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4 Atomic Physics The remainder of this report is devoted to an overview of contem- porary atomic, molecular, and optical physics (AMO physics). This and the following two chapters survey each of these topics in turn. The final two chapters describe some scientific interfaces of AMO physics and a few of its applications. The field of atomic physics encompasses three major streams of research. One deals with studies of the elementary laws of nature. This research often involves high-precision measurements many of the precision measurement techniques of modern science have come from it. The second stream of research is devoted to understanding the structure of atoms and how atoms interact with light. The third stream involves dynamical processes- how atoms interact with electrons, atoms, and ions. This research merges naturally into molecular phys- ics; examples can be found in both this chapter and the next. ELEMENTARY ATOMIC PHYSICS Research in elementary atomic physics has flowered during the last decade. Problems include the limits of quantum electrodynamics, the nature of fundamental symmetries and invariance principles, parity- violating interactions, the isotropy of space, the foundations of quan- tum mechanics, and the effect of gravity on time (see Figure 1.11. Some 53
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54 ATOMIC, MOLECULAR, AND OPTICAL PHYSICS of these studies are carried out at a level of precision that in modern science. Much of the research in this branch of atomic physics involves the study of elementary atomic systems, a category that encompasses hydrogen and hydrogenlike atoms, the leptonic atoms muonium and positronium, and a few - elementary particles—the electron, the positron, the proton, and the neutron. The subject has obvious overlaps with nuclear and high-energy physics: our criterion for inclusion in AMO physics is more the identity of the observer than the identity of the system. Thus we include studies of the neutral current interaction in atoms and the search for the electric dipole moment of the neutron, carried out by atomic and molecular physicists, but not a search for the proton-antiproton atom carried out by particle physi- cists. A conspicuous goal of this research is to push to extremes the theoretical and experimental limits on quantum electrodynamics (QED). Nowhere else in physics is the confrontation between theory and experiment so relentless. In this field an accuracy of 1 part in 106 is not unusual, and one notable problem, the anomalous moment of the electron, is currently being fought in the eighth decimal place. is unrivaled Advances in Quantum Electrodynamics QED is one of the most successful theories ever developed in physics. It is successful in describing nature over a range of lengths spanning 25 decades, from subnuclear dimensions, 10-~6 cm, to distances as large as 109 cm, where satellite measurements have verified the cubic power law falloff of the Earth's magnetic field M~nv theories are patterned after QED; its study has been one of the most rewarding pursuits of modern theoretical physics. Atomic physics provided the first experimental evidence for QED, and it continues to provide the most demanding tests of the theory. Two theoretical advances of the past decade are the discovery of how to combine QED with the weak interaction to create what is called the electroweak theory and the creation of the theory of strong interactions known as quantum chromodynamics. The electroweak theory and quantum chromodynamics belong to a class called gauge theories. Much of the intuition and many of the theoretical techniques for generating gauge theories have come from QED. Confirming where QEDis valid, and where it is not, is crucial to understanding this important class of theories. One troubling problem lies at the core of QED: the calculated corrections to the electron mass or charge are divergent. QED avoids
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ATOMIC PHYSICS 55 this difficulty by a renormalization procedure in which nonconvergent quantities such as mass and charge are replaced by their experimental values. Calculations are carried out using perturbation theory, essen- tially an expansion in a power series of the fine-structure constant (a = 1/1371. Although the theory appears to work well, it is not known whether the series ultimately converges. The most exacting tests of QED have come from measurements of the anomalous magnetic moment of the electron and the Lamb shift of hydrogen. Experiments on these during the past decade are among the triumphs of contemporary experimental physics. Under their impetus the theory has been carried forward in one of the most elaborate calculations of contemporary theoretical physics. This confrontation between experiment and theory is unique in all of physics. A major challenge to elementary-particle physics is to understand quark-antiquark bound-state systems. These have a close analog in QED—positronium. Precise solutions of the two-body relativistic problem are still lacking. New experiments on the structure of positronium may offer valuable clues to the theory. Magnetic Moment of the Electron and Positron The first measurement of the electron's magnetic moment anomaly (the departure of the g factor from the Dirac value, exactly 2) had a precision of about 1 percent; today we know it to 40 parts in 109 (see Figure 4.11. This astonishing accuracy is a result of the discovery that a single electron can be isolated in an electromagnetic trap and studied for periods up to hours under conditions of almost complete isolation. Spin resonance and various other motions are detected by the interac- tion of the electron with a tuned circuit. The same interaction can be used to cool the electron to such a low temperature that it is nearly at rest in the trap. The method works equally well with positrons, and the equality of the electron and positron magnetic moments has been confirmed to 5 parts in 10~. The calculation of the electron magnetic moment anomaly to a precision comparable with the experimental precision is one of the most demanding tests of QED, and one of the most demanding calculations ever made in physics. Computers were used extensively with symbolic as well as numerical techniques. The calculation re- quires evaluating 891 Feynman diagrams, many of which involve 10-dimensional numerical integrals.
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ATOMIC PHYSICS 57 Lamb Shift of Hydrogen The Lamb shift in hydrogen (the small splitting in energy between the 2s and 2p states) is the second major test of QED. Nature sets a formidable obstacle to the measurement: the 2p state is so short lived that the uncertainty principle limits the natural precision in energy of the Lamb shift to 10 percent. Fortunately, the uncertainty principle only sets the scale of difficulty of a measurement the final precision depends on the experimenter's skill and stamina. A recent experiment employed an intense atomic beam to achieve a resonance line width that was substantially narrower than would be expected from the uncertainty principle at first glance. (The long-lived atoms were preferentially selected.) The final precision was 9 parts in 106. At this level of precision the character of the Lamb shift problem changes; the Lamb shift becomes sensitive to the structure of the proton, and hadronic effects must be taken into account. One way out of the dilemma is to think of the Lamb shift as a probe of the proton, thereby testing hadronic physics; another way is to determine the proton structure by high-energy experiments and then combine the high- energy and atomic results to test QED. There is a third alternative: one can avoid all the complexities of hadronic interactions by studying pure leptonic atoms. Muonium and Positronium Two species of leptonic atoms are known and both have recently emerged as primary test systems for studying QED. These are muonium (muon-electron) and positronium (positron-electron). Be- cause these atoms decay in a microsecond or less it is a formidable task to satisfy the demands of high-precision spectroscopy for very low energy (the leptons are invariably created at high energy) and a nonperturbative environment, preferably empty space. The annihila- tion lifetime, hyperfine separation, and Lamb shift of positronium have now been measured precisely; all three effects have provided rigorous tests of theory. Muonium production has been revolutionized by the creation of meson factories, high-intensity proton accelerators such as the Los Alamos Meson Physics Facility (LAMPF), SIN in Zurich, and TRIUMF in Vancouver. Using a high-intensity muon source, the hyperfine separation of muonium has recently been measured to 3 parts in 108. This result now stands as a primary test for QED and the muon's behavior as a heavy electron. By way of contrast, the hyperfine
58 ATOMIC, MOLECULAR, AND OPTICAL PHYSICS splitting of hydrogen fails as a test of QED at the level of 1 part in 106 because of hadronic effects, notwithstanding that it has been measured more precisely than 1 part in 10'2. The discovery of how to make thermal positronium in a vacuum has promoted positronium to a forefront position as a test of elementary theory. Ever since positronium was discovered there has been intense interest in studying its optical spectrum, and optical spectroscopy has recently been successful. By combining the new positronium tech- niques with methods of modern laser spectroscopy, the 1s-2s transition has been measured. Because the two bodies have equal mass, positronium offers a stringent test of two-body relativistic theory. Progress in the optical measurements has been very rapid indeed, and in just about 1 year the accuracy of the optical spectra of positronium has reached the few megahertz level achieved in hydrogen several years ago. Muonic and Hadronic Atoms Muonic and hadronic atoms are those in which a negative muon or hadron ~ A-, K-, I-, p, etc.) is bound to a nucleus by the Coulomb interaction. The spectroscopy of these atoms has been studied by observing their spontaneous emissions, which occur in the x-ray and gamma-ray regions. These data yield values for the hadron's mass and magnetic moment as well as properties of the nuclei. The precision of these measurements was recently increased by employing crystal diffraction spectrometers at the meson factories. For muonic atoms these measurements establish sensitive limits to the mass of the scalar bosons postulated by the electroweak gauge theory. The most precise value of the muon's basic properties its mass and magnetic moment- have come from measurements of the Zeeman erect of muonium (the electron-muon atom). The recent discovery of how to make muonium in a vacuum opens the way to a new generation of all of these experiments. Time-Reversal Symmetry The origin of the charge conjugation and parity violation (CP violations) observed in the decay of the neutral K meson is one of the great mysteries in physics. If our present understanding is correct, this violation implies a violation of symmetry under time reversal. Despite many careful experiments on a variety of systems, no other violation of time-reversal symmetry has yet been observed.
A TOMIC PHYSICS 59 The most sensitive test for time-reversal symmetry has been a search for an electric dipole moment of the neutron. The original version of this experiment, which used the separated oscillatory field method of molecular-beam resonance, started the experimental search for parity violations in physics, drawing awareness for the first time that parity violations might be expected to occur. Nearly every theory that attempts to explain the CP violation predicts that the neutron will have an electric dipole moment. As the experimental limit has been progres- sively lowered, many of these theories have been disproved. The sensitivity of the experiment is now incredibly high; it can be compared to confirming the symmetry of a sphere the size of the Earth with a distance less than one tenth the width of the dot in this exclamation point! Nevertheless, a new generation of experiments is under way, and the sensitivity is expected to increase by a factor of 100. In a series of experiments using atoms and molecules, upper limits have been set on the electric dipole moments of the electron and proton, as well as on possible time-reversal-violating interactions between the electron and nucleus. The ongoing search for electric dipole moments in neutrons, atoms, and molecules provides one of the few possibilities in high- or low-energy physics for solving the CP riddle. Neutral-Current Parity Violations in Atomic Physics A key element of the theory that has now unified the electromagnetic with the weak interaction is the prediction that the weak neutral current interactions between electrons and nucleons should produce a parity violation in atoms. The result is that the photons emitted by atoms should "prefer" one circular polarization over the other by a small amount. The effect is extremely small the wave function is typically distorted by 1 part in 10~°. In one class of experiments the parity-violating effect causes the polarization of light to rotate; the required experimental sensitivity is 10-7 radian. Observation of these effects is a triumph of experimental ingenuity. Successful experiments have now been carried out with four atomic species: bismuth, cesium, thallium, and lead. These experiments demonstrate neutral-current interactions by low-energy elastic interactions, an arena far distant from high-energy physics where such effects were first observed. The atomic and high-energy experiments are complementary, and at pre- sent they are approximately equal in accuracy. Furthermore, the atomic results can be used to put constraints on alternatives to the standard electroweak model, and they provide the opportunities to
60 A TOMIC, MOLECULAR, AND OPTICAL PHYSICS investigate new classes of phenomena, for instance the possible existence of a second neutral boson, heavier than the recently discov- ered Z° particle. The atomic experiments appear to provide the most sensitive test yet proposed for such a particle. A molecular-beam magnetic resonance technique, similar to the one used to search for the neutron electric dipole moment, has recently been used to study parity-violating interactions between the neutron and various nuclei. As the neutrons passed through a metal sample a large rotation of the neutron spin due to the weak interaction was observed. The results, which disagreed with the theoretical predic- tions, have led to a better understanding of nuclear structure. The experimental neutron rotation method constitutes a new tool for examining nuclear structure. Although the principal tools for studying the electroweak and the strong interaction are those of particle physics, when one contrasts the "table-top" scale of atomic experiments with the scale of high-energy research, it is evident that atomic research is extremely cost effective. Foundations of Quantum Theory: Is Quantum Mechanics Complete? Although quantum mechanics is widely recognized as a triumph of twentieth-century thought, persistent questions remain about the valid- ity of the underlying assumptions and the completeness of the theory. The famous debate between Bohr and Einstein attests to the depth of the problem. The fact that Bohr's interpretation is now accepted as the standard model for quantum mechanics does not, of course, preclude the possibility that quantum mechanics may not be able to tell us all that there is to know. Quantum mechanics could be incomplete. In the mid-1960s, the debate on quantum mechanics was dramati- cally altered. John S. Bell discovered that if the quantum-mechanical description of phenomena could be supplemented by any further information- including hidden variables that would allow a determin- istic interpretation of quantum phenomena the information could lead to observably different results. Bell showed that correlations in mea- surements on particles whose initial state was highly correlated would have to lie below a given limit if quantum mechanics were incomplete but that the limit would be somewhat larger if the description by quantum mechanics were complete. The distinction between the two alternatives was presented as an inequality between observables: the completeness of quantum mechanics could be determined by an experimental study of Bell's inequalities.
ATOMIC PHYSICS 61 The experiments involve studies of the correlation in the polariza- tions of photons successively emitted by a single atom in a cascade of fluorescent steps. The experiments are difficult, and the results were at first ambiguous. Recently, however, Bell's inequalities have been studied in an experiment whose results are clear and decisive. By combining laser-induced fluorescence with modern optical detection methods, the two alternatives could be distinguished with an uncer- tainty that is about one tenth of the difference. Bell's inequalities were decisively confirmed. The results offer little hope that quantum me- chanics can be supplemented by a further description: quantum mechanics appears to be complete. The limitations of quantum mechanics remain a serious question at the foundations of physics, for the laws of physics grow out of human observations, and there is no reason to believe that they should remain valid in realms where they have never been applied. Nevertheless, Bell's work and the ensuing experiments show that the most obvious possible defect in quantum mechanics is not, in fact, a weakness. The debate will have to turn elsewhere. Studies of Time and Space Among the most dramatic research in the general area of high- precision measurement are the studies on phenomena underlying our assumptions about the nature of time and space. Of particular interest are recent experiments on the gravitational red shift and the isotropy of space. The gravitational red shift refers to the change in the rate of time, or of the frequencies of atomic transitions, due to a gravitational field. The shift has been measured accurately by comparing the rate of a rocketborne hydrogen maser atomic clock with one on the Earth's surface. The red shift was measured with an accuracy of about 2 parts in 104. This is a tour de force, for it requires a precision in comparing the two clocks of greater than 1 part in 10~4. In addition to confirming the predictions of general relativity, the experiment provided a signif- icant advance in the practical development of atomic clocks and in the art of comparing clocks at large distances. Fundamental to the theory of special relativity is the assumption that the speed of light in space is a universal constant. In particular, the speed is assumed to be the same in all directions. This has been studied by laser interferometry, and the isotropy of space with respect to the speed of light has been confirmed to within 1 part in 108.
62 ATOMIC, MOLECULAR, AND OPTICAL PHYSICS These are but two examples from studies that include topics such as the search for cosmological change in the fundamental constants or the comparative evolution of time scales based on different types of atomic clocks. In addition, experimental methods developed in AMO physics are being applied in astrophysics and cosmology. For example, hydro- gen maser clocks play vital roles in very-long-baseline radio interferometry, while laser interferometry is at the heart of an impor- tant class of gravity-wave detectors. Future Directions Measurements of the electron-magnetic-moment anomaly using sin- gle trapped electrons are not yet at the fundamental limit. A new version of the experiment has been proposed that may lead to a hundredfold improvement. Provided that the theoretical calculations undergo similar progress, this would test QED and CPT invariance with a precision of 1 in 10~3. Trapped-ion methods are steadily advancing and may lead to a large increase in precision of atomic clocks. Such clocks could provide new tests of general and special relativity. The new trap technology is also expected to provide improved values for the ratio of the electron mass to the proton mass and to provide techniques for comparing the masses of nuclei to unprecedented precision. Precision spectroscopy of positronium is coming of age. During the next decade physicists can look forward to detailed measurements of the Lamb shift and relativistic effects in positronium. These advances will put increasing pressure on QED theory. The Lamb shift of high-, hydrogenlike ions has been observed with tunable lasers, and first results have been obtained from potentially more-accurate measure- ments on this shift in the innermost level. These techniques can be expected to advance to the point where they provide definitive tests of the Z dependence of the Lamb shift, testing essentially different QED contributions. Muonium has recently been obtained in vacuum, and the Lamb shift has been observed. Intense sources of muons and pions are now available, opening the possibility of developing intense pulsed sources of muonium and pionium that are matched to the duty factor of pulsed lasers. A large and important new field is thus developing laser spectroscopy of exotic atoms.
A TOMIC PHYSICS 63 ATOMIC STRUCTURE The elucidation of atomic structure is one of the triumphs of quantum mechanics. The enterprise has been so successful, however, that atomic structure is sometimes regarded essentially as a closed book. This is hardly the case. Consider the following. Trouble with Hydrogen The nonrelativistic Schrodinger equa- tion for hydrogen is solved in just about every elementary text on quantum mechanics; it seems unlikely that a serious challenge could remain. Nevertheless, the problem of hydrogen in an applied magnetic field of arbitrary strength is unsolved. Not only are general solutions lacking, for all but the lowest states there are not even any useful approximate solutions. At present, we cannot predict qualitatively how energy levels evolve in regions where the electric and magnetic forces are comparable. The Missing Hamiltonian One view of physics is that once the Hamiltonian is known the problem is essentially solved all that remains is to work out details. Without arguing the pros or cons of this view, we simply mention that the many-body relativistic Hamiltonian is not known. The problem of treating many-body systems within the framework of QED poses an important challenge to atomic physics. Even for H- and He, the simplest two-electron systems, there are no systematic ways to identify the relevant Feynman diagrams. Retarda- tion effects between three or more particles lie at the heart of the difficulty. The problem is more than academic it is of increasing urgency to astrophysical and plasma problems. These instances suggest that problems of atomic structure continue to lie in the mainstream of physics. The field is moving forward vigorously, propelled by new spectroscopic techniques and other experimental innovations, and by new theoretical approaches re- flecting fresh points of view and increasing computational skill and power. Loosely Bound Atomic States The advent of the laser and the development of better sources of negative ions have made it practical to study systems in which one electron is bound loosely. These systems are interesting because it is only near the atomic core that the motion is complex. Over the rest of space the motion of the loosely bound electron is understood precisely.
A TOMIC PHYSICS 77 a uniform electric field. The approximate symmetry reveals a close connection between the structure of high Rydberg states and ion-atom collisions. Approximate conservation laws are a recurring theme of atomic physics; whenever they are discovered they help to unify and systematize widely diverse data. Toward the Complete Scattering Experiment Recent advances in experimental technology, including position- sensitive detection, polarized beams, improvements in energy resolu- tion, and fast electronics, have made possible a new range of measure- ments approaching the complete scattering experiments in which every possible quantum number is specified. The first scattering experiments in which all the quantum-mechanical observables were determined involved exciting the UP states of He by electron bombardment. This is a four-body problem, but it is nonethe- less simple because the total electron spin of the target is zero both before and after the collision; and there is no nuclear spin. In such a case, electron-spin effects are negligible and there is no hyperfine structure to be considered. By studying the electron-photon angular correlations following the collision, all the excitation amplitudes, and their relative phases, can be obtained. The experimental data yield accurate values for the electron-atom interaction potential, and this provides an accurate check of the approximations needed to carry out ab initio calculations. Recently complete scattering experiments have been carried out for the polarized electrons scattered from polarized hydrogen and from xenon. Comparisons of Positron and Electron Scattering Although the positron and electron differ only in charge, their scattering behavior can differ enormously. For example, in slow collisions with helium, the electron-scattering cross section is over 100 times that of the positron, though at sufficiently high energies the two scatter identically. Ramsauer minima are evident in positron scattering of He and H2, though not in electron scattering. The positron- and electron-scattering cross sections for He and H2 come rapidly into agreement for energies above 125 eV but not for Ne, N2, and heavier targets. In most cases studied, electron scattering is stronger than positron scattering. These differences and similarities can be understood qualitatively by recognizing that the long-range polarization interaction, which is 1
78 ATOMIC, MOLECULAR, AND OPTICAL PHYSICS important in low-energy scattering, is always attractive and that it is asymptotically identical for positrons and electrons. The short-range interactions, on the other hand, can be very different. For electrons, the exchange interaction partially cancels out the attractive field of the nucleus; for positrons, the exchange interaction vanishes and the short-range field is repulsive. ACCELERATOR-BASED ATOMIC PHYSICS There is a body of atomic phenomena that is seen in collisions involving energetic ion-beam methods. This area of research is some- times called accelerator-based atomic and molecular physics most of the experiments employ some type of accelerator. though it could equally well be called high-energy atomic and molecular physics, for the scientific interest often focuses on strongly interacting, highly distorted and excited systems. Also included in this classification are studies of accelerator-produced beams of H-, high-charged ions and muonic atoms discussed elsewhere in this report. A fast beam of highly charged ions can collisionally generate systems whose electronic ionization energies and excitation levels are several kiloelectron volts. These collision fragments offer unique opportunities for electron and photon spectroscopy on highly ionized systems that challenge theory in a new domain of few-electron strongly bound atoms. The transient collision system may have a combined nuclear charge that is so high that a new phenomenon occurs the spontaneous production of an electron-positron pair. Understanding the dynamics of the collision presents a theoretical challenge to deal with the interaction of a fast, highly charged particle with electrons, atoms, or molecules. The scientific implications of research in accelerator-based atomic physics extend from quantum electrodynamics to molecular and solid- state physics; its practical applications extend from the creation of new sources and detectors to the development of ion-implantation tech- niques. Progress in this field has been stimulated by dramatic discov- eries of new physical phenomena such as continuum electron capture and x-ray transitions in superheavy quasi-molecules and by steady progress in our ability to deal with the dynamics of violently colliding atomic-ionic systems. The examples below illustrate some of these advances.
ATOMIC PHYSICS 79 Atomic Coherence and Out-of-Round Atoms By studying the angular distribution of decay products from colli- sions, the shapes of excited atomic states can be determined. For example, when atoms pass through solid foils or reflect from solid surfaces, situations arise where the collision products all spin in the same direction or where the charge clouds are completely aligned. The light that is emitted as the excited states decay is not isotropic; it emerges in some preferred direction at a given instant. Weak internal forces can perturb the shapes of the excited states causing the spin or the charge cloud to process. This precession produces a sort of searchlight effect in which the intensity of the light that is observed in a particular direction oscillates in time. These oscillations, called quantum beats, arise from the interference of two or more quantum states that are excited simultaneously. The periods of oscillation can be very short, but the time resolution in these experiments now ap- proaches 1 picosecond (10-~2 s), allowing the beats to be observed. Measurements of transient nonspherical atoms are most straightfor- ward in electron-scattering experiments, but the concept has far more general applications. For instance, it has solved a long-standing puzzle: Lyman-alpha radiation is copiously emitted when a molecular hydro- gen ion breaks into a proton and a hydrogen atom during a collision with a projectile such as helium. This means that the hydrogen atom emerges in an excited state, in contradiction to the conventional model, which predicts that it should be in the ground state. When the shape of the ion during the collision was determined experimentally, the charge distribution was found to have a node, as in the 2p atomic state, but the node was oriented randomly with respect to the internuclear axis. The solution to the puzzle follows immediately, for it can be shown that if the node is parallel to the axis the molecular ion must be in a pi state, which dissociates to an excited atom, whereas if it is perpendicular it forms a sigma state, which dissociates to a ground-state atom. The reason for the copious Lyman-alpha radiation is simply that the elongated charge cloud is formed randomly with respect to the axis. This is exactly opposite to the behavior under photoexcitation in which the relative orientation is fixed because of angular momentum conser- vation. Quantum Electrodynamics of Highly Charged Systems Precise tests of quantum electrodynamics have been made in the regime where particles interact weakly either with each other, as in
80 ATOMIC, MOLECULAR, AND OPTICAL PHYSICS hydrogen or muonium, or with an external magnetic field, as in measurements of the electron or muon magnetic moment. A less-well- explored subject is high-, highly ionized atoms, in which the constant that measures the strength of the coupling of the electrons to the nucleus, ZOL, is not a small parameter. Because of the strong Z dependence of the QED effects, the precise tests in loosely bound low-, atoms provide no quantitative information on the validity of QED in strongly bound high-, atoms. Thus independent tests of QED and the renormalization prescription for highly relativistic strongly bound electrons are necessary. Hydrogenlike beams, produced by foil stripping fast heavy-ion beams, have been used to measure the 2S Lamb shift in systems with Z as large as 18 (argon). Precision spectroscopy on fast heavy-ion beams has also been used to measure the 25 Lamb shift in heliumlike systems. These experiments have stimulated theoretical efforts to deal simultaneously with radiative corrections and interactions of strongly bound electrons, one of the unsolved problems of QED. In addition, the energy of Lyman-alpha photons produced by foil-excited fast-ion beams of iron and chlorine has been measured. High-precision spec- troscopy of slow recoil ions is in progress and is expected to reveal the large Is Lamb shift in a high-, system. Pair Production in Transient Superheavies Nature provides no stable species with Z greater than 92, but during close collisions between energetic heavy ions, quasi-molecules are formed whose combined charge can greatly exceed 137. For example, two uranium nuclei at a collision energy near 1 GeV can achieve an effective nuclear charge of 184. Under such extreme conditions the quasi-molecular system is highly relativistic, offering opportunities to study atomic processes in superheavy systems. If the effective value of Z is greater than 173, the K-shell electron binding energy will exceed twice the rest-mass energy of an electron. It is predicted that in this situation a K vacancy can spontaneously decay by creating an elec- tron-positron pair. In other words, if the nuclear charge is large enough, the vacuum becomes unstable. A second type of atomic pair production, caused by the time-varying fields during the collision, has been observed. A surprising structure in the energy spectrum of the positrons has been observed; this may be the result of the anticipated spontaneous decay. In addition to atomic pair production, quasi- molecules offer opportunities to investigate radiative transitions in
ATOMIC PHYSICS 81 systems where the transient magnetic field can reach 109 times the strength that can be created in laboratory electromagnets. Inner-Shell Molecular Orbitals and Molecular Orbital X Rays Inner-shell vacancy production was long believed to proceed mainly via Coulomb ionization. It is now known that this mechanism is frequently eclipsed by inner-shell electron promotion mechanisms: the inner atomic orbitals evolve into molecular orbitals during the colli- sion, from which they undergo transitions at near degeneracies to vacant orbitals whose ultimate evolution is to excited atomic levels. A relativistic treatment is essential, as well as a careful treatment of the many-body aspects of the problem. Considerable progress has been made in understanding the essential individual molecular orbital tran- sition and how outer-shell vacancies are dynamically transformed into inner-shell vacancies. The results are of some practical importance: inner-shell vacancy production plays an important role in processes such as heavy-ion energy deposition in biological materials and also in ion-beam compression of fusion pellets. X rays have been observed from discrete transitions between molecular orbitals formed during heavy-ion collisions. Radiative rates increase so rapidly with transition energy that this process is actually easier to observe for transitions between inner orbitals than between outer orbitals. Energy spectra and production probabilities for these x rays are sensitive probes for predictions of inner-shell processes within the molecular orbital model. Charge Transfer The transfer of an electron in collisions between ions and atoms is one of the most elementary rearrangement processes, and understand- ing charge exchange is an important step toward understanding com- plex reaction processes. Over the past decade, we have learned a great deal about electron transfer of both outer- and inner-shell electrons. The prototype charge-transfer problem is the capture of a single- electron by a fast point-charge projectile. The problem might seem well suited to a simple perturbation treatment, but this does not work. In the last few years comprehensive theoretical treatments have emerged. It is now recognized that capture of the electron by the Coulomb field of the projectile is not the dominant process at high velocity; simulta- neous interactions with both the target and projectile Coulomb fields, the so-called second-order processes, are important.
82 ATOMIC, MOLECULAR, AND OPTICAL PHYSICS In attempting to understand charge transfer it was discovered that electron capture is not confined to bound final states but that it extends into the ionization continuum of the projectile. This process, first observed in the early 1970s, gives rise to a singularity or cusp in the spectrum of the ionization electrons that is centered at an energy that corresponds to an electron moving at the projectile velocity. The continuum capture process accounts for a large fraction of the ioniza- tion events at low energies, yet it was completely overlooked in earlier treatments of ionization. The most recent experimental evidence for the second-order nature of the electron capture is the observation of the Thomas peak. The projectile first scatters a nearly free electron, so that the electron attains the projectile speed, and then the projectile captures the electron with the help of the large Coulomb field of the target nucleus, which serves to scatter the electron parallel to the projectile trajectory. For proton projectiles the peak occurs in the angular distribution of the capturing projectile at an angle of 0.5 mrad (5 cm over the length of a football field). Slow-Recoil Ion Production As a fast, highly charged projectile passes through a neutral target of a light element, neon, for example, it can in a single collision remove nearly every target electron. The collision can transfer an enormous amount of energy to the electrons of the target, several kiloelectron volts, while transferring little translational energy to the nucleus of the target, a few electron volts or less. Thus, a fast heavy-ion beam is an efficient "hammer" for producing slow, highly excited ions. These ions are useful for spectroscopy and for the study of collisions with neutral targets. Slow highly charged ions have been contained in electrostatic and electromagnetic traps for periods up to seconds. Metastable ions, such as the heliumlike neon ion, have been observed to capture an electron from a background gas and to radiate x rays and light. The captured electron goes into a highly excited orbit, thus forming a sort of population inversion in the final-state ions. The method has been used to create small external beams of slow highly charged ions, up to bare neon and heliumlike argon. Ultraviolet and x-ray emission from the slow ions do not suffer from the Doppler-shift problem of light from fast-ion beam sources. Slow ions are just beginning to be exploited for precision spectros- copy. For example, Lyman-alpha radiation in argon has been ob-
ATOMIC PHYSICS 83 served. Precise measurements of its wavelength provide a measure- ment of the is Lamb shift in a new regime. In addition, low-recoil atoms may provide possible sources for new short-wavelength laser systems. Tunable X Rays Relativistic electrons and positrons can produce intense radiation as they pass through crystals along potential channels. To a laboratory observer these particles behave like very-high-frequency one- and two-dimensional oscillators. As the electrons move through the chan- nels, they can weave about the planes, or revolve around the strings of positive lattice sites. An electron bound to a lattice plane forms a kind of one-dimensional atom, and an electron bound to an atomic string forms something like a two-dimensional atom. The electrons can emit tunable x rays, with characteristic energies up to 50 keV, highly directed in the forward direction. The x-ray spectrum reflects the electronic structure of the crystalline medium. ATOMIC PHYSICS REQUIRING LARGER FACILITIES Two areas require access to larger facilities than are usually em- ployed in AMO research: accelerator-based atomic physics and AMO physics with synchrotron light sources. To provide the scientific background for the special recommendations on facilities for this research (Chapter 3), the new opportunities in these areas are summa- rized in this section. Accelerator-Based Atomic Physics Given the necessary tools, we will be able, in the next decade, to address an array of opportunities in the physics of highly charged ions. Advances in ion source and heavy-ion accelerator technology are placing at our disposal intense beams, both fast and slow, of ions of unprecedentedly high charge state. Hydrogenlike uranium and bare uranium ions have already been produced in relativistic heavy-ion beams, and slow beams of fully stripped argon from the new generation of ion sources have been produced. With fast relativistic beams, the structure of very-high-charged few-electron systems, for which QED and relativistic effects on level structures and on decay rates are huge, will be studied. Collision processes such as charge transfer with relativistic heavy-ion beams of unprecedentedly high charge will be
84 ATOMIC, MOLECULAR, AND OPTICAL PHYSICS
A TOMIC PHYSICS 85 open to study. Beams of fast heavy ions, as well as synchrotron radiation, will be used to form ions in traps, producing highly charged but cool ions on which precision spectroscopy and collision experi- ments may be performed. Intense beams of both fast and slow multiply charged ions will enable merged-beam and crossed-beam studies of capture, ionization, and dielectronic recombination in collisions be- tween multiply charged ions and between electrons and these ions. Such processes, while common in nature's hotter theaters, are only now coming into our grasp in the laboratory. Slow beams from the new generation of multiply charged ion sources will make possible the study of the structure of multiply excited highly charged systems and of collision processes, both inner and outer shell, involving vacancies with binding energies up to tens of kiloelectron volts. (See Figure 4.5.) Such projectiles carry enormous amounts of electronic energy (14 keV for bare argon, about half a million electron volt for bare uranium) and will certainly give rise to new and violent physical phenomena when they encounter atomic or solid collision partners. New collision regimes will be opened: slow beams with inner-shell vacancies will allow us to probe for the first time collisions in which the inner-shell energy is shared with essentially all the colliding system's electrons during the collision, and energetic elec- trons and x rays emitted from the composite colliding system will be the rule rather than the exception. Technological advances in data gathering, such as position-sensitive detectors and computer-based multiparameter data-acquisition sys- tems, will bring us even closer to the ideal experiment in which all FIGURE 4.5 Atomic Physics with Highly Charged Ions. Atomic collision processes involving multiply charged ions are important in astrophysical scenarios—particularly in stellar interiors—and in earthbound thermonuclear devices. These processes can be studied using accelerated ion beams. The upper figure shows the acceleration column of the Holifield Heavy Ion Research Facility, tandem Van de Graaff accelerator, which delivers beams of fast heavy ions with an energy per charge of approximately 25 MeV. The fast ions can be further stripped of electrons by passing them through gases or foils and then used by atomic physicists to probe ionization and capture collisions. Recent advances in the design of ion sources now make it possible to produce intense beams of highly charged ions that, in contrast to ions from a high-energy source, move very slowly. These sources provide important new opportunities for investigating atomic- collision processes and to carry out spectroscopy on multiply charged species. The lower figure shows an electron cyclotron resonance source, one example of the new generation of low-energy ion sources that are just becoming available. [Photos courtesy of Oak Ridge National Laboratory (top) and the Lawrence Berkeley Radiation Laboratory (bottom).]
86 ATOMIC, MOLECULAR, AND OPTICAL PHYSICS collision parameters before and after the encounter are experimentally determined. Atomic, Molecular, and Optical Physics with Synchrotron Radiation Synchrotron radiation now plays an indispensable role in atomic and molecular physics as an intense, reliable source of electromagnetic radiation spanning decades of the spectrum between the ultraviolet and hard x-ray ranges. A new generation of synchrotron-radiation sources is technically feasible. Intensity can be increased by orders of magnitude, and the radiation can be delivered in reliable picosecond pulses. Circularly polarized as well as linearly polarized x rays can be produced. The way would be open for studying the role of many-body effects in atomic structure and dynamics, exploring the limitations of independent- particle self-consistent-field models, and testing modern theoretical approaches to electron-electron Coulomb correlation. Synchrotron light beautifully complements the other major source of light used in photophysics lasers. Laser sources are brighter and better resolved, but they operate only in a limited (though expanding) part of the spectrum. Synchrotron radiation is continuously tunable far beyond the limits of laser sources. Synchrotron-radiation sources can produce reliable picosecond pulses 109 times per second, again com- plementing the much lower pulse rate of the more intense laser radiation. An electron storage ring (in France) has recently been used successfully to operate a free-electron laser. The scientific potential of this technology is great: photoexcitation of virtually any atomic or molecular subshell is possible, often with sufficient intensity to measure all secondary products (photons, elec- trons, and ions) including energies, ejection angles, and polarization or spin states. The incident wavelength can be freely tuned to excite resonances, threshold regions, or multiply excited final states. Many advances have already resulted from this powerful capability. For example, significant insights into correlations have emerged from studies of such diverse phenomena as autoionization, continuum- continuum coupling, postcollision interaction, and multielectron exci- tation. Molecular physics has advanced through studies of vibrational autoionization, shape resonances, and the breakdown of the single- particle model due to strong vibronic coupling for inner-valence ionization. The picosecond time structure of synchrotron light is only
A TOMIC PHYSICS 87 now beginning to be used in studies of intramolecular relaxation and energy-transfer processes. The possibility of reaching the innermost shells of large atoms with hard synchrotron radiation provides access to processes in which relativistic and QED effects are prominent. Opportunities exist for measuring the frequency dependence of the Breit interaction and the screening of the self-energy in shells for which it has to date eluded calculation. Inner-shell threshold excitation with hard synchrotron radiation makes it possible to explore the domain where excitation and de-excitation of an atom occur in a single process, as in resonant x-ray and Auger Raman scattering. Finally, the joint use of lasers and synchrotron light has just been initiated, giving access to photoelectron spectroscopy of excited states of atoms in a manifold of hitherto inaccessible levels.
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Representative terms from entire chapter: