The positron-hydrogen atom scattering system is considered within the S-wave model. Convergence in the elastic scattering, excitation, ionization, and positronium formation channels is studied as a function of the number and type of states used to expand the total wave function. It is found that all unphysical resonances disappear only if near-complete pseudostate expansions are applied to both the atomic and positronium centers.
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 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.
Hyperspherical close-coupling method is used to calculate the elastic, positronium formation and excitation cross sections for positron collisions with atomic hydrogen at energies below the H(n=4) threshold for the J=2 partial wave. The resonances below each inelastic threshold are also analyzed. The adiabatic hyperspherical potential curves are used to identify the nature of these resonances.
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 long-standing problem to account for the electron-positron annihilation in positron Hydrogen scattering above the Positronium formation threshold has been resolved by the use of the three-body Faddeev formalism. The multichannel three-body theory for scattering states in presence of a complex absorbing potential is developed in order to compute the direct $e^+ e^-$ annihilation amplitude, the amplitude of Positronium formation and respective cross sections. A number of $e^+ e^-$ direct annihilation cross sections and Positronium formation cross sections in the energy gap between Ps$(1s)$ and…
We study the classical dynamics of the collinear positron-hydrogen scattering system below the three-body breakup threshold. Observing the chaotic behavior of scattering time signals, we in- troduce a code system appropriate to a coarse grained description of the dynamics. And, for the purpose of systematic analysis of the phase space structure, a surface of section is introduced being chosen to match the code system. Partition of the surface of section leads us to a surprising conjec- ture that the topological structure of the phase space of the system is invariant under exchange of the dynam…
The importance of the excited states of Positronium (Ps) in the formation cross sections(both differential and total) of the negative hydrogen ion (H^-) are investigated theoretically for the charge transfer reaction, Ps (n = 1, 2) + H --> e+ + H^- for a wide range of incident energies (e. g., threshold - 500 eV) . The calculations are performed in the frame work of a qualitative model, the post collisional Coulomb Modified Eikonal Approximation (CMEA) . A comparative study is also made between the capture from ground and excited states of the Ps. The present CMEA model takes account of higher…
Comment on "Revisiting the divergent multipole expansion of atom-surface interactions: Hydrogen and positronium, $α$-quartz, and physisorption" (arXiv:2308.04656v3)
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 $R \approx 3.4$ $a_0$.
We present a convergent variational basis-set calculational scheme for elastic scattering of positronium atom by hydrogen atom in S wave. Highly correlated trial functions with appropriate symmetry are needed for achieving convergence. We report convergent results for scattering lengths in atomic units for both singlet ($=3.49\pm 0.20$) and triplet ($=2.46\pm 0.10$) states.
Reply to Comment on "Revisiting the divergent multipole expansion of atom-surface interactions: Hydrogen and positronium, alpha-quartz, and physisorption" (arXiv:2501.14803)
The present theoretical work addresses the study of the formation of a positive Antihydrogen ion in a single charge exchange reaction where a positronium ( ground or excited state) interacts with a ground state anti-hydrogen atom, being embedded in a dense Debye plasma. The calculations are carried out in the frame work of a Coulomb Distorted Eikonal Approximation. The result shows that Ps(3S) is the most interesting state to enhance the anti H^+ production at the energy close to the reaction threshold. Regarding the Debye screening, it may be inferred that in lower energy regime, the screenin…
The production of anti-hydrogen ions in the GBAR experiment will occur via a two step charge exchange process. In a first reaction, the anti-protons from the ELENA ring at CERN will capture a positron from a positronium target producing anti-hydrogen atoms. Those interacting in the same positronium target will produce in a second step anti-hydrogen ions. This results in a dependence for the anti-ions production rate which is roughly proportional to the positronium density squared. We present a scheme to increase the anti-ions production rate in the GBAR experiment by tailoring the anti-proton …
The probabilities of bound-free electron-positron pair creation are calculated for head-on collisions of bare uranium nuclei beyond the monopole approximation. The calculations are based on the numerical solving of the time-dependent Dirac equation in the target reference frame with multipole expansion of the projectile potential. In addition, the energy dependence of the pair-creation cross section is studied in the monopole approximation.
A problem to account for the direct electron-positron annihilation in positron-hydrogen scattering above the positronium formation threshold has been resolved within the time independent formalism. The generalization of the optical theorem is derived for the case when an absorption potential is present in the Hamiltonian. With this theorem the annihilation cross section is fully determined by scattering amplitudes. This allows us to separate out analytically the contribution of the positronium formation from the overall annihilation cross section. The rest is determined as the direct annihilat…
We report results of differential cross sections for elastic scattering, target-elastic Ps excitations and target-inelastic excitation of hydrogen in a five-state coupled-channel model allowing for Ps(1s)H(2s,2p) and Ps(2s,2p)H(1s) excitations using a recently proposed time-reversal-symmetric regularized electron-exchange model potential. The present model yields a singlet Ps-H S-wave resonance at 4.01 eV of width 0.15 eV and a P-wave resonance at 5.08 eV of width 0.004 eV. We also study the effect of the inclusion of the excited Ps and H states on the convergence of the coupled-channel scheme…
The Configuration Interaction (CI) method using orbitals centered on the nucleus has recently been applied to calculate the interactions of positrons interacting with atoms. Computational investigations of the convergence properties of binding energy, phase shift and annihilation rate with respect to the maximum angular momentum of the orbital basis for the e^+Cu and PsH bound states, and the e^+-H scattering system were completed. The annihilation rates converge very slowly with angular momentum, and moreover the convergence with radial basis dimension appears to be slower for high angular mo…
The collision between a positronium (Ps) and a muonium (Mu) is studied for the first time using the static-exchange model and considering the system as a four-center Coulomb problem in the center of mass frame. An exact analysis is made to find the s-wave elastic phase-shifts, the scattering-lengths for both singlet and triplet channels, the integrated/total elastic cross section and the quenching cross section due to ortho to para conversion of Ps and the conversion ratio.
Positronium-hydrogen (Ps-H) scattering is of interest, as it is a fundamental four-body Coulomb problem. We have investigated low-energy Ps-H scattering below the Ps(n=2) excitation threshold using the Kohn variational method and variants of the method with a trial wavefunction that includes highly correlated Hylleraas-type short-range terms. We give an elegant formalism that combines all Kohn-type variational methods into a single form. Along with this, we have also developed a general formalism for Kohn-type matrix elements that allows us to evaluate arbitrary partial waves with a single cod…
The presence of vortices in the ionisation of hydrogen atoms by positrons at intermediate impact energies is investigated. The present findings show that a previously reported minima in the fully-differential cross section is the signature of a vortex in the continuum positron-electron-proton system. The behaviour of the real and imaginary parts of the complex-valued transition matrix is studied in order to determine and characterize the vortex in momentum space. The obtained information is translated to fully-differential ionisation cross sections, feasible of being measured with currently av…
Predicted twenty years ago, positron binding to neutral atoms has not yet been observed experimentally. A new scheme is proposed to detect positron-atom bound states by colliding Rydberg positronium (Ps) with neutral atoms. Estimates of the charge-transfer reaction cross section are obtained using the first Born approximation for a selection of neutral atom targets and a wide range of incident Ps energies and principal quantum numbers. We also estimate the corresponding Ps ionization cross section. The accuracy of the calculations is tested by comparison with earlier predictions for Ps charge …
The scattering of ortho-positronium (Ps) by hydrogen atoms has been investigated in a five-state coupled-channel model allowing for Ps(1s)H(2s,2p) and Ps(2s,2p)H(1s) excitations using a recently proposed electron-exchange model potential. The higher ($n\ge 3$) excitations and ionization of the Ps atom are calculated using the first Born approximation. Calculations are reported of scattering lengths, phase shifts, elastic, Ps- and H-excitation, and total cross sections. Remarkable correlations are observed between the S-wave Ps-H binding energy and the singlet scattering length, effective range…
Fragmentation of ground state ortho Positronium (Ps) in collision with Li ion (Li+) is studied in the framework of post collisional Coulomb distorted eikonal approximation (CDEA) for the target elastic case . The present model takes account of the two center effect on the ejected e which is crucial for a proper description of the projectile ionization involving an ionic target. Both the fully differential (TDCS) and the doubly differential (DDCS) cross sections (energy spectra) are investigated at intermediate and high incident energies. A broad distinct Electron loss peak (ELP) centered aroun…
The two-center basis generator method is used to obtain cross sections for excitation, capture, and ionization in Li$^{3+}$, C$^{3+}$, and O$^{3+}$ collisions with ground-state hydrogen at projectile energies from 1 to 100 keV/u. The interaction of the C$^{3+}$ and O$^{3+}$ projectiles with the active electron is represented by a model potential. Comparisons of cross sections with previously reported data show overall good agreement while discrepancies in capture for C$^{3+}$ collisions at low energies are noted. The present results show that excitation and ionization are similar across the th…
Electron-positron pair production in low-energy collisions of heavy nuclei is considered beyond the monopole approximation. The calculation method is based on the numerical solving of the time-dependent Dirac equation with the full two-center potential. Bound-free and free-free pair-production probabilities as well as the energy spectra of the emitted positrons are calculated for the collisions of bare uranium nuclei. The calculations are performed for collision energy near the Coulomb barrier for different values of the impact parameter. The obtained results are compared with the correspondin…
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…
We consider the most accurate tests of bound state QED theory of the hyperfine splitting in two-body atoms related to the HFS interval of the 1s state in muonium and positronium and the 2s state in hydrogen, deuterium and the helium-3 ion. We summarize their QED theory and pay special attention to involved effects of strong interactions and to recent optical measurements of the 2s HFS interval in hydrogen and deuterium. We present results for specific ratios of the 1s-2s frequencies in hydrogen and deuterium which happen to be among the most accurately measured and calculated quantities.
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
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…
We determine effective collisional radii of positronium (Ps) by considering Ps states in hard-wall spherical cavities. $B$-spline basis sets of electron and positron states inside the cavity are used to construct the states of Ps. Accurate Ps energy eigenvalues are obtained by extrapolation with respect to the numbers of partial waves and radial states included in the bases. Comparison of the extrapolated energies with those of a pointlike particle provides values of the effective radius $ρ_{nl}$ of Ps($nl$) in collisions with a hard wall. We show that for $1s$, $2s$, and $2p$ states of Ps, th…
We have completed the calculation of pure-recoil corrections of order $(Z α)^6$ to Coulombic bound states of two spin-1/2 fermions without approximation in the particle masses. Our result applies to systems of arbitrary mass ratio such as muonium and positronium, and also hydrogen and muonic hydrogen (with the neglect of proton structure effects). We have shown how the two-loop master integrals that occur in the relativistic region can be computed in analytic form, and suggest that the same method can be applied to the three-loop integrals that would be present in a calculation of order $(Z α)…
A simple locally accurate uniform approximation for the nodeless wavefunction is constructed for a {\it neutral} system of two Coulomb charges of different masses $(-q,m_1)$ and $(q,m_2)$ at rest in a constant uniform magnetic field for the states of positive and negative parity, ${(1s_0)}$ and ${(2p_0)}$, respectively. It is shown that by keeping the mass and charge of one of the bodies fixed, all systems with different second body masses are related. This allows one to consider the second body as infinitely-massive and to take such a system as basic. Three physical systems are considered in …
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…
The formulation of a suitable nonlocal model potential for electron exchange is presented, checked with electron-hydrogen and electron-helium scattering, and applied to the study of elastic and inelastic scattering and ionization of ortho positronium (Ps) by helium. The elastic scattering and the $n = 2$ excitations of Ps are investigated using a three-Ps-state close-coupling approximation. The higher ($n\ge 3$) excitations and ionization of Ps atom are treated in the framework of Born approximation with present exchange. Calculations are reported of phase shifts, and elastic, Ps-excitation, a…
Consideration of antigravity for antiparticles is an attractive target for various experimental projects. There are a number of theoretical arguments against it but it is not quite clear what kind of experimental data and theoretical suggestions are involved. In this paper we present straightforward arguments against a possibility of antigravity based on a few simple theoretical suggestions and some experimental data. The data are: astrophysical data on rotation of the Solar System in respect to the center of our galaxy and precision spectroscopy data on hydrogen and positronium. The theoretic…
The many-body system comprising a He nucleus, three electrons, and a positron has been studied using the exact diagonalization technique. The purpose has been to clarify to which extent the system can be considered as a distinguishable positronium (Ps) atom interacting with a He atom and, thereby, to pave the way to a practical atomistic modeling of Ps states and annihilation in matter. The maximum value of the distance between the positron and the nucleus is constrained and the Ps atom at different distances from the nucleus is identified from the electron and positron densities, as well as f…
