Positronium negative ion

• Comment: The examples of weasel and peacock I gave are not the only ones, there are others throughout the July 9th draft. Ldm1954 (talk) 15:32, 9 July 2026 (UTC)

• Comment: As if June 9 there are too many issues; I started a little cleanup, then decided this needs more work than I want to do:
  1. Too many terms such as "particular interest", "crucial step", "essential ingredient". Please read WP:Weasel, WP:Peacock and WP:NPOV and revise.
  2. Too many unsourced claims that read as opinions or WP:OR. Examples are "given the difficulty in generating this system and its very short lifetime", "it is impossible to find an analytical solution for the Schrödinger equation", "nearly-zero outgassing properties".(The last statement is also incorrect science.)
  3. The lead needs more context for the non-scientist, see MOS:LEAD.
  This is not everything, just examples. Ldm1954 (talk) 12:12, 9 July 2026 (UTC)

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Positronium negative ion

File:Positronium negative ion.svg Cartoon representation of the positronium negative ion
Identifiers
ChEBI	CHEBI:46710
ECHA InfoCard
E number
CompTox Dashboard (EPA)	{{#property:P3117}}
Related compounds
Related compounds	Positronium hydride; Dipositronium
Except where otherwise noted, data are given for materials in their standard state (at 25 °C [77 °F], 100 kPa).
Infobox references

The positronium negative ion (${\text{Ps}}^{-}$) is a bound state of two electrons ($e^{-}$) and one positron ($e^{+}$). It is the simplest three-body system composed exclusively of leptons, making it an interesting for studying the quantum mechanical three-body problem. Additionally, the production of this ion represents the first step towards generating energy-tunable positronium beams, a field of research in fundamental physics.

History

The existence of a bound state between two electrons and a positron was first theoretically predicted by John Archibald Wheeler in 1946. In his work Polyelectrons, he theorized the existence of exotic bound systems, including the di-positronium, observed for the first time in 2007, and the positronium positive ion.

Since then, many theoretical works on ${\text{Ps}}^{-}$ have been published, concerning its binding energy, lifetime and other characteristics. Nevertheless, given the difficulty in generating this system and its very short lifetime, the first experimental observation was achieved only in 1981 by Allen P. Mills.

In 2007 another important milestone was achieved with the first high-efficiency production of this ion. This new method to generate ${\text{Ps}}^{-}$ provided a much higher positron-to-${\text{Ps}}^{-}$ conversion efficiency compared to the method used by Mills.

Energy levels and annihilation

File:Ps- structure.svg

Simplified scheme of the positronium negative ion spin configuration and distances, inspired by other works.

The internal structure of ${\text{Ps}}^{-}$ presents characteristics similar to an electron weakly bound to a positronium (Ps) atom. The expectation values for the positron-electron and electron-electron distances have been computed, obtaining 2.90 Å ($e^{+}$-$e^{-}$ distance) and 4.52 Å ($e^{-}$-$e^{-}$ distance).

Given the fact that ${\text{Ps}}^{-}$ is a three-body system, it is impossible to find an analytical solution for the Schrödinger equation. Furthermore, the Born–Oppenheimer approximation cannot be applied, since the three bodies possess exactly the same mass. Therefore, many efforts were performed towards the numerical computation of the ground state energy, which turns out to be $E_{\mathrm{g}}=-7.13\text{eV}$. The negative sign indicates that ${\text{Ps}}^{-}$ is stable against dissociation into its constituent particles. Nevertheless, it is an unstable system against annihilation. This happens, from a quantum mechanical point of view, when the wave functions of an electron and of the positron partially overlap in space. The positron can possess up or down spin orientation, without any restriction. Nevertheless, the two electrons must be in a singlet state, due to the Pauli exclusion principle. As a consequence, the annihilation process may occur either with an electron that possesses the same spin orientation of the positron or with an electron with opposite spin. These two cases present profound differences due to the distinct selection rules for the processes. In the first case, an odd number of gamma rays is generated (most probably three), as it happens for ortho-positronium. In the second case, an even number of gamma rays is generated (most probably two), as in the case of para-positronium. This may suggest that the decay rate of ${\text{Ps}}^{-}$ can be found by taking the spin-average of the ortho-Ps and para-Ps decay rates. This would result in

$$\frac{3\cdot {\mathrm{\Gamma }}_{\text{ortho-Ps}}+1\cdot {\mathrm{\Gamma }}_{\text{para-Ps}}}{4}=\frac{3\cdot 7.04\cdot 10^6{\text{s}}^{-1}+1\cdot 7.99\cdot 10^9{\text{s}}^{-1}}{4}\approx 2.00{\text{ns}}^{-1}$$

where the values used in the calculation have been precisely measured.

Many authors computed theoretically the decay rate for ${\text{Ps}}^{-}$ and achieved to precisely measure it, resulting in a value equal to $\mathrm{\Gamma }=2.09{\text{ns}}^{-1}$. Indeed, this value is very similar to the spin-averaged one. The measured decay rate corresponds to an average lifetime for ${\text{Ps}}^{-}$ of $\tau =479\text{ps}$, partially explaining the reason why this ion is so elusive.

Production

The first successful attempts to produce ${\text{Ps}}^{-}$ employed the so called beam-foil method. This consists in a positron beam impinging on a thin carbon foil target. The positrons' energy is adjusted such that a fraction of them penetrates the whole target. These positrons may exit from the other side of the target and bound two electrons with a certain probability, giving rise to ${\text{Ps}}^{-}$.

More recently, a new way of producing ${\text{Ps}}^{-}$ was developed by the group of Yasuyuki Nagashima. This new method is based on increasing the electronic cloud close to the surface of a metal, where positrons are expelled. To achieve this, a known procedure is to cover the surface of a metallic sample with a sub-monolayer of an alkali metal. Upon this coverage procedure, the electron work function of the system is strongly reduced. The spontaneous emission of ${\text{Ps}}^{-}$ from a surface is governed by the quantity$${\varphi }_{{\text{Ps}}^{-}}={\varphi }_{+}+2{\varphi }_{-}-7.13\text{eV}$$

where

${\varphi }_{+}$

and

${\varphi }_{-}$

are the positron and electron work functions respectively. If

${\varphi }_{{\text{Ps}}^{-}}$

, called

${\text{Ps}}^{-}$

affinity, is negative, then the emission of

${\text{Ps}}^{-}$

happens spontaneously. Therefore, given the strong dependence on the electron work function, the reduction of the latter implies an increase of the

${\text{Ps}}^{-}$

production efficiency.

File:Positronium negative ion efficient production.svg

High-efficiency production of positronium negative ions.

Positrons that penetrate the sample undergo several anelastic scattering events, losing their energy. The vast majority of them annihilate immediately with the conduction electrons of the metal or thermalize and then annihilate. But a non-negligible fraction thermalizes inside the sample and then diffuses. In some cases, the diffusion is directed towards the target surface and ${\text{Ps}}^{-}$ may be formed, with the positron bounding two electrons, and emitted under the previous conditions.

The target is usually made of tungsten, due to its slightly negative value for the

${\text{Ps}}^{-}$

affinity. Indeed, the emission of

${\text{Ps}}^{-}$

from clean tungsten surfaces has been observed. Different alkali metals have been used for the sub-monolayer growth and so far sodium has provided the best performance in terms of efficiency and duration. Sodium deposition is performed in situ, just after a short annealing of the tungsten. This is crucial to clean the target surface and to ensure a high-quality sodium deposition. This production protocol is able to achieve conversion efficiencies of positrons into

${\text{Ps}}^{-}$

up to 1.5%.

Experimental research

The increased availability of ${\text{Ps}}^{-}$ in laboratories opened up the possibility of large-scale experimental research involving this ion. There are two main research fields concerning this ion, one devoted to its own fundamental properties and the other devoted to the production of neutral positronium beams.

Production of positronium beams

File:Positronium beam production.svg

Schematic diagram of the production of a positronium beam via ${\text{Ps}}^{-}$ emission.

The production of ${\text{Ps}}^{-}$ represents the first, crucial, step towards the generation of positronium beams. Given its zero electric charge, it is very challenging to accelerate and focus positronium to form a beam. For this reason, it is necessary to first produce a ${\text{Ps}}^{-}$ beam, exploiting the high-efficiency generation method described above. The second step is to remove one electron via a process called photo-detachment. This method involves the use of a high-power laser cavity. The ${\text{Ps}}^{-}$ beam crosses the laser beam, which provides sufficient energy to remove one electron via single-photon absorption.

The photo-detachment has been performed using a 1064 nm wavelength laser. To maximize the photo-detachment probability a high photon flux is required. For this reason, a pulsed regime was used, allowing for a much higher light intensity compared to the continuous-wave operation. Nevertheless, Monte Carlo simulations have been performed, showing that achieving photo-detachment in continuous wave mode is feasible.

Positronium beams can be used for several purposes. Some of these include experimental tests of the CPT symmetry and of the Einstein Equivalence Principle (EEP) through positronium interferometry, as well as the study of antimatter gravity.

Quantum analysis of three-body systems

The positronium negative ion is the lightest system known so far composed of three elementary particles. Additionally, it contains both matter and antimatter and it is composed exclusively of leptons. Therefore, its constituents, as well as the entire system, do not possess any color charge, thus they cannot interact through the strong interaction. Therefore, unlike atomic systems such as the hydrogen negative ion ($\mathrm{H}{\phantom{A}}^{-}$), ${\text{Ps}}^{-}$ is completely free from uncertainties related to the presence of hadrons. These features make the positronium negative ion a perfect probe for the study of Quantum Electrodynamics (QED), allowing for precise comparisons between theoretical predictions and experimental measurements.

Given the absence of a central massive nucleus, ${\text{Ps}}^{-}$ represents a unique benchmark for the three-body problem. Sophisticated computational techniques, such as the use of Hylleraas-type wave functions, must be applied to precisely calculate the ground state energy, including its relativistic and QED energy shifts.

See also

• Annihilation
• Antimatter
• Di-positronium
• Positron
• Positronium
• Standard Model
• Three-body problem

External links

• Review on positronium negative ion
• CERN lecture on positronium

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