Muonic hydrogen, the H-p+ bound state, . . . is more sensitive to the . . . structure of the proton.
The hydrogen atom has been such a provocative and productive window onto the physical universe that physicists have gone to every length possible to create hydrogen-like systems. Such hydrogen-like "atoms" consist of two particles, one positively charged (like the proton) and the other negatively charged (like the electron), bound together by the mutual attraction of their opposite charges. Just as the hydrogen atom provides an exacting test of physical theories, these quasi-atoms can stretch the demands on theoretical concepts in novel ways. There are three classes of hydrogen-like atoms. The first class goes by the name exotic atoms, the second class are called Rydberg atoms, and the third class are ordinary atoms whose electrons are all stripped away, except one, leaving a lone electron around a highly charged nucleus.
In the case of an exotic atom, physicists bring together an exotic particle and an ordinary particle or two exotic particles to form a short-lived entity that is structurally like hydrogen. The exotic particles involved are unstable and have short lifetimes. For example, one such exotic particle, the muon, has a mean lifetime of 2.1971 X 10-6 seconds; the positron is stable when isolated, but it annihilates quickly when it encounters an ever-present electron in typical laboratory environments; the pion has a mean lifetime of 2.603 X 10-8 seconds. Hydrogen-like atoms constructed from these particles represent challenging objects of study, but the dividends that come with success make the challenge well worth the effort.
In positronium a positron is substituted for the proton and the positron and an electron are bound together in a hydrogen-like atom. Muonic hydrogen, perhaps the simplest exotic atom, unites a negatively charged muon with a positively charged proton. In this instance, a muon simply replaces the electron. In muonium, an electron is bound to a positive muon. As we shall see, there are other examples of exotic atoms. Positronium, muonic hydrogen, and muonium have been studied rather extensively.
The challenge presented by these hydrogen-like atoms is at least twofold. First, the particles must be brought together so that their electrical attraction can bind them into an atom-like unit. Since these exotic particles are formed at energies much too high to allow binding to occur, the particles must be de-energized (slowed down) to the point that their mutual electrical attraction can take hold. Second, experimental techniques must be devised that permit these short-lived hydrogen-like atoms to be studied.
Why go to the trouble? The fascination with hydrogen-like atoms starts with the same fascination physicists have with hydrogen itself. The reason is simplicity—just two particles are involved. For such a simple system, physicists can apply basic physical theories such as quantum mechanics, relativity, and quantum electrodynamics (QED) with minimal assumptions compromising the outcome. Often, for two-particle systems, physicists can solve the mathematical equations that arise exactly. This is not the case with the next simplest atom, helium—a three-particle system—and a relatively simple atom such as carbon confronts physical theory with formidable problems. The fascination is extended because these hydrogen-like atoms provide the opportunity to subject basic theories to new and stringent tests. No matter how successful a theory seems to be, physicists are always eager to expose it to situations where either the theory is further substantiated or it fails. Failure simply raises new questions and holds the potential for important new insights.
Positronium was the first exotic atom to be observed. The positron was predicted from Dirac's 1928 work in which he united the new quantum mechanics with relativity, and it was first observed by Carl Anderson in 1932. Soon thereafter, in 1934, Stjepan Mohorovicic predicted that an "atom," consisting of a positron and an electron, could be observed.1 It wasn't until 1951, however, that positronium was created and observed by Martin Deutsch of the Massachusetts Institute of Technology.2 Deutsch accomplished this by slowing positrons emitted in the decay of an isotope of sodium until the positrons captured electrons from the surrounding gas.
Muonic hydrogen was first observed in 1956 by L. W. Alvarez and colleagues.3 When evidence for the muon first appeared to S. H. Neddermeyer and C. D. Anderson in 1937 of the California Institute of Technology, and was quickly confirmed by J. C. Street and E. G. Stevenson of Harvard, it effectively threw a wrench into the physical works.4 "Who ordered that?" asked Rabi, with obvious surprise and consternation. For years a three-word sentence adorned the blackboard in Richard Feynman's Caltech office: "Why the muon?" The muon question obviously intruded on Feynman's thoughts; in fact, the same question has troubled the thoughts of many physicists. Muonic hydrogen was first observed serendipitously in an experiment in which particles called K mesons were being stopped in a ten-inch hydrogen bubble chamber. (K mesons are about half as massive as a proton and can carry no charge, positive charge, or negative charge.) In the beam of K mesons, there were also muons, some of which formed a bound system with protons. Muonium itself was discovered by Vernon W. Hughes and his associates in 1960.5
These hydrogen-like atoms are, as the name indicates, like hydrogen, but they have crucial differences. In positronium the positron and the electron, each with the same mass, revolve around a point midway between them, which is their common center of mass. (This is just the same as the hydrogen atom except the proton is almost 2,000 times more massive than the electron so that the latter seems to revolve around the former.) From Bohr's model of the hydrogen atom, we can predict that the spatial extent of positronium, in its lowest energy state, is larger than is hydrogen. In fact, it is about twice as large.
The muon is a weighted-down electron. The mass is 206.8 times larger than the electron. When the muon takes the place of the electron in muonic hydrogen, it orbits much closer to the proton so the size of the muonic hydrogen atom is smaller. The radius of the lowest energy state in hydrogen is about 0.5A whereas in muonic hydrogen it is about 0.003A. In the muonium atom, a positive muon becomes the effective nucleus. It is much lighter than the proton; specifically, the muon is about one-tenth the mass of the proton. This means that the muonium atom is larger than hydrogen.
The size differences between hydrogen and its counterparts are interesting and important. But there is more. The muon and the positron, like the electron, belong to the particle family called leptons. Leptons are immune to the strong force that acts between nuclear particles—protons and neutrons. It is this strong force that overwhelms the electrical repulsion between protons and brings them together to form an atomic nucleus. Neither the positron nor the muon feel this strong force. This means that exotic atoms are even simpler than hydrogen with its proton nucleus, the source of the strong force.
Vernon Hughes has stated the motivations for studying exotic atoms. These include the opportunities to determine the properties of the particles themselves, to study the interactions among the bound particles, to test modern theory, and to search for the effects of weak, strong, and unknown interactions on the bound state of the particles.6 As Hughes has said, the study of exotic atoms serves fundamental purposes. In both positronium and muonium, the interacting particles are both leptons; thus, the two particles interact exclusively through the electromagnetic interaction without the strong force hovering in the background. This means that these "atoms" provide an unobstructed view of the electromagnetic interaction with no possible influence, or interference, from the strong force. Or consider muonic hydrogen, in which the muon orbits much closer to the proton and thus opens the possibility of probing structural properties of the proton from a closer vantage point as well as witnessing any influence of the strong force close-up.
The spectrum of hydrogen has been studied more intensively and more exhaustively than any other atom. The energy states of hydrogen are known about as well as anything can be known. As is the case with hydrogen, probing these exotic "atoms" with light holds the possibility of examining their spectra and thereby exposes their physical properties and opens opportunities to test physical theories. In principle, positronium and muonium should permit physicists to make predictions that make demands on theory in addition to those made by hydrogen. For example, unlike the proton, which is made up of quarks, both the positron and the muon are structureless particles, which means that the spacing of their energy states is determined only by the QED interaction. This makes these hydrogen-like atoms an ideal arena for testing QED. Further, the corrections to theory demanded by the Lamb shift in these exotic atoms could, in principle, mean that these theories face new, stringent tests. Quantum transitions among various energy states in both positronium and muonium have been observed and measured. For example, just recently, the 1S-2S energy interval in muonium was measured,7 and its experimental result was consistent with theory.
The study of exotic atoms is an active area of contemporary research. Many hydrogen-like atoms have been detected and investigated. Among them, in addition to those mentioned above, is pionium, in which an electron is bound to a positive pion and there are hydrogen-like atoms in which the electron has been replaced by exotic particles such as the negative pion, the negative kaon, and the antiproton. As accurate data accumulate, physicists will enjoy searching for the subtle new insights that these curious atoms are likely to provide. Certainly, exotic hydrogen-like atoms will expose the intricacies of physical theory in unique and provocative ways.
The second class of hydrogen-like atoms is called Rydberg atoms. A Rydberg atom is an ordinary atom in which one electron has been elevated to a very high quantum state. The energy states of atoms are identified with the quantum number n, called the principal quantum number. The ground state, or lowest state, is the n = 1 state, which is where atoms spend most of their time. The first excited state is the n = 2 energy state, the second excited state is n = 3, and so on.
The size of an atom is determined by the average distance between the nucleus and the outermost electrons when the atom is in its ground state. When the hydrogen atom is in its ground state, its sole electron is, on average, about 0.5A away, so the hydrogen atom has a diameter of about 1A. If the electron in the hydrogen atom is excited to the n = 2 energy state, the diameter of the atom increases by a factor of n2, or by a factor of four. When hydrogen becomes a Rydberg atom, its electron can reside in energy states with n = 80, 90, or higher. Rydberg atoms have been observed with n equal to several hundred. This makes Rydberg atoms very large—up to 100,000 times the size of an atom in its lowest quantum state. Like exotic atoms, Rydberg atoms are very fragile, but unlike exotic atoms, they are very long-lived, provided they are isolated and free from collisions by other atoms.
All Rydberg atoms are hydrogen-like. This is because the electron in an elevated energy state is far from both the nucleus and all the other electrons that, in their normal quantum states, remain relatively close to the nucleus. Therefore, if a Rydberg electron could look inward toward its nucleus, it would see a compact sphere consisting of Z positive nuclear protons (plus neutral neutrons) closely surrounded by Z— 1 negative electrons. Thus the Rydberg electron moves around a core with a net charge of +1, just like a hydrogen atom.
Although the existence of Rydberg atoms has been known since the late nineteenth century, the first hydrogen Rydberg atom was probably observed in outer space in 1965.8 (The qualifier reflects the difficulty of pinning down the first of most anything.) Not only is hydrogen present throughout space, but space provides a congenial environment for Rydberg atoms. Such atoms are fragile and cannot endure the bombardment that would occur in a gaseous sample in a laboratory on Earth. In space, however, each atom is serenely isolated and undisturbed by collisions with other atoms.
Rydberg atoms began to appear in laboratory experiments in the 1970s when tunable dye lasers became a powerful means to create and study them in controlled detail. With these lasers, scientists can excite the outer electron of essentially any atom and form a hydrogen-like Rydberg atom. The most commonly used atoms for Rydberg studies are the alkali metals: lithium, sodium, potassium, and so on. To keep Rydberg atoms from being pum-meled by other atoms, destroying their delicate status, experimenters form a beam of atoms moving through a high vacuum. In such beams, atoms move parallel to each other and are effectively captured in isolation.
Apart from the strangeness of these huge atoms, why do scientists study them? What can be learned from Rydberg atoms? One motivation for studying them is their spectacular response to both electric and magnetic fields. When an electric field is applied to an ordinary hydrogen atom, its energy states are slightly shifted. However, when hydrogen becomes a gigantic Rydberg atom, its response to an electric field is likewise gigantic. The energy states shift by large amounts and, in the process, they sometimes cross each other. At the point of crossing the two states have the same energy, that is, they are degenerate. Degenerate energy states are provocative because they imply an underlying simplicity.9 Discovering such simplicities will bring new insights into the world of atoms.
Another reason for studying Rydberg atoms is that they have the potential for shedding light on the dim domain between the quantum world of the atom and the classical world of everyday objects. Quantum mechanics is the enormously successful theory that describes the building blocks of the physical universe. As such, physicists regard quantum mechanics as more basic than the classical laws of physics. Physicists like to think, and have good reason to do so, that as quantum mechanics is applied to larger and larger objects, quantum physics should be seen to blend into classical physics; that is, in the domain between the microscopic and macroscopic worlds, an equivalence between quantum and classical physics should emerge. This idea of quantum theory merging into classical theory was explicitly expressed by Niels Bohr in his correspondence principle.
The quantum world is characterized by abrupt discontinuity; the classical world by continuity. The low energy states of an atom are distinctly quantum-like: the energy differences among neighboring energy states are large. By contrast, the energy differences among the high energy states of a Rydberg atom are small and, in energy terms, the transitions between them are rela tively smooth. From low energy states to high energy states, atoms move from jolting discontinuity toward smooth continuity, from the distinctly quantum domain toward the classical domain.
What would a classical atom look like? Consider the planetary system. A planet is located at a particular position on a well-defined orbit. Contrast that with the ground state of the hydrogen atom, where the electron cannot be located in a particular position nor can a definite orbit be identified. With keen foresight, Heisenberg essentially banished orbits and positions on orbits from his thinking when he created the first version of quantum mechanics. He did this because neither electron orbits nor positions could be either observed or measured and he concluded that immeasurable concepts had no place in a physical theory.
Perhaps it is fortunate that Heisenberg did not know about Rydberg atoms. In recent years, long after Heisenberg's death, physicists have devised very clever ways to examine Rydberg atoms. They have found that in such atoms the electron can be partially localized on an orbit that traces out a distinctly elliptical path.10 Physicists do not find an electron, but a bell-shaped blob that moves along an elliptical orbit. Like the planets in their orbits, the electron-blob moves most rapidly when it is closest to the center of the Rydberg atom and most slowly when it is farthest. In short, the Rydberg atom exhibits behavior that is consistent with the laws of classical physics.
It is increasingly important to understand nature on a scale in between the quantum and classical worlds. Technological methods have moved into this transitional realm with dramatic results. Scanning tunneling microscopes can image individual atoms and reveal the atomic character of surfaces of solids. Individual atoms can be moved about and materials tailored for specific purposes. Electronic circuit elements have been reduced to dimensions of molecules. As scientists come to understand how the quantum domain gives way to the classical domain, these technologies will multiply and their applications expand. Hydrogen-like atoms may benefit technological development.
The third class of hydrogen-like atoms are highly ionized atoms; that is, atoms whose electrons have been stripped away leaving only one electron in orbit around the nucleus. In hydrogen, the electron moves under the electromagnetic influence of the proton. However, as Willis Lamb's experiment revealed, the hydrogen's electron moves in a space that is teeming with activity: electron-positron pairs pop into brief existence and virtual photons all exert their influence. This lively environment causes the shift in hydrogen's 2SY2 state, now called the Lamb shift, and this shift provided a test of QED.
Now consider a highly ionized atom. Uranium is an example. Uranium has ninety-two electrons orbiting around a nucleus with ninety-two protons and a larger number of neutrons. Experimentalists have been able to strip away ninety-one electrons, leaving one electron revolving around the highly charged uranium nucleus, thereby forming the U+91 ion. This electron moves in a space much more strongly influenced by electromagnetic effects than is the case in the hydrogen atom. In fact, the sole electron around a uranium nucleus experiences an electric field many times stronger than any field that can be produced in the laboratory. What does the Lamb shift look like for this hydrogen-like atom? Does QED provide an explanation? The answer to the first question is amazing: the Lamb shift is about 1 X 108 times larger in U+91 than it is in hydrogen. Now, can QED explain this large shift? The observed Lamb shift is essentially consistent with the prediction of QED.11 The experimental uncertainties carried by this result are relatively large, but work is underway to refine procedures and increase the precision. Will QED be found wanting? It remains to be seen.
"Imitation," the saying goes, "is the sincerest form of flattery." Hydrogen-like atoms, whether they are exotic atoms comprised of short-lived particles, bloated Rydberg atoms, or highly ionized uranium atoms, share the structural features of hydrogen. As such, they are simple and there is nothing more appealing to a physicist than simplicity. Hydrogen and its surrogates continue to reward physicists with the never-ending bounty only the simplest atom can provide.
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