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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
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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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Representative terms from entire chapter:
optical physics
56 ATOMIC, MOLECULAR, AND OPTICAL PHYSICS
:~MIC~WAVE INPUT
>
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.
