# Positronium

Positronium is an exotic atom made up of an electron and its antiparticle , the positron . ${\ displaystyle e ^ {-} e ^ {+} \! \,}$ ${\ displaystyle e ^ {-} \! \,}$ ${\ displaystyle e ^ {+} \! \,}$

## properties

A distinction is made between ortho- and parapositronium . While the spins of electron and positron (1/2 each) are in the same direction in the orthopositronium, i.e. the total spin of the system is 1, they are opposite in the parapositronium, which means that the total spin here is 0.

The electron and positron annihilate so that the positronium only has a short lifetime . Parapositronium decays into two photons with an average lifetime of 0.125  ns . For reasons of invariance under charge conjugation, orthopositronium can only decay into an odd number of photons, for reasons of Lorentz invariance (conservation of energy momentum), i.e. at least three. Since this process is less likely, it has a significantly longer lifetime of 142 ns.

Bohr's atomic model is sufficient to calculate the radius in the ground state :

${\ displaystyle r = n ^ {2} {\ frac {4 \ pi \ varepsilon _ {0} \ hbar ^ {2}} {\ mu e ^ {2}}} = 0 {,} 106 \, {\ textrm {nm}} \ qquad {\ textrm {with}} \ qquad n = 1}$ (Principal quantum number)${\ displaystyle \ qquad {\ textrm {and}} \ qquad \ mu = {\ frac {m_ {e} m_ {p}} {m_ {e} + m_ {p}}} = {\ frac {m_ {e }} {2}} \, \, \,}$

( is the mass of the electron, the mass of the positron). ${\ displaystyle m_ {e}}$${\ displaystyle m_ {p}}$

This corresponds to twice the radius of the electron shell of the ground state of the hydrogen atom.

Positronium can also be treated by a special form of the two-body Dirac equation. A system of two point particles with Coulomb interaction can be exactly separated in the (relativistic) momentum space . The resulting ground state energy was calculated very precisely by J. Shertzer using a finite element method .

The Dirac equation with a Hamilton operator for two Dirac particles and a static Coulomb potential is not relativistically invariant. However, one adds the terms with , , added (or , wherein the fine structure constant , the result is), then relativistic invariant. Only the leading term is taken into account. The contribution to order is the Breit term; however, the term for order is rarely used because the Lamb shift already occurs in order , which requires quantum electrodynamics . ${\ displaystyle 1 / c ^ {2n}}$${\ displaystyle n = 1.2 \ ldots}$${\ displaystyle \ alpha ^ {2n}}$${\ displaystyle \ alpha}$${\ displaystyle \ alpha ^ {2}}$${\ displaystyle \ alpha ^ {4}}$${\ displaystyle \ alpha ^ {3}}$

## Prediction and discovery

Theoretically, the positronium atom was predicted in 1932 by Carl David Anderson and z. B. Stjepan Mohorovičić . Physicist Martin Deutsch at the Massachusetts Institute of Technology provided the first evidence .

### Di-positronium

Di-positronium , or dipositronium , is a molecule made up of two positronium atoms and thus an analogy to the hydrogen molecule made up of two normal hydrogen atoms. Its existence was predicted and theoretically described by John Archibald Wheeler as early as 1946, but it was not until 2007 that David Cassidy and Allen Mills were able to experimentally produce and demonstrate the molecule.

### Positronic water

Positronic water is a hypothetical short-lived, water- like molecule made up of one oxygen and two positronium atoms . Compared to normal water, the hydrogen atoms are replaced by positronium.

In 1998, Jiang and Schrader predicted on the basis of quantum Monte Carlo simulations that positronic water could exist, but was not as chemically stable as normal water because the binding energy was only about 30% as large.

In practice, positronic water has not yet been produced.

## Individual evidence

1. AH Al-Ramadhan, DW Gidley: New precision measurement of the decay rate of singlet positronium . In: Phys. Rev. Lett. tape 72 , no. 11 , 1994, pp. 1632-1635 , doi : 10.1103 / PhysRevLett.72.1632 .
2. ^ RS Vallery, PW Zitzewitz, DW Gidley: Resolution of the Orthopositronium-Lifetime Puzzle . In: Phys. Rev. Lett. tape 90 , no. 20 , 2003, p. 203402 , doi : 10.1103 / PhysRevLett.90.203402 .
3. a b T.C. Scott, J. Shertzer, RA Moore: Accurate finite element solutions of the two-body Dirac equation . In: Physical Review A . 45, No. 7, 1992, pp. 4393-4398. bibcode : 1992PhRvA..45.4393S . doi : 10.1103 / PhysRevA.45.4393 . PMID 9907514 .
4. ^ Chris W. Patterson: Anomalous states of Positronium . In: Physical Review A . 100, No. 6, 2019, p. 062128. doi : 10.1103 / PhysRevA.100.062128 .
5. ^ S. Mohorovičić: Possibility of new elements and their meaning for astrophysics . In: Astronomical News . 253, No. 4, 1934, pp. 93-108. doi : 10.1002 / asna.19342530402 .
6. ^ Molecules of Positronium Observed in the Laboratory for the First Time . Press release, University of California, Riverside , September 12, 2007.
7. Jonathan Fildes: Mirror particles form new matter . BBC News, September 12, 2007.
8. N. Jiang, DM Schrader: Positronic Water, Ps 2 O . In: Phys. Rev. Lett. tape 81 , no. 23 , p. 5113 , doi : 10.1103 / PhysRevLett.81.5113 .