A new {\it ab initio} theoretical formulation to calculate $Z_{eff}$ and hence the positron annihilation rates is presented using the on-shell and half-offshell T-matrix scattering amplitudes without any explicit use of the scattering wave function. The formulation is exact and universal, as long as the dynamics of the system can be described by a Lippmann-Schwinger type equation. It could serve as an effective tool as all the $T-$, $K-$, and $S-$matrix formulations, yield directly the scattering amplitudes; not the wave function. We also present a basic numerical test of the formulation.
The process of a positron $\unicode{x2013}$ bound-electron annihilation with simultaneous emission of two photons is investigated theoretically. A fully relativistic formalism based on $\textit{ab initio}$ QED description of the process is worked out. The developed approach is applied to evaluate the annihilation of a positron with $K$-shell electrons of a silver atom, for which a strong contradiction between theory and experiment was previously stated. The results obtained here resolve this long-standing disagreement and, moreover, demonstrate a sizeable difference with approaches so far used…
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 t…
A model-potential approach to calculating positron-molecule binding energies and annihilation rates is developed. Unlike existing ab initio calculations, which have mostly been applied to strongly polar molecules, the present methodology can be applied to both strongly polar and weakly polar or nonpolar systems. The electrostatic potential of the molecule is calculated at the Hartree-Fock level, and a model potential that describes short-range correlations and long-range polarization of the electron cloud by the positron is then added. The Schrodinger equation for a positron moving in this eff…
The annihilation parameters of positrons with electrons in different shells of Argon, Iron and Copper atoms are calculated below the positronium (Ps) formation thresholds. Quite accurate ab initio calculations of the bound state wavefunctions of Argon, Iron and Copper orbitals are obtained from Cowan computer code. A least-squares variational method (LSVM) is used for determining the wavefunction of the positrons. The program is employed for calculating the s-wave partial cross sections of positrons scattered by Iron and Copper atoms. Our results of the effective charge are compared with avail…
Understanding the dynamics of positron cooling in gases, including the fraction of positrons surviving to thermalisation, is critical for accurate interpretation of positron lifetime spectra, for the development of efficient positron cooling in traps and accumulators, and for a cryogenically cooled, ultra-high-energy-resolution, trap-based positron beam. Here, positron cooling and annihilation in noble gases is simulated using accurate scattering and annihilation cross sections calculated \emph{ab initio} with many-body theory. It is shown that a strikingly small fraction of positrons survive …
A model-potential method is employed to calculate binding, elastic scattering, and annihilation of positrons for a number of atoms and small nonpolar molecules, namely, Be, Mg, He, Ar, H$_2$, N$_2$, Cl$_2$, and CH$_4$. The model potential contains one free parameter for each type of atom within the target. Its values are chosen to reproduce existing ab initio positron-atom binding energies or scattering phase shifts. The calculations are performed using a Gaussian basis for the positron states, and we show how to obtain values of the scattering phase shifts and normalized annihilation rate $Z_…
Bound electron contribution to the Doppler-shift of gamma-ray spectra in the positron-electron annihilation process of molecular methane has been studied in gas phase. Two accurate ab initio quantum mechanical schemes, i.e. the delocalized molecular orbital (MO) and the localized natural bond orbital (NBO) schemes, are applied to study the multi-centred methane molecule. The present ab initio calculations of methane indicate that the C-H bonds are polarized with the partial negative charge of -0.36 a.u. on the carbon atom and the partial positive charge of +0.09 a.u. on each of the hydrogen at…
The elastic collision between two ortho-positronium (e.g. S=1) atoms is studied using an ab-initio static-exchange model (SEM) in the center of mass (CM) frame considering the system as a four-body Coulomb problem where all the Coulomb interaction terms in the direct and exchange channels are treated exactly. A coupled-channel methodology in momentum space is used to solve Lippman-Schwinger equation following the integral approach. A new SEM code is developed in which the Born-Oppenheimer (BO) scattering amplitude acts as input to derive the SEM amplitude adapting the partial wave analysis. Th…
In previous papers we have proposed a method for the ab initio calculation of fully differential cross-sections for electron scattering in liquids and applied it to liquid argon, xenon and krypton. In this paper, we extend the procedure to the consideration of positron scattering in liquid helium, which is complicated by the annihilation process as well as the fact that the electron definition for the region "owned" by a target atom used previously does not have a positron analogue. We explore several physically motivated definitions to obtain effective positron scattering in the dense fluid. …
Positrons bind to molecules leading to vibrational excitation and spectacularly enhanced annihilation. Whilst positron binding energies have been measured via resonant annihilation spectra for $\sim$90 molecules in the past two decades, an accurate \emph{ab initio} theoretical description has remained elusive. Of the molecules studied experimentally, calculations exist for only 6, and for these, standard quantum chemistry approaches have proved severely deficient, agreeing with experiment to at best 25% accuracy for polar molecules, and failing to predict binding in nonpolar molecules. The mec…
We analyze low-energy scattering of positrons on Ar atoms and N2 molecules using Modified Effective-Range Theory (MERT) developped by O'Malley, Spruch and Rosenberg [Journal of Math. Phys. 2, 491 (1961)]. We use formulation of MERT based on exact solutions of Schroedinger equation with polarization potential rather than low-energy expansions of phase shifts into momentum series. We show that MERT describes well experimental data, provided that effective-range expansion is performed both for s- and p-wave scattering, which dominate in the considered regime of positron energies (0.4 - 2 eV). We …
Total cross sections for the scattering of low-energy electrons and positrons by atomic beryllium in the energy range below the first inelastic thresholds are calculated. A Ramsauer-Townsend minimum is seen in the electron scattering cross sections, while no such effect is found in the case of positron scattering. A minimum total cross section of 0.016 a.u. at 0.0029 eV is observed for the electron case. In the limit of zero energy, the cross sections yield a scattering length of -0.61 a.u. for electron and +13.8 a.u. for positron scattering.
Calculations of gamma spectra for positron annihilation on a selection of molecules, including methane and its fluoro-substitutes, ethane, propane, butane and benzene are presented. The annihilation gamma spectra characterise the momentum distribution of the electron-positron pair at the instant of annihilation. The contribution to the gamma spectra from individual molecular orbitals is obtained from electron momentum densities calculated using modern computational quantum chemistry density functional theory tools. The calculation, in its simplest form, effectively treats the low-energy (therm…
We investigate positron scattering upon endohedrals and compare it with electron-endohedral scattering. We show that the polarization of the fullerene shell considerably alters the polarization potential of an atom, stuffed inside a fullerene. This essentially affects both the positron and electron elastic scattering phases as well as corresponding cross-sections. Of great importance is also the interaction between the incoming positron and the target electrons that leads to formation the virtual positronium. We illustrate the general trend by concrete examples of positron and electron scatter…
The model-potential approach previously developed by the authors to study positron interactions with molecules is used to calculate the positron binding energy for $n$-alkanes (C$_n$H$_{2n+2}$) and the corresponding cycloalkanes (C$_n$H$_{2n}$). For $n$-alkanes, the dependence of the binding energy on the conformation of the molecule is investigated, with more compact structures showing greater binding energies. As a result, thermally averaged binding energies for larger alkanes ($n\gtrsim 9$) show a strong temperature dependence in the range of 100-600 K. This suggests that positron resonant …
Effect of charge-transfer recombination for positronium (Ps) scattering is studied on Ps-H system using coupled-channel formalism considering a new rearrangement channel Ps+H --> e^+ + H^- and exchange. The correlation and continuum effects introduced by this charge-transfer channel result to substantial convergence to the low energy scattering parameters. Effects on scattering length, PsH binding energy, and low-energy (0-10 eV) phase-shifts and cross sections are evaluated and H$^-$ formation cross sections are reported from above the threshold (6.438 eV) to 100 eV.
Annihilation momentum densities and correlation enhancement factors for low-energy positron annihilation on valence and core electrons of noble-gas atoms are calculated using many-body theory. s, p and d-wave positrons of momenta up to the positronium-formation threshold of the atom are considered. The enhancement factors parametrize the effects of short-range electron-positron correlations which increase the annihilation probability beyond the independent-particle approximation. For all positron partial waves and electron subshells, the enhancement factors are found to be relatively insensiti…
Diagrammatic many-body theory is used to calculate the scattering phase shifts, normalized annihilation rates $Z_{\rm eff}$ and annihilation gamma spectra for positron collisions with the hydrogen-like ions He$^+$, Li$^{2+}$, B$^{4+}$ and F$^{8+}$. Short-range electron-positron correlations and longer-range positron-ion correlations are accounted for by evaluating nonlocal corrections to the annihilation vertex and the exact positron self-energy. The numerical calculation of the many-body theory diagrams is performed using B-spline basis sets. To elucidate the rôle of the positron-ion repulsio…
A many-body theory approach developed by the authors [Phys. Rev. A 70, 032720 (2004)] is applied to positron bound states and annihilation rates in atomic systems. Within the formalism, full account of virtual positronium (Ps) formation is made by summing the electron-positron ladder diagram series, thus enabling the theory to include all important many-body correlation effects in the positron problem. Numerical calculations have been performed for positron bound states with the hydrogen and halogen negative ions, also known as Ps hydride and Ps halides. The Ps binding energies of 1.118, 2.718…
In this paper we use a zero-range potential (ZRP) method to model positron interaction with molecules. This allows us to investigate the effect of molecular vibrations on positron-molecule annihilation using the van der Waals dimer Kr2 as an example. We also use the ZRP to explore positron binding to polyatomics and examine the dependence of the binding energy on the size of the molecule for alkanes. We find that a second bound state appears for a molecule with ten carbons, similar to recent experimental evidence for such a state emerging in alkanes with twelve carbons.
In the article by Ma~\emph{et al.}~[Phys.~Rev.~A {\bf 94}, 052709 (2016)], $γ$-ray spectra for positron annihilation on molecules were calculated in the independent-particle approximation with the positron wavefunction set to unity. Based on comparisons with experimental data they concluded that inner valence electrons play a dominant role in positron annihilation. These conclusions are incorrect and resulted from fallacious analysis that ignored the known effect of the positron wavefunction on the spectra.
Resonant electron-positron pair production by a high-energy gamma quantum in the field of a nucleus and a quasi-monochromatic laser wave was theoretically studied. Under the resonant condition an intermediate virtual electron (positron) in the laser field becomes a real particle. Due to that fact the initial process of the second order in the fine structure constant in a laser field effectively reduces into two successive processes of the first order: the laser-stimulated Breit-Wheeler process and the laser-assisted process of an intermediate electron (positron) scattering by a nucleus. It is …
The confined variational method is used to generate a basis of correlated gaussians to describe the interaction region wave function for positron scattering from the H$_2$ molecule. The scattering length was $\approx -2.7$ $a_0$ while the zero energy $Z_{\rm eff}$ of 15.7 is compatible with experimental values. The variation of the scattering length and $Z_{\rm eff}$ with inter-nuclear distance was surprisingly rapid due to virtual state formation at $R \approx 3.4$ $a_0$.
A many-body theory approach is developed for the problem of positron-atom scattering and annihilation. Strong electron-positron correlations are included non-perturbatively through the calculation of the electron-positron vertex function. It corresponds to the sum of an infinite series of ladder diagrams, and describes the physical effect of virtual positronium formation. The vertex function is used to calculate the positron-atom correlation potential and nonlocal corrections to the electron-positron annihilation vertex. Numerically, we make use of B-spline basis sets, which ensures rapid conv…
Many-body theory is developed to calculate the $γ$-spectra for positron annihilation with valence and core electrons in the noble gas atoms. A proper inclusion of correlation effects and core annihilation provides for an accurate description of the measured spectra [Iwata \textit{et al.}, Phys. Rev. Lett. {\bf 79}, 39 (1997)]. The theory enables us to calculate the enhancement factors $γ_{nl}$, which describe the effect of electron-positron correlations for annihilation on individual electron orbitals $nl$. We find that the enhancement factors scale with the orbital ionization energy $I_{nl}$ …
In the annihilation of a positron with a bound atomic electron, the virtual gamma photon created may excite the atomic nucleus. We put forward this effect as a spectroscopic tool for an energy-selective excitation of nuclear transitions. This scheme can efficiently populate nuclear levels of arbitrary multipolarities in the MeV regime, including monopole transitions and giant resonances. In certain cases, it may have a higher cross sections than the conventionally used Coulomb excitation.
