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 Scientist, 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 Scientist, 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.