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Vol.3, No.1, 42-47 (2011) Natural Science
Copyright © 2011 SciRes. OPEN ACCESS
Recent interests on positron (+
e), positronium (Ps) and
antihydrogen (H)
Hasi Ray1,2
1Department of Science, National Institute of Technical Teachers’ Training and Research (NITTTR), Salt Lake City, Kolkata, India
2Positron Laboratory, Department of Physics & Astronomy, UCR, Riverside, California, USA; hasi_ray@yahoo.com
Received 21 August 2010revised 25 September 2010; accepted 28 September 2010.
A brief survey is made to highlight the recent
interests in positron, positronium and antimat-
ter physics. Positron is the first antiparticle
observed which was predicted by Dirac. Posi-
tronium is itself its antiparticle and bi-posi-
tronium molecule is recently observed in labo-
ratory which was predicted by Wheeler in 1946.
The simplest antiatom i.e. antihydrogen is ob-
served in the laboratory and the process to
achieve the stable confinement of antihydrogen
within the trap are in progress to test the stan-
dard model.
Keywords: Positron; Positronium; Antihydrogen;
Dipositronium; Antimatter; Bose-Einstein
Condensation; Standard Model
Dirac was awarded the Nobel prize in Physics in 1933
by the Royal Academy of Sciences for developing the
basic new ideas of physics, namely his theory of wave
mechanics leading upto his relativistic theory of elec-
trons (1928) and holes (1930). Before appearance of
Schrodinger’s theory, Heisenberg brought out his fa-
mous quantum mechanics starting from quite different
stand points and viewed his problem from the very be-
ginning with such a broad angle that it took care of sys-
tems of electrons, atoms, and molecules. Schrodinger
thought that it should be possible to find a wave equation
for the motions executed by the electrons which would
define these waves in the same way as the wave equation
which determined the propagation of light. Although
Heisenberg’s and Schrodinger’s theories had different
starting points and were developed by the use of differ-
ent processes of thought, they produced the same results
for problems treated by both theories. Dirac has set up a
wave mechanics which starts from the most general
conditions. He imposed the condition that the postulate
of relativity theory has to be fulfilled. Dirac divided the
initial wave equation into two simpler ones, each pro-
viding solutions independently. It later appeared that one
of the solution systems required the existence of positive
electrons having the same mass and charge as the known
negative electrons. This initially posed considerable dif-
ficulty for Dirac’s theory [1], since positively charged
particles were known only in the form of the heavy atom
nucleus. This difficulty which at first opposed the theory
has later become a brilliant confimation of its validity.
The existence of the spin of electrons and its qualities
are a consequence of this theory. In 1913, Bohr had ex-
pressed the idea that Planck's constant should be taken as
the determining factor for movements within the atom,
as well as, for emission and absorption of light waves.
Bohr assumed, after Rutherford, that an atom consists of
an inner, heavy, positively charged core, around which
negative, light electrons circulate in closed paths, held to
the nucleus by Coulomb attraction. Robert Oppenheimer
pointed out that an electron and its hole would be able to
annihilate each other, releasing energy on the order of
the electron’s rest energy in the form of energetic pho-
tons; if holes were protons, stable atoms would not exist.
Hermann Weyl also noted that a hole should act as
though it has the same mass as an electron, whereas the
proton is about two thousand times heavier. The issue
was finally resolved in 1932 when the positron (e
) was
discovered by Carl Anderson [2], with all the physical
properties predicted for the Dirac hole.
The Nobel prize for Physics in 1936 was awarded by
V. F. Hess (1/2) for his discovery of cosmic radiation
and C. D. Anderson (1/2) for his discovery of the posi-
tron. The year 1895 was a turning-point in the history of
physics: Rontgen discovered X-rays and this was rapidly
followed by Becquerel’s discovery of radioactive radia-
tion, and by the discovery of the negative electron by J. J.
Thomson (1897) - one of the fundamental elements of
atomic structure. Becquerel demonstrated that the radia-
tion emitted by uranium shared certain characteristics
with X-rays but, unlike X-rays, could be deflected by a
H. Ray / Natural Science 3 (2011) 42-47
Copyright © 2011 SciRes. OPEN ACCESS
magnetic field and therefore must consist of charged
particles. The existence of cosmic radiation became
manifest during the search for sources of radioactive
radiation. The presence of cosmic radiation offered im-
portant problems on the formation and destruction of
matter. Carl Anderson, in the course of his comprehen-
sive studies on the nature and qualities of cosmic radia-
tion, succeeded in finding one of the buildingstones of
the universe, the positron. Becquerel and Thomson were
awarded the Nobel Prizes for physics in 1903 and 1906
respectively for their discoveries. Marie Curie with her
husband Pierre Curie, were recognized the Nobel prize
in 1901 for their discovery of the radioactive elements
radium and polonium. In 1911, Marie Curie (November
7, 1867 to July 4, 1934) was again honored with a Nobel
prize, but in chemistry, for successfully isolating pure
radium and determining radium’s atomic weight.
2.1. Positron
Positron is the first observed antiparticle e.g. antielec-
tron. A Wilson cloud chamber, which is used for detect-
ing particles for ionizing radiation, picture taken by Carl
D. Anderson in 1931 showed a particle entering from
below and passing through a lead plate; the direction of
curvature of the path caused by a magnetic field indi-
cated that the particle was a positively charged one but
with the same mass and other characteristics as an elec-
tron. The discovery by Anderson, in 1932, of the crea-
tion of pairs of electrons and positrons by electromag-
netic radiation, and the subsequent interpretation of this
observation, in the light of Dirac's already existing rela-
tivistic theory of the spinning electron, initiated a fruitful
branch of physics which is now often known under the
name of “pair theory”. The state of disturbance of elec-
tron-positron field in the neighbourhood of an atomic
nucleus is still imperfectly understood.
2.2. Positronium
In 1934, S. Mohorovicic [3] theoretically predicted
the existence of the bound system of a positron (e
) and
an electron (e) which is known today as Positronium
(Ps), named by Ruark in 1945 [4]. There are two types
of Ps; one is known as para-Ps and the other is ortho-Ps.
Para-Ps is a spin singlet state that is in this state of Ps,
the spins of positron and electron are antiparallel and it
has a life time 125 pico seconds in vacuum. Ortho-Ps is
a spin-triplet state, here the spins of positron and elec-
tron are parallel and its life time 140 nano seconds in
vacuum. Deutsch [5] observed Ps in the laboratory in
1951 in gaseous medium. The distribution of time delays
between the emission of a nuclear gamma-ray from the
decay of 22
Na and the appearance of an annihilation
quantum had been measured for positrons stopping in a
large number of gases and gas mixtures. From the direct
observation of the continuous gamma-ray spectrum due
to the three-quantum annihilation of triplet positronium
in nitrogen confirmed the abundant formation of Ps;
since due to electron exchange with the gas molecules
having an odd number of electrons, such as nitric oxide,
the triplet state of Ps converted very rapidly to the
singlet state.
2.3. Dipositronium Molecule
The e
being the antiparticle of electron (e
) and Ps
being itself its antiatom and the lightest hydrogen-like
exotic element, motivated the growing interest of physi-
cists and chemists. Cassidy and Mills [6] showed that
when intense positron bursts were inplanted into a thin
film of porous silica, dipositronium molecule (2
Ps ) was
created on the internal pore surfaces. They found [7] that
molecule formation occured much more efficiently than
the competing process of spin exchange quenching, ob-
serving a reduction in the amount of Ps emitted from an
atomically clean Al (1,1,1) surface that depends on the
incident positron beam density. If dipositronium is cre-
ated, then some Ps that might otherwise have been ther-
mally desorbed in the long lived triplet state instead de-
cays at the 2
Ps rate of ~ 4 1
ns [8,9]. Since the mole-
cule decays predominantly via two gamma rays while
the long lived triplet Ps decays via three photons one
could in principle, detect 2
Ps using energy selective
detectors. The earlier observation of Ps [10] and the
recent observation of 2
Ps molecule [6] in the labora-
tory, both the composites were predicted by Wheeler [11]
in 1946, have paved the way of further multipositronium
work and added a new dimension in antiatom physics
[12-13]. It is of interest to know the properties of 2
[8]. This molecule has two electrons and two positrons
instead of two protons in hydrogen molecule (2
). All
the four constitutents are of equal masses and it is the
lightest molecule. The spin magnetic moment of positron
in 2
Ps is much more stronger than spin magnetic mo-
ment of proton in 2
. Due to very large spin magnetic
moment of positron, the hyperfine structure of Ps be-
comes comparable to its fine structure. So the spectral
behaviours of Ps is expected to be much different from a
normal H. Binding energy of dipositronium or 2
Ps is
Eb = –0.435 eV [14] while in 2
molecule it is Eb
= –4.478 eV. The binding energy of Ps
, Eb =
–0.3266 eV [10]. Like 2
, 2
Ps molecule exists in an
overall singlet state [15].
H. Ray / Natural Science 3 (2011) 42-47
Copyright © 2011 SciRes. OPEN ACCESS
2.4. Polyelectrons
Wheeler added a note [11] regarding the question of
stability of large polyelectrons. According to him, if the
stability of the system with two positrons and two elec-
trons i.e. the 2
Ps molecule is granted, then the next
question regarding the stability comes for such four-
particle system i.e. 4
Ps [16], when account is taken of
the balance between the zero-point kinetic energy of
these light masses and the potential energy of van der
Waals attraction between them. Soon after the prediction
of Wheeler in 1946, Hylleraas and Ore [17] calculated
the binding energy of 2
Ps . No further work [18] on
larger polyelectrons appeared in literature. We are trying
to calculate the binding energy of a system with four
positrons and four electrons. It is expected that 4
may have a binding energy, Eb smaller in magnitude
than 2
Ps because of placing a second 2
Ps (see Fig-
ure 1) inside a 2
Ps (see Figure 2) which may cause a
slight reduction in the magnitude of binding energy be-
tween the two atoms at the ends of the chain. The sym-
bol in figures indicate the electrostatic binding be-
tween e and e in Ps . The latest reported binding
energies of a few systems are presented in Table 1 for
ready informations.
2.5. Bose-Einstein Condensation (BEC) of Ps
Another remarkable phenomenon of Ps is the forma-
tion of Bose Einstein condensate. The Bose-Einstein
condensation (BEC) occurs when a macroscopic fraction
of an ensemble of particles obeying Bose statistics col-
lapses into a single state at low temperatures.
In a non-interacting Bose gas confined by the external
harmonic potential
22 22 22
ext xyz
Vr mwxwywz ,
the critical temperature for BEC is given by [21]
kT N
 (1)
is the geometric mean of the
oscillator frequencies, and
m and
N are, respec-
tively, the particle mass and the number of bosons in the
trap. The above result is obtained using local density
approximation (LDA), where the temperature of the gas
is assumed to be much larger than the spacing between
single particle levels: ,,
 . In this case the
density of thermal atoms can be written as
[] []
[] []
Figure 1. Di-positronium 2
Ps .
[] [] [] []
[] [] [] []
 
 
Figure 2. 4-positronium 4
Table 1. Latest reported binding energies of a few systems.
Name SymbolBinding
Energy Name SymbolBinding
(eV) (eV)
Positronium Ps –6.80 Hydrogen H –13.60
Di-positronium 2
Ps –0.43a Hydrogen 2
molecule molecule
Positronium-ion Ps
–0.33b Hydro-
? e
4-positronium 4
Ps ? Positronium
PsH –1.06d
molecule Hydride
Vr kT
extB B
nr n
is the boson thermal wave-
length. At =C
TT the boson chemical potential takes
the critical value ==0
, corresponding to the
bottom of the external potential, and the density
in the centre of the trap satisfies the critical condition
holding for a homogene-
ous system. Here ‘h’ is Planck’s constant, ‘
k’ is
Boltzmann constant and =2h
. As the temperature
is lowered below Tc the number of particles in the zero
momentum state 0
n develops a macroscopic value
0=1 c
nn TT (3)
is comprised of an ee
bound in a hydrogenic orbit.
Its mass, 2e
m, is extremely light compared to H, an im-
portant ingredient [23] for achieving reasonable Bose
condensation temperatures. As a purely leptonic, mac-
roscopic quantum matter-antimatter system this would
be of interest in its own right, it would also represent a
milestone on the path to produce an annihilation gamma-
ray laser.
2.6. Antihydrogen and Its Spectra
In addition, the first confirmed production of cold an-
tihydrogen (
) atoms in a confinement trap [24] in
2002 and the initiative to achieve the stable confinement
of neutral atoms within the trap has created a consider-
able excitement to both the physicists and chemists.
is an ideal system for testing the standard model [25,26]
H. Ray / Natural Science 3 (2011) 42-47
Copyright © 2011 SciRes. OPEN ACCESS
prediction of the symmetry between matter and antimat-
ter. According to this model, systems made up of anti-
matter should behave identically to those composed of
matter. Just as a hydrogen atom (
) consists of an
electron orbiting a proton, an antihydrogen atom (
consists of a positron orbiting an antiproton. The guess-
ing is that the sprectrum of
looks exactly like that
. After all, the emission spectrum of H is due to an
excited electron jumping from the excited energy level
down to a lower level(s): presumably the positron in
has the same separation of energy levels. Any difference
between the emission spectrum in
be a new indication. The use of laser spectroscopy to
measure and compare the electronic structures of
that of normal
(e.g. antiatom and atom) is a new
and an interesting area [27].
According to Dirac’s theory, antimatter particles
should have the same mass, but opposite charge as their
matter equivalents e.g. the simplest antimatter of elec-
tron is positron. Antimatter is naturally formed during
the radioactive decay of some elements. However, such
naturally occurring antimatter is too little to be able to
produce significant collection of the system. They are
quasi stationary system i.e. their life time is very short
( pico seconds) - this period of time proves inade-
quate for collection and experimentation. This had led to
the need for further research and study on how to pro-
duce large amounts of antimatter under controlled condi-
3.1. High Temeperature BEC
The spin polarized atomic hydrogen H (i.e. both
the proton and electron have the down spins) or H
both the proton and electron have the up spins) is ex-
pected to form no molecule and it will remain a gas (in
the atomic state) down to zero temperature. At densities
16 3
the system is weakly interacting and will
Bose condense at temperatures of roughly 10–2 K. Al-
though a gas of H or H is a good approximation to
an ideal Bose system, workers have been unable to
achieve high enough densities or low enough tempera-
tures to observe its Bose condensation [22]. The exciton
gas produced by pumping an insulator like Cu2O with a
short laser pulse is also a promising candidate. This sys-
tem is in many ways very analogous to the positronium
system we discuss here. A collection of the spin polar-
ized ortho Ps (Ps i.e. both the positron and electron
have the down spins or Ps i.e. both the positron and
electron have the up spins) seems to be viable in the
laboratory to achieve high temperature BEC. The critical
temperature Tc for BEC of ideal bosons of mass m and
density n is given by
=2 2.61
Thmkn . Hence
the small mass of Ps at a very low density,
12 3
should facilitate BEC by leading to a
large 2
3.2. The Standard Model
Antimatter can be used to sensitively test the theoreti-
cal underpinnings of the standard model. Essential to the
quantum field theory governing interactions of funda-
mental particles is the so-called CPT theorem, which
involves discrete symmetries. The CPT theorem requires
that the laws of physics be invariant under the following
operation: all particles are replaced by their antiparticle
counterparts (charge conjugation), all spatial coordinates
are reflected about the origin (parity), and the flow of
time is reversed (time reversal). The CPT theorem has
important implications for antimatter, including the mass
equivalence of particle and antiparticle.
The precision tests of CPT invariance using antimatter
include the electron/positron mass ratio and the pro-
ton/antiproton mass ratio. An ideal system for more pre-
cise studies of the CPT theorem is the antihydrogen
atom. The CPT theorem requires that hydrogen and an-
tihydrogen have the same spectrum. Since hydrogen is
one of the best understood and most precisely studied
systems in all of physics, it is natural to try to compare
the spectra of hydrogen and antihydrogen.
3.3. The Weak Equivalence Principle
Another reason why
is worth studying is its po-
tential to test the weak equivalance principle (WEP) of
Einstein’s general relativity, which requires the gravita-
tional acceleration of a falling body be independent of its
composition. This has been tested rigorously for differ-
ent objects of matter, but tests of antimatter and direct
comparison of a matter object and its antimatter equiva-
lent, such as protons and antiprotons, have proved very
difficult, mainly due to the difficulty of shielding for
even very small electromagnetic fields. This is necessary
since the elctromagnetic force is much stronger than
, on the other hand, is thought to be stable
and neutral and tests using this should thus be enabled at
much higher accuracy. Slow neutral
suitable for a
free fall measurement, is currently being proposed by
Walz and Hänsch; the laboratory of CEA/Sacley, France
[28] is presently engaged in producing the slow neutral
needed for this experiment. They have proposed the
use of
ion in order to collect ultra cold
For this a dense Ps target is necessary to follow up: p
+ Ps
+ e
which is followed by
+ Ps
+ e
. This
ion could be cooled to μK
temperatures (i.e. m/s velocities). The excess positron
can be laser detached in order to recover neutral
H. Ray / Natural Science 3 (2011) 42-47
Copyright © 2011 SciRes. OPEN ACCESS
3.4. Technological Application
Whenever antimatter collides with its equivalent mat-
ter, they will annihilate each other. This collision and
annihilation will release large amounts of energy be-
cause in the process, the mass of both particle and anti-
particle will be converted into pure energy - usually in
the form of high-energy photons (known as gamma rays).
The energy be released from such a collision (according
to Einstein’s equation, ‘2
=Emc’) could be used to gen-
erate electricity using advanced technology and equip-
3.5. Present Research Status
Intensive studies are currently being undertaken by
numerous institutions regarding the behavior and appli-
cation of the antimatter. CERN’s unique new antimatter
factory, the Antiproton Decelerator (AD) has begun de-
livering antiprotons to experiments. These experiments
will study antimatter in depth to determine if there is a
difference between it and ordinary matter. Any differ-
ence between antimatter and matter would be extremely
interesting since it is not yet understood why the uni-
verse is made mostly of matter. Physicists believe that
the Big Bang created equal amounts of antimatter and
matter [30], which would then have annihilated, leaving
nothing. The great mystery is why there was enough
matter left over to from the universe. Two experiments,
ATHENA [31] and ATRAP [32], aim to add positrons -
anti-electrons - to the caged antiprotons to make atoms
of antihydrogen. A third, ASACUSA [33], traps the an-
tiprotons in a cage conveniently provided by nature the
helium atom. The goal of all three is a detailed compari-
son of matter and antimatter leading to an understanding
of why nature has a preference for matter over antimat-
As technology advances through the years, better and
cheaper ways of producing significant amounts of anti-
matter are expected to be developed and antimatter may
become a good source of renewable and sustainable en-
ergy. This is not yet possible today, but in the future, this
might be a significant possibility.
Author is thankful to Saha Institute of Nuclear Physics (SINP),
Kolkata for providing the facilities to prepare the manuscript and
grateful to Prof. Bichitra Ganguly (SINP) for her active helpful sug-
gestions to improve it. Author is thankful to SERC, DST, Govt. of
India for the project funding Ref. No. SR/WOSA/PS-13/2009 and Prof.
Anuradha De (NITTTR) for her kind mentorship.
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