilized for targets having ionization threshold <6.8 eV. Comparison with existing data shows overall good agreement. Due to limited cross section studies on present targets, most of the results presented in this article have been reported for the first time.

ANTICOOL: Simulating positron cooling and annihilation in atomic gases

The Fortran program ANTICOOL, developed to simulate positron cooling and annihilation in atomic gases for positron energies below the positronium-formation threshold, is presented. Given positron–atom elastic scattering phase shifts, normalised annihilation rates Zeff, and γ spectra as a function of momentum k, ANTICOOL enables the calculation of the positron momentum distribution f(k,t) as a function of time t, the time-varying normalised annihilation rate Z̄eff(t), the lifetime spectrum and time-varying annihilation γ spectra. The capability and functionality of the program is demonstrated via a tutorial-style example for positron cooling and annihilation in room temperature helium gas, using accurate scattering and annihilation cross sections and γ spectra calculated using many-body theory as input. Program summaryProgram title:ANTICOOLProgram Files doi:http://dx.doi.org/10.17632/kjstc6xskg.1Licensing provisions: GPLv3Programming language: Fortran 90Nature of problem: Calculation of dynamics of antiparticle cooling and annihilating in atomic gases. Developed for positron cooling and annihilation in atomic gases, but easily modifiable and applicable to other binary elastic-collision cooling processes governed by quantum-mechanical cross sections.Solution method: Monte Carlo simulation.Restrictions: Elastic scattering and annihilation only: positron energies must be below the positronium-formation threshold. It is a single particle program, i.e., positron–positron interactions are not included and binary collisions with the gas atoms are assumed.

Probing Positron Cooling in Noble Gases via Annihilation γ Spectra.

γ spectra for positron annihilation in noble-gas atoms are calculated using many-body theory for positron momenta up to the positronium-formation threshold. These data are used, together with time-evolving positron-momentum distributions determined in the preceding Letter [Phys. Rev. Lett. 119, 203403 (2017)PRLTAO0031-9007], to calculate the time-varying γ spectra produced during positron cooling in noble gases. The γ spectra and their S[over ¯] and W[over ¯] shape parameters are shown to be sensitive probes of the time evolution of the positron momentum distribution and thus provide a means of studying positron cooling that is complementary to positron lifetime spectroscopy.

Positron scattering from simple molecules

A modified version of spherical complex optical potential formalism is employed to calculate the positron scattering cross sections over a wide energy range from near positronium formation threshold to 5000 eV. In the present study, the interaction potential of the positron–target scattering system is developed under an optical potential framework for the calculation of positron scattering total cross sections for CH4, CO, CO2, H2, N2O and NO molecules. The results obtained are in good agreement with most of the available experimental and theoretical values in terms of its shape and magnitude. A characteristic increase in cross section is observed for all the molecules near the positronium formation threshold, which signifies the emergence of positronium formation along with other inelastic channels.

Spatial profiles of positrons injected at low energies into water: influence of cross section models

We present a collated set of interaction cross sections for positrons in water, and study how the choice of ionisation energy sharing and of anisotropy in elastic cross sections influences low-energy spatial transport. A Monte Carlo code has been developed to model the transport of a beam of positrons injected at 60 eV into water, in which we compare several ionisation energy sharing models, and also vary the anisotropic scattering behaviour for elastic collisions. While the cross sections are primarily applicable to water vapour, we have investigated the inclusion of coherent elastic scattering which is present in liquid water. We present comparative profiles of positron number density, energy deposition, positronium formation, and secondary electron generation. Anisotropic scattering can increase radial diffusion by a factor of two, and a similar effect occurs as a result of coherent elastic scattering, though only at energies below the positronium formation threshold. The results emphasise the need for detailed knowledge of scattering cross sections that are differential in both scattering angles and energy transfer.

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

We present correlation-polarization potentials for the calculation of scattering cross sections of positrons with atoms and molecules. The potentials are constructed from a short-range correlation term and a long-range polarization term. For the short-range correlation term we present four different potentials that are derived from multi-component density functionals. For the long-range polarization term we employ a multi-term expansion. Quantum scattering calculations are presented for low energy collisions of positrons with two atomic targets (argon and krypton) and two molecular targets (nitrogen and methane). For collision energies below the threshold for Positronium formation our calculations of scattering cross sections are in good agreement with recent data sets from experiments and theory.Graphical abstract

Do positrons measure atomic and molecular diameters?

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 (Boronski-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.

Positron elastic scattering from alkaline earth targets

A previously reported model potential approach [Poveda et al., Phys. Rev. A 87 , 052702 (2013)] was extended to study low energy positron elastic scattering from beryllium and magnesium. The cross sections were computed for energies ranging from 10-5 eV up to well above the positronium formation threshold. The present results are in good agreement with previous reports, including the prediction of a p -wave resonance in the cross section for magnesium. The emergence of this shape resonance is connected to a trend observed in the evolution of the partial wave cross section in going from Be to Mg target. This trend lead us to speculate that a sharp d -wave resonance should be observed in positron elastic scattering from calcium. The positron-target binding energies are investigated in detail, both using the scattering information and by direct computation of the bound state energies using the model potentials.

Merkuriev Cut-off in e+ − H Multichannel Scattering Calculations

We present the results of positron-Hydrogen multichannel scattering calculations performed on the base of Faddeev-Merkuriev equations. We discuss an optimal choice of the Merkuriev’s Coulomb splitting parameters. Splitting the Coulomb potential in two-body configuration space is applicable for a limited energy range. Splitting the potential in three-body configuration space makes it possible to perform calculations in a broader range of energies and to optimize the numerical convergence. Scattering cross sections for zero total angular momentum for all processes between the positronium formation threshold and the third excitation threshold of the Hydrogen atom are reported.

Observation of a resonance in the photodetachment of positronium negative ions

SynopsisThe positronium negative ion, e−e+e−, is one of the simplest three body bound-states. As its constituents have a unique mass ratio, the ion is an attractive candidate for the investigation of the genuine three-body problem. In the present work, laser spectroscopy of this ion has been demonstrated in the UV region. A shape resonance near the positronium (n=2) formation threshold was clearly observed and the resonance energy was estimated.

Positron scattering on molecular hydrogen: Analysis of experimental and theoretical uncertainties

Experiments performed in recent years on positron scattering from molecular hydrogen indicated a rise of the total cross section in the limit of zero energy, but essentially disagree on the amplitude of this rise. Mitroy and collaborators [J.-Y. Zhang et al., Phys. Rev. Lett. 103, 223202 (2009)] predicted a scattering length somewhat different from values deduced experimentally. Using a Markov chain Monte Carlo modified effective range theory (MCMC-MERT) we show that the prediction of Mitroy and collaborators allows one to validate the recent experimental results and determine possible uncertainties. By comparing the MERT analysis with the fixed-nuclei density functional calculations we also deduce that probably the effect of virtual positronium formation (or coupling to the virtual positronium state) determines an almost constant value of the total cross section from 3 eV up to the positronium-formation threshold.

Positron scattering and annihilation on noble-gas atoms

Positron scattering and annihilation on noble gas atoms below the positronium formation threshold is studied ab initio using many-body theory methods. The many-body theory provides a near-complete understanding of the positron-noble-gas-atom system at these energies and yields accurate numerical results. It accounts for positron-atom and electron-positron correlations, e.g., polarization of the atom by the incident positron and the non-perturbative process of virtual positronium formation. These correlations have a large effect on the scattering dynamics and result in a strong enhancement of the annihilation rates compared to the independent-particle mean-field description. Computed elastic scattering cross sections are found to be in good agreement with recent experimental results and Kohn variational and convergent close-coupling calculations. The calculated values of the annihilation rate parameter $Z_{\rm eff}$ (effective number of electrons participating in annihilation) rise steeply along the sequence of noble gas atoms due to the increasing strength of the correlation effects, and agree well with experimental data.

Optimisation of the thickness of the moderator for positron annihilation process study in Ar gas

To investigate the deceleration and annihilation processes of positron in noble gas, we attempted to optimise the thickness of the positron moderator. The results of the decreasing trend of free positron intensity and ortho-positronium intensity with the thickness, and the annihilation rate suggest that the energy of almost all the positrons passed through the metal foils was much above the positronium formation threshold of 9 eV. Total thickness of 0.1 g cm-2 of the moderator and the Ar gas was required to stop almost all the positron in Ar gas.