ÐÓ°ÉÔ­´´

MOST people think of atoms as consisting of a positively charged nucleus,
made up of protons and neutrons, surrounded by orbiting electrons that are
negatively charged. Molecules have several nuclei, possibly of different
types, and the electrons play an important role in holding the molecule
together. It is, however, possible to create atoms, and even molecules,
from subatomic particles other than electrons, protons and neutrons. In
particular, physicists have made ‘exotic’ atoms and molecules that contain
a heavy negative particle revolving around the nucleus or nuclei. This particle
might be a heavy version of an electron called a muon, or an even heavier
nuclear particle such as a pion or an antiproton .

Pions are produced when many different kinds of sub nuclear or nuclear
particles, such as protons and atomic nuclei, collide and break up at high
energies. A pion is about one seventh the mass of proton or neutron and
can be negatively or positively charged. It does not live for very long
– 10-**8 seconds. A negatively charged pion decays into a negative muon,
which in turn decays into an electron. Like other charged nuclear particles,
a charged pion is not only affected by the electromagnetic force but also
interacts with nuclei and other nuclear particles through the strong nuclear
inter action. This is the force that holds the components of nuclei together.
Like the muon, it also responds to the weak nuclear interaction which governs
particle decays.

The negative muon, like the electron, is not a nuclear particle and
so interacts only through the electromagnetic and weak interactions. Compared
with other unstable subatomic particles, the muon lives quite a long time
– just over 2 microseconds. Other, so-called ‘strange’ particles are produced
when particles collide at even higher energies. The negative kaon and the
sigma hyperon can also form exotic atoms. These particles also feel both
the strong and electromagnetic forces and decay rapidly; the negative kaon
into pions, muons, electrons and neutrons and the sigma minus into a neutron
and a pion.

In view of the brief lives of most of these negative particles, studying
exotic atoms and molecules may not seem very interesting or important. But
a wealth of data can be obtained from the atomic and molecular changes that
happen in the atoms before the exotic particle disintegrates – in particular,
information about the two fundamental forces that shape the structure of
atoms, molecules and nuclei, the electromagnetic and strong nuclear forces.

Physicists have, for example, used atoms containing muons – muonic atoms
– to investigate the fine details of electromagnetic processes at the atomic
level and also details of the size and shape of the nuclear charge. Under
certain conditions, muonic molecules can ‘catalyse’ nuclear fusion between
hydrogen isotopes at low temperatures. Pionic, kaonic, antiprotonic and
hyperonic atoms yield information on the strong interaction between the
heavy particle and the atomic nucleus. Pionic atoms and molecules form in
living tissue so physicians can use negative pions in radiotherapy.

Exotic atoms are also a good way of testing the theory used to describe
the structure of atoms and molecules – quantum theory. A key feature of
this theory is that atoms and molecules can have only certain energies.
Quantum theory can, at least for the simplest atoms and molecules, predict
what these ‘quantised’ energy states are.

A hydrogen atom, for instance, which consists of a proton bound to an
electron, has a series of levels of possible binding energies. The atom
usually likes to occupy the lowest energy state, or ground state. Consequently,
if the atom finds itself in a high energy state, it hops down rapidly through
the lower states until it reaches the ground state. Each hop from a higher
state to a lower state results in energy being emitted, usually as photons
of a characteristic frequency (these changes in energy are called radiative
transitions) – or by giving energy to another electron which then escapes
from the atom.

Measuring the energy emitted (or absorbed if the atom jumps from a low
to a high energy state) gives us the difference in energy between two levels.
In this way, physicists can build up a picture of how matter behaves at
the atomic and molecular level and test predictions from quantum theory.

Just studying the radiative transitions in ordinary atoms provides a
great deal of information. But substituting a heavier negative particle
for one of the electrons and measuring the energies of its radiative transitions
can give information not only about the overall structure of the atom but
also details about the nucleus. In fact, research first started on muonic
atoms as long ago as 1947 when John Wheeler, then at Princeton, realised
that a muon survived long enough to form a muonic atom and then undergo
radiative transitions.

In the early 1950s, Val Fitch and James Rainwater at Columbia University
in New York carried out the first experiment on the radiative transitions
of muonic atoms. To obtain muonic atoms, beams of muons are fired at a target.
The muons first lose some energy by knocking out electrons from the atoms
of the target. Some atoms then capture a muon by drawing it into an atomic
orbit in a high-energy quantum state. The muon drops rapidly through a cascade
of energy levels to a lower energy, simultaneously emitting a spectrum of
X-rays.

These experiments started a new field of physics. During the first 10
years, progress was slow, however, partly because the researchers could
not measure the energy of the X-rays accurately enough to use in their calculations.
In the early 1960s, however, new radiation detectors improved the accuracy
of measurements from a few per cent to about one-tenth of 1 per cent.

One of the first useful results of the experiments was in confirming
some predictions of quantum electrodynamics, or QED for muons – a sub-branch
of quantum mechanics that takes into account Einstein’s theory of relativity
and the quantum properties of electromagnetic fields.

All experiments on exotic atoms may be used to investigate the force
between an orbiting particle and the nucleus. In the case of muonic atoms,
this force is very nearly, but not exactly, the same as that predicted by
classical physics for the force between two charged bodies (the inverse
square law). When the distance between such bodies becomes small enough
(in other words, the electric field becomes strong enough), then there are
small deviations from the classical law of force. These deviations arise
because classical physics regards the space between charged bodies as a
vacuum. According to QED, however, the vacuum is seething with ‘virtual’
pairs of electrons and positrons popping in and out of existence, which
line up along the field of force and increase its strength.

Exotic atoms test QED

Muonic atoms are smaller than electronic atoms because the muon is more
massive than the electron, so these deviations show up more clearly. Measurements
of muonic atoms have now tested the predictions of QED very accurately.

Physicists can determine the mass and magnetic moment of exotic particles
from measurements on their atoms. When an orbiting particle undergoes a
radiative transition, the emitted photon has an energy that is proportional
to the mass of the particle. This approach gives the mass of the pion, for
example, with an accuracy of two parts per million. The differences between
energy levels corresponding to different orientations of the particle’s
magnetic field reveal the strength of magnetism.

Experiments on muonic atoms also provide information about the size
and shape of nuclear charge. The standard atomic theory developed by Neils
Bohr in 1910, treats the nucleus as a point charge. It successfully predicts
the energy levels for simple atoms containing electrons, but in a muonic
atom, the transitions to the lowest energy levels are quite different from
those predicted by the Bohr theory. This is because in the much smaller
muonic atom, the lowest orbits are much closer to the nucleus, so they are
more sensitive to the effects of its size and shape.

A more useful description is to regard the nucleus as a sphere with
a constant density of charge. In the case of an atom of lead with an orbiting
muon, the calculated energy of the transition between the two lowest states
for a point charge is 16 million electronvolts, but the actual measured
value is very different – only 6 million electronvolts. In this case, the
radius of the lowest ‘orbit’ of the muon is actually the same as that of
the nucleus.

For the nuclei of very light elements, it is the square of the average
radius of the charge density that determines how much the energy of the
lowest level shifts from that predicted for a point nucleus; completely
different radial shapes with the same average square radius would give the
same energy. But our group at the University of Surrey showed that for muonic
atoms with heavier nuclei, the measurements determine a slightly more complicated
quantity, called the Barrett radius after one of us. Physicists can now
measure such radii incredibly accurately to 10-18. Combined with information
obtained from the scattering of electrons by atoms this now gives a very
accurate picture of the radial size and shape of the nuclear charge.

In the case of exotic atoms containing nuclear particles – pions, kaons
or antiprotons – the X-rays emitted during radiative transitions also give
information about the strong nuclear force. This again affects the atomic
orbits close to the nucleus. Studies on the strong interaction usually rely
on experiments involving collisions between particles – say, pions and nuclei
– at high energies. Investigating the shifts in the position of the atomic
energy levels compared with those predicted by Bohr theory provides a way
of studying strong interactions between a pion, kaon or antiproton and a
nucleus at extremely low energies.

Often, the lowest energy levels broaden. This is because the exotic
particle’s lifetime is shortened by being completely absorbed by the nucleus.
Figure 1 shows an example of an energy diagram for pionic oxygen, as the
pion descends through the energy levels emitting X-rays. Before reaching
the ground state, the nucleus usually captures the pion.

Kaonic atoms have turned up some surprises. The simplest kaonic hydrogen
is the most difficult exotic atom to understand. For some reason, scattering
experiments between kaons and nuclei give a different value for the binding
energy of kaonic hydrogen – a kaon and a proton – from that obtained by
measuring radiative transitions. It may be that the kaon and proton interact
in some bizarre way that researchers do not yet understand, or the (admittedly
extremely difficult) atomic experiments are wrong.

As well as studying exotic atoms, we have been looking at simple molecules
containing a negative muon, pion, or kaon. The original motivation came
because we were interested in using beams of negative pions to kill cancer
cells. We have been working with the TRIUMF laboratory at the University
of British Columbia in Vancouver. The laboratory not only studies the fundamentals
of pion chemistry but also carries out radiotherapy on patients. Pion therapy
works by releasing a burst of energy when the pion is captured by a nucleus,
which then disintegrates, killing the cell. Pion beams are particularly
attractive for radiotherapy because they release their energy at the end
of their range in matter. This means that clinicians can select a beam energy
so that when the beam penetrates the body, it deposits its energy at the
correct depth to destroy the cancerous tissue without damaging surrounding
normal cells.

How does the pion release its energy? This is where the study of molecules
comes in. According to a model developed by Leonid Ponomarev and S. Gershtein
in the Soviet Union and Hubert Schneuwly at the University of Fribourg in
Switzerland, once the pions have lost most of their kinetic energy, they
are captured by biological molecules in the tissue. Each pion goes into
a molecular orbital and then falls into an atomic orbit about one of the
atoms in the molecule. Eventually, the pion drops into an energy level close
to the nucleus of the atom and probably reacts with the nucleus, releasing
energy in the process.

To show that these pion molecular orbits can exist, we turned to quantum
theory normally used for molecules containing ordinary electrons (known
as quantum chemistry). We came across a snag, however, in trying to extend
these ideas to our exotic molecules because of the heavier mass of the negative
particle.

Take, for example, the simplest molecule known, the hydrogen molecular
ion (New ÐÓ°ÉÔ­´´, 14 January 1989), which consists of two hydrogen nuclei
(protons) and one electron. Because the proton is much heavier than the
electron and, therefore, moves much more slowly, the motion of the two protons
can be ignored when calculating the motion of the electron. This approach
is known as the Born-Oppenheimer approximation. It makes calculating the
energy levels in molecules much easier.

In reality, the two protons do move. They vibrate along the line joining
them. The usual method of testing whether the Born-Oppenheimer approximation
is valid is to compare the vibrational energy of the two protons with the
average energy of motion of the electron, its kinetic energy. For the hydrogen
molecular ion, the vibrational energy is only 2 per cent of the electron
kinetic energy, so it seems reasonable to use the Born-Oppenheimer approximation.

If, however, we calculate the same values for similar molecular ions
containing a pion or a kaon, we find that the vibrational energy of the
two protons is a third of the kinetic energy of a pion, and for a kaon,
the vibrational and kinetic energy may be almost the same. We may guess,
therefore, that it may not be feasible to apply the Born-Oppenheimer approximation
to exotic molecules and this, of course, makes the calculations much more
difficult.

Another application of exotic chemistry where the Born-Oppenheimer approximation
is not useful is in muon catalysed nuclear fusion. This is a rather unusual
reaction in which a muon ‘catalyses’ the fusion of two heavier forms of
hydrogen nuclei, deuterium and tritium nuclei, to release nuclear energy
(‘High hopes for cold fusion’, New ÐÓ°ÉÔ­´´, 25 April 1985). Unlike thermonuclear
fusion, which requires temperatures similar to that in the centre of the
Sun, muon-catalysed fusion happens at moderate temperatures. It is genuine
‘cold’ fusion. Researchers would like to transform the reaction into an
economic source of energy but there are problems to overcome, so cold fusion
reactors are a long way in the future.

Real cold fusion

Basically, what happens is that a muon can bind a tritium and a deuterium
nucleus into a molecular ion dtm– – where d stands for deuterium, t stands
for tritium and m represents the muon. Because a muon is more massive than
an electron, the muonic molecular ion is much smaller than the equivalent
electronic molecule. In fact, the muon draws the deuterium and tritium nuclei
so close that they overcome the mutual electrical repulsion due to their
positive charges and fuse to form a helium nucleus, with the resulting release
of energy. The muon is then free to go off and catalyse another nuclear
reaction.

How fast the nuclear fusion goes, however, depends on some subtle initial
chemistry. When muons are fired at a mixture of deuterium and tritium, the
muon first attaches itself to a tritium nucleus to form a tiny muonic atom,
which then binds very weakly with a deuterium molecule. Understanding this
weakly bound quantum state is extremely important in making the reaction
efficient. But the energy involved is tiny so calculations have to be incredibly
accurate to reveal its value – to a thousandth of an electronvolt.

This means that the Born-Oppenheimer approximation is quite inaccurate
for describing this weakly bound state, so researchers such as Masayusu
Kamimura of Kyushu University in Japan have developed an alternative method
to carry out such calculations.

We decided to use Kamimura’s method to look at kaonic molecular ions
for the same reason. In this case, the Born-Oppenheimer approximation does
not work because the kaon is so massive. Not only is the basic strong interaction
between a kaon and a proton stronger than between a pion and a proton, but
the kaonic molecular ion is also much smaller than the pionic, muonic or
the ordinary hydrogen molecular ion, thus increasing the effects of nuclear
forces. Our results show that the strong force makes the binding energy
of the molecule 4 per cent weaker than what it would be if we did not take
the strong force into account. In fact, the kaon molecular ion exists only
in its ground state. The strong force also causes the kaon and the proton
to attract each other, resulting in quite fast nuclear reactions between
them. But we still, however, do not understand exactly how the strong force
works between the kaon and the proton.

Physicists can make molecular ions with even heavier exotic particles,
such an antiproton or a sigma-hyperon particle, which has a mass of 2343
electrons. We hardly expect the Born-Oppenheimer approximation to have any
sort of validity in these cases. Making these unusual exotic atoms and molecules
and measuring their energies, therefore, so as to test them against theoretical
predictions, is encouraging theorists to develop better methods of calculating
the complex interactions of two of the fundamental forces of nature that
shape the everyday world around us. And in the case of molecules, it is
also helping to describe three-body systems.

Roger Barrett and Daphne Jackson are in the department of physics at
the University of Surrey. Habatwa Mweene completed his PhD at Surrey one
year ago and has returned to the University of Zambia.