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 estimate the values of the s-wave scattering lenght and the effective range for e+ - Ar and e+ - N2 collisions.
The aim of this work is to identify the mechanisms responsible for very large rates and other peculiarities observed in low-energy positron annihilation on molecules. The two mechanisms considered are: (i) Direct annihilation of the incoming positron with one of the molecular electrons. This mechanism dominates for atoms and small molecules. I show that its contribution to the annihilation rate can be related to the positron elastic scattering cross section. This mechanism is characterized by strong energy dependence of the annihilation rate at small positron energies if a low-lying virtual le…
Measurements of energy-resolved positron-molecule annihilation show the existence of positron binding and vibrational Feshbach resonances. The existing theory describes this phenomenon successfully for the case of infrared-active vibrational modes which allow dipole coupling between the incident positron and the vibrational motion. Presented here are measurements of positron-molecule annihilation made using a recently developed cryogenic positron beam capable of significantly improved energy resolution. The results provide evidence of resonances associated with infrared-inactive vibrational mo…
This article presents an overview of current understanding of the interaction of low-energy positrons with molecules with emphasis on resonances, positron attachment and annihilation. Annihilation rates measured as a function of positron energy reveal the presence of vibrational Feshbach resonances (VFR) for many polyatomic molecules. These resonances lead to strong enhancement of the annihilation rates. They also provide evidence that positrons bind to many molecular species. A quantitative theory of VFR-mediated attachment to small molecules is presented. It is tested successfully for select…
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.
A model-potential approach has been developed to study positron interactions with molecules. Binding energies and annihilation rates are calculated for positron bound states with a range of alkane molecules, including rings and isomers. The calculated binding energies are in good agreement with experimental data, and the existence of a second bound state for $n$-alkanes (C$_n$H$_{2n+2}$) with $n\geq12$ is predicted in accord with experiment. The annihilation rate for the ground positron bound state scales linearly with the square root of the binding energy.
Enhanced positron annihilation on polyatomic molecules is a long-standing and complex problem. We report the results of calculations of resonant positron annihilation on methyl halides. A free parameter of our theory is the positron binding energy. A comparison with energy-resolved annihilation rates measured for CH$_3$F, CH$_3$Cl, CH$_3$Br [Barnes et al. Phys. Rev. A {\bf 74}, 012706 (2006)] shows good agreement and yields estimates of the binding energies.
The energies at geometries close to the equilibrium for the e$^+$BeO and e$^+$LiF ground states were computed by means of diffusion Monte Carlo simulations. These results allow us to predict the equilibrium geometries and the vibrational frequencies for these exotic systems,and to discuss their stability with respect to the various dissociation channels. Since the adiabatic positron affinities were found to be smaller than the dissociation energies for both complexes, we propose these two molecules as possible candidates in the challenge to produce and detect stable positron-molecule systems.
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 dominant mechanism of low-energy positron annihilation in polyatomic molecules is through positron capture in vibrational Feshbach resonances (VFR). In this paper we investigate theoretically the effect of anharmonic terms in the vibrational Hamiltonian on the positron annihilation rates. Such interactions enable positron capture in VFRs associated with multiquantum vibrational excitations, leading to enhanced annihilation. Mode coupling can also lead to faster depopulation of VFRs, thereby reducing their contribution to the annihlation rates. To analyze this complex picture, we use couple…
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…
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_…
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.
The positronium molecule (Ps$_2$) has not been experimentally observed yet because its tiny (4.5 eV) binding energy cannot be detected when the molecule annihilates by emitting two photons with energy of 0.51 MeV each. It is shown in this paper that the electric dipole transition between the recently found L=1 excited-state and the L=0 ground-state with its characteristic photon energy of 4.94 eV is a clear signature of the existence of the positronium molecule and the possibility of its experimental observation is realistic. The probability of this transition is about 17 % of the total decay …
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 model for positron binding to polar molecules is considered by combining the dipole potential outside the molecule with a strongly repulsive core of a given radius. Using existing experimental data on binding energies leads to unphysically small core radii for all of the molecules studied. This suggests that electron-positron correlations neglected in the simple model play a large role in determining the binding energy. We account for these by including polarization potential via perturbation theory and non-perturbatively. The perturbative model makes reliable predictions of binding energies…
UKRmol+ is a new implementation of the UK R-matrix electron-molecule scattering code. Key features of the implementation are the use of quantum chemistry codes such as Molpro to provide target molecular orbitals; the optional use of mixed Gaussian -- B-spline basis functions to represent the continuum and improved configuration and Hamiltonian generation. The code is described, and examples covering electron collisions from a range of targets, positron collisions and photionisation are presented. The codes are freely available as a tarball from Zenodo.
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 …
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…
Using a complex model potential, we have calculated the total, integrated elastic, momentum transfer, absorption, and differential cross sections for positrons scattered from molecular hydrogen. The widely available software package GAUSSIAN is used to generate the radial electronic charge density of the molecule which is used to produce the interaction potentials. The quasifree absorption potential, previously developed and used for positron-atom scattering, is extended to positron scattering from molecular targets. It is shown that this model potential approach produces accurate results even…
Effect of the electric quadrupole moment, $Q$, is studied for positron-atom bound systems. It is demonstrated that for $Q >50$ a.u. the electric quadrupole potential is sufficiently strong to bind positron (or electron) even in the absence of the dipole polarization potential. Such large values of $Q$ are not known for atomic ground states, however, they exist in molecules and excited atoms. In the state $2s2p~^3P^o_2$ of beryllium, the quadrupole contribution makes difference between stable bound state and decay to Be$^+$ ion and positronium. In a majority of atoms the quadrupole contribution…
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 quasistatic limit of the velocity-gauge strong-field approximation describing the ionization rate of atomic or molecular systems exposed to linear polarized laser fields is derived. It is shown that in the low-frequency limit the ionization rate is proportional to the laser frequency, if a Coulombic long-range interaction is present. An expression for the corresponding proportionality coefficient is given. Since neither the saddle-point approximation nor the one of a small kinetic momentum is used in the derivation, the obtained expression represents the exact asymptotic limit. This result…
The nuclear polarization of $\mathrm{H}_2$ molecules formed by recombination of nuclear polarized H atoms on the surface of a storage cell initially coated with a silicon-based polymer has been measured by using the longitudinal double-spin asymmetry in deep-inelastic positron-proton scattering. The molecules are found to have a substantial nuclear polarization, which is evidence that initially polarized atoms retain their nuclear polarization when absorbed on this type of surface
The two-center Dirac equation for an electron in the external electromagnetic field of two colliding heavy ions in the limit in which the ions are moving at the speed of light is exactly solved and nonperturbative amplitudes for free electron-positron pair production are obtained. We find the condition for the applicability of this solution for large but finite collision energy, and use it to explain recent experimental results. The observed scaling of positron yields as the square of the projectile and target charges is a result of an exact cancellation of a nonperturbative charge dependence …
A new mechanism for the production of electron-positron pairs from the interaction of a laser field and a fully stripped diatomic molecule in the tunneling regime is presented. When the laser field is turned off, the Dirac operator has resonances in both the positive and the negative energy continua while bound states are in the mass gap. When this system is immersed in a strong laser field, the resonances move in the complex energy plane: the negative energy resonances are pushed to higher energies while the bound states are Stark shifted. It is argued here that there is a pair production enh…
