Core Concepts

Closed-form analytical expressions for the angular distribution and total cross sections of single-quantum positron annihilation with bound electrons in the near-threshold region are obtained, considering the effects of atomic screening.

Abstract

The paper discusses the single-quantum positron annihilation process in the region where the parameters Zα and vq (positron velocity) are much less than 1, but Zα/vq is of the order of 1.

Key highlights:

- Analytical expressions for the differential and total cross sections are derived for s- and p-electrons in the leading order, showing that the cross section with angular momentum of the bound electron l > 1 is suppressed.
- The impact of atomic screening on the cross sections is investigated, and a simple analytical expression is obtained that is universal and independent of the explicit form of the atomic potential.
- It is shown that the screening effect significantly increases the differential and total cross sections compared to the Coulomb potential.
- Analogous results are also obtained for the bound-free e+e- photoproduction process.

The paper provides a comprehensive theoretical treatment of the single-quantum positron annihilation process at low energies, offering closed-form analytical expressions that can be useful for both theoretical and experimental studies in this field.

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arxiv.org

Stats

We obtain a simple analytical expression for the total cross section in the screened potential:
σscr
K = 4π/3 * α(Zα)^5 / (m^2*vq) * B1S * [A0(q)27π^2/32(Zα)^2 + A1(q)*vq^2]
σscr
L = π/6 * α(Zα)^5 / (m^2vq) * [A0(q)(27π^2/32B2S + 3/4B2P)*(Zα)^2 + A1(q)B2Svq^2]
where A0(q), A1(q) are the screening factors for the positron s-wave and p-wave, and B1S, B2S, B2P are the screening factors for the bound electron wave functions.

Quotes

"It is worth noting that this result is universal and independent of the explicit form of the atomic potential."
"We show that the screening effect can be taken into account by changing the value of wave function normalization, while the phase of the wave function does not affect the result."

Key Insights Distilled From

by Peter.A. Kra... at **arxiv.org** 10-01-2024

Deeper Inquiries

The analytical expressions for single-quantum positron annihilation (SQA) derived in this work can be extended to higher-order processes by incorporating perturbative techniques from quantum electrodynamics (QED). For instance, one could consider multi-photon processes or the inclusion of additional virtual particles in the Feynman diagrams, which would require the evaluation of more complex matrix elements. This could involve using the Dyson series to account for higher-order corrections in the interaction potential, leading to a more comprehensive understanding of the annihilation process.
Moreover, the framework established for the Coulomb potential can be adapted to more complex atomic systems by employing effective potentials that account for electron correlation effects and screening in multi-electron atoms. Techniques such as configuration interaction or coupled-cluster methods could be utilized to derive wave functions that better represent the bound states of electrons in heavier atoms. Additionally, the use of numerical methods, such as the finite element method or Monte Carlo simulations, could provide insights into the behavior of positron annihilation in systems with more intricate electronic structures.

To validate the theoretical predictions regarding single-quantum positron annihilation, several experimental techniques and setups could be employed. One promising approach is the use of positronium spectroscopy, where positrons are allowed to form positronium atoms with bound electrons. By measuring the decay rates and energy levels of positronium, researchers can compare the experimental results with the theoretical predictions derived in this work.
Another technique involves using high-energy particle accelerators to produce low-energy positrons and directing them towards targets composed of light nuclei. Advanced detectors, such as time-of-flight spectrometers and gamma-ray detectors, can be utilized to measure the angular distribution and total cross sections of the annihilation events. These measurements can then be compared with the analytical expressions obtained in the study, providing a direct test of the theoretical framework.
Additionally, the use of synchrotron radiation facilities could allow for precise measurements of the energy dependence of the cross sections, further validating the predictions made for both screened and unscreened potentials.

The single-quantum positron annihilation process has several potential applications beyond fundamental physics, particularly in the fields of medical imaging and materials science. In medical imaging, positron emission tomography (PET) utilizes the annihilation of positrons to produce high-resolution images of metabolic processes in the body. The theoretical insights gained from understanding SQA can enhance the accuracy of PET imaging by improving the interpretation of annihilation events and optimizing the design of imaging systems.
In materials science, positron annihilation spectroscopy (PAS) is a powerful technique used to probe the electronic structure and defects in materials. By analyzing the characteristics of the gamma rays emitted during positron annihilation, researchers can gain insights into the microstructural properties of materials, such as vacancy concentrations and defect types. The analytical expressions derived in this work can help refine the models used in PAS, leading to more accurate assessments of material properties.
Furthermore, the understanding of positron annihilation processes can contribute to the development of novel materials with tailored electronic properties, such as semiconductors and nanomaterials, by providing a deeper understanding of how positrons interact with different atomic structures. This knowledge can facilitate advancements in various technologies, including electronics, photonics, and energy storage systems.

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