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1
Introduction to
Nuclear Physics
All phenomena in the universe are believed to arise from the actions
of just three fundamental forces: gravitation and the less familiar
strong force and electroweak force. The complex interplay between
these last two forces defines the structure of matter, and nowhere are
the myriad manifestations of this interplay more evident than in the
nucleus of the atom. Much of the substance of the universe exists in the
form of atomic nuclei arranged in different ways. Within ordinary
nuclei, the weak gravitational attraction between the constituent
particles is overwhelmed by the incomparably more powerful strong
nuclear force, but gravitation's effect is large indeed in neutron stars-
bizarre astrophysical objects whose properties are very much like
those of gigantic nuclei.
Studies of the nucleus can thus be viewed as a link between the
worlds of the infinitesimal and the astronomical. Collectively, the
various nuclei can be regarded as a laboratory for investigating the
fundamental forces that have governed our universe since its origin in
the big bang. Indeed, as this report illustrates, the study of nuclear
physics is becoming ever more deeply connected with that of cosmol-
ogy as well as elementary-particle physics.
Before venturing into these exciting realms, we will quickly survey
the field of nuclear physics at an elementary level in order to learn the
language. Although nuclear physics has the reputation of being a
difficult subject, the basic concepts are relatively few and simple.
9
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10 NUCLEAR PHYSICS
10-2 m
10-14 m
~ Raspberry
_
-
-
-
~ Nucleus
-
i Quark
-
_
_
_,
-
_-
_
__
_
_
· ~
,~
Proms
_. ~
,
-
__
Nuc:
-
_- ~. ~ -
_
-_
-10 m
-15 m
FIGURE l.l Approximate dimensions for the structure of matter from raspberries to
quarks (the cellular and molecular levels of structure have been omitted).
THE ATOMIC NUCLEUS
The atomic nucleus is an extremely dense, roughly spherical object
consisting primarily of protons and neutrons packed fairly closely
together (see Figure 1.1~. Protons and neutrons are collectively called
nucleons, and for many years it was thought that nucleons were truly
elementary particles. We now know, however, that they are not
elementary but have an internal structure consisting of smaller parti
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INTRODUCTION TO NUCLEAR PHYSICS 11
cles and that there are other particles in the atomic nucleus along with
them. These aspects of the nucleus are discussed below. Protons and
neutrons are very similar, having almost identical physical properties.
An important difference, however, lies in their electric charge: protons
have a unit positive charge, and neutrons have no charge. They are
otherwise so similar that their interconversion in the decay of radio-
active nuclei is a common occurrence.
The character of the nucleus provides the diversity of the chemical
elements, of which 109 are now known, including a number of
man-made ones. (The cosmic origin of the elements is a different
question-one that is addressed by the specialized field of nuclear
astrophysics.) Each element has a unique proton number, Z. This
defines its chemical identity, because the proton number (equal to the
number of unit electric charges in the nucleus) is balanced, in a neutral
atom, by the electron number, and the chemical properties of any
element depend exclusively on its orbital electrons. The smallest and
lightest atom, hydrogen, has one proton and therefore one electron; the
largest and heaviest naturally occurring atom, uranium, has 92 protons
and 92 electrons. In a rough sense, this is all there is to the diversity of
the chemical elements and the fantastic variety of forms inanimate
and animate that they give rise to through the interactions of their
electron clouds.
To explain the stability of the elements, however, and to study
nuclear physics, we must also take into account the neutron number,
N. of each nucleus. This number can vary considerably for the nuclei
of a given element. The nucleus of ordinary hydrogen, for example, has
one proton and no neutrons, the latter fact making it unique among all
nuclei. But a hydrogen nucleus can also exist in a form that has one
proton and one neutron (Z = 1, N = 1~; this nucleus is called a
deuteron, and the atom, with its one electron, is called deuterium.
Chemically, however, it is still hydrogen, as is the even heavier,
radioactive form tritium, which has one proton and two neutrons (Z =
1, N = 21; a tritium nucleus is called a triton.
These separate nuclei of a single chemical element, differing only in
neutron number, are the isotopes of that element. Every element has at
least several isotopes stable and unstable (radioactiveWand some of
the heavier elements have already been shown to have more than 35.
Although the chemical properties of the isotopes of a given element are
the same, their nuclear properties can be so different that it is important
to identify every known or possible isotope of the element unambigu-
ously. The simplest way is to use the name of the element and its mass
number, A, which is just the sum of its proton and neutron numbers:
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12 NUCLEAR PHYSICS
A = Z + N. Because different combinations of Z and N can give the
same value of A, nuclei of different elements can have the same mass
number (chlorine-37 and argon-37, for example). To emphasize the
uniqueness of every such separately identifiable type of nucleus,
scientists refer to them as nuclides.
There are about 300 naturally occurring stable nuclides of the
chemical elements and about 2400 radioactive (i.e., spontaneously
decaying) ones. Of the latter, the great majority do not exist naturally
but have been made artificially in particle accelerators or nuclear
reactors. These machines of modern physics can also create experi-
mental conditions that are drastically unlike those ordinarily existing
on Earth but that are similar, perhaps, to those characteristic of less
hospitable corners of the universe. Thus they enable us, in our efforts
to understand the laws of nature, to extend our intellectual grasp into
domains that would otherwise be inaccessible.
Experimental and theoretical investigations of the broad range of
nuclides available to us represent the scope of nuclear physics. In the
study of nuclear spectroscopy, for example, experimentalists perform
many kinds of measurements in order to characterize the behavior of
the nuclides in detail and to find patterns and symmetries that will allow
the huge amounts of information to be ordered and interpreted in terms
of unifying principles. The theorists, on the other hand, search for
these unifying principles through calculations based on the available
facts and the fundamental laws of nature. Their aim is not only to
explain all the known facts of nuclear physics but to predict new ones
whose experimental verification will confirm the correctness of the
theory and extend the bounds of its applicability.
A similar approach applies to the study of nuclear reactions, in
which experimentalists and theorists seek to understand the changing
nature and mechanisms of collisions between projectile and target
nuclei at the ever-increasing energies provided by modern accelera-
tors. The many ways in which target nuclei can respond to the
perturbations produced by energetic projectile beams provide a rich
fund of experimental data from which new insights into nuclear
structure and the laws of nature can be gained. In extreme cases, new
states of nuclear matter may be found.
THE NUCLEAR MANY-BODY PROBLEM
The essential challenge of nuclear physics is to explain the nucleus as
a many-body system of strongly interacting particles. In physics, three
or more mutually interacting objects whether nucleons or stars are
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INTRODUCTION TO NUCLEAR PHYSICS 13
considered to be "many" because of the tremendous mathematical
difficulties associated with solving the equations that describe their
motions. With each object affecting the motions of all the others
through the interactions that exist among them, and with all the
motions and hence all the interactions changing constantly, the prob-
lem very quickly assumes staggering proportions. In fact, this many-
body problem is now just barely soluble, with the largest computers,
for three bodies. For four or more, however, it remains generally
insoluble, in practice, except by methods relying on various approxi-
mations that simplify the mathematics.
What nuclear physicists try to do-within the constraints imposed by
the many-body problem is to understand the structure of nuclei in
terms of their constituent particles, the dynamics of nuclei in terms of
the motions of these particles, and the fundamental interactions among
particles that govern these motions. Experimentally, they study these
concepts through nuclear spectroscopy and the analysis of nuclear
reactions of many kinds. Theoretically, they construct simplifying
mathematical models to make the many-body problem tractable.
These nuclear models are of different kinds. Independent-particle
models allow the motion of a single nucleon to be examined in terms of
a steady, average force field produced by all the other nucleons. The
best-known independent-particle model is the shell model, so called
because it entails the construction of "shells" of nucleons analogous to
those of the electrons in the theory of atomic structure. At the other
extreme, collective models view the nucleons in a nucleus as moving in
concert (collectively) in ways that may be simple or complex- just as
the molecules in a flowing liquid may move smoothly or turbulently. In
fact, the best-known collective model, the liquid-drop model, is based
on analogies with the behavior of an ordinary drop of liquid.
The above descriptions are necessarily oversimplified. The actual
models in question, as well as related ones, are very sophisticated, and
their success in explaining most of what we know about nuclear
structure and dynamics is remarkable. As we try to push this knowl-
edge to ever deeper levels, however, we must take increasingly
detailed account of specific nucleon-nucleon interactions. Doing so
brings out the other half of the essential challenge of nuclear physics:
that nucleons are strongly interacting particles.
THE FUNDAMENTAL FORCES
In nature, the so-called strong force holds atomic nuclei together
despite the very substantial electrostatic repulsion between all the
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14 NUCLEAR PHYSICS
positively charged protons. The distance over which the strong force is
exerted, however, is extremely short: about 10- ~5 meter, or 1
femtometer-commonly called 1 fermi (fm) after the great nuclear
physicist Enrico Fermi. A fermi is short indeed, being roughly the
diameter of a single nucleon. The time required for light to traverse this
incredibly short distance is itself infinitesimal: only 3 x 10-24 second.
As we will see, the characteristic duration of many events taking place
in the nucleus is not much longer than that: about 10-23 to 10-22
second, corresponding to a distance traveled, at the speed of light, of
only about 3 to 30 fm.
This is the domain- incomprehensibly remote from our everyday
experience-of the strong force, which dominates the nucleus. Nucle-
ons within the nucleus are strongly attracted to one another by the
strong force as they move about within the confines of the nuclear
volume. If they try to approach each other too closely, however, the
strong force suddenly becomes repulsive and prevents this from
happening. It is as though each nucleon had an impenetrable shield
around it, preventing direct contact with another nucleon. The behav-
ior of the strong force is thus very complex, and this makes the analysis
of multiple nucleon-nucleon interactions (the nuclear many-body prob-
lem) much more challenging.
At the opposite extreme of the fundamental forces is gravitation, a
long-range force whose inherent strength is only about 10-38 times that
of the strong force. Since the gravitational force between any two
objects depends on their masses, and since the mass of a nucleon is
extremely small (about 10-24 g), the erects of gravitation in atomic
nuclei are not even close to being measurable. Nonetheless, the
universe as a whole contains so many atoms, in the form of hugely
massive objects (stars, quasars, galaxies), that gravitation is the
dominant force in its structure and evolution. And because gravitation
is extremely important in neutron stars, as mentioned earlier, these
supermassive nuclei are all the more interesting to nuclear astrophys-
icists.
Lying between gravitation and the strong force, but much closer to
the latter in inherent strength, is the electroweak force. This rather
complex force manifests itself in two ways that are so different that
until the late 1960s they were believed to be separate fundamental
forces just as electricity and magnetism, a century ago, were thought
to be separate forces rather than two aspects of the one force,
electromagnetism. Now we know that electromagnetism itself is but a
part of the electroweak force; it is therefore no longer considered to be
a separate fundamental force of nature.
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INTRODUCTION TO NUCLEAR PHYSICS 15
Electromagnetism is the force that exists between any two electri-
cally charged or magnetized objects. Like gravitation, its influence can
extend over great distances, and it decreases rapidly in strength as the
distance between the objects increases. Its inherent strength is rela-
tively large, however, being about 0.7 percent of that of the strong
force at separation distances of about 1 fm. Electromagnetism is the
basis of light and all similar forms of radiation (x rays, ultraviolet and
infrared radiation, and radio waves, for example). All such radiation
propagates through space via oscillating electric and magnetic fields
and is emitted and absorbed by objects in the form of tiny bundles of
energy called photons. In some radioactive decay processes, extremely
energetic photons called gamma rays are emitted by the nuclei as they
change to states of lower total energy. A photon is considered to be the
fundamental unit of electromagnetic radiation: a quantum. This pro-
found idea revolutionary in its time but now commonplace lies at
the heart of quantum mechanics, the physical theory that underlies all
phenomena at the submicroscopic level of molecules, atoms, nuclei,
and elementary particles.
The other manifestation of the electroweak force is the weak force,
which is responsible for the decay of many radioactive nuclides and of
many unstable particles, as well as for all interactions involving the
particles called neutrinos, which we discuss below. The weak force in
nuclei is feeble compared with the electromagnetic and strong forces,
being only about 10-5 times as strong as the latter, but it is still
extremely strong compared with gravitation. The distance over which
it is effective is even shorter than that of the strong force: about 10-'8
m, or 0.001 fm roughly 1/1000 the diameter of a nucleon. The weak
force governs processes that are relatively slow on the nuclear time
scale, taking about 10- ~° second or more to occur. As short as this time
may seem, it is about one trillion times longer than the time required for
processes governed by the strong force.
The prediction in 1967 and its subsequent experimental confirma-
tion that the electromagnetic and weak forces are but two aspects of
a single, more fundamental force, the electroweak force, were tri-
umphs of physics that greatly expanded our understanding of the laws
of nature. However, because these two component forces are so
different in the ways in which they are revealed to us (their essential
similarities start to become clear only at extremely high energies, far
beyond those of conventional nuclear physics), it is usually convenient
to discuss them separately, just as we often discuss electricity and
magnetism separately. Thus they are still often described as though
each were fundamental. In this book, we will let the circumstances
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16 NUCLEAR PHYSICS
decide how they should be discussed: as electromagnetic and weak, or
as electroweak. For the remainder of this chapter, we will discuss them
separately.
The fundamental forces are often called fundamental interactions,
because the forces exist only by virtue of interactions that occur
between particles. These interactions, in turn, are mediated by the
exchange of other particles between the interacting particles. This may
seem like Chinese boxes, but as far as we know, it stops right there: in
the realm of elementary-particle physics, which we must now briefly
introduce in order to see where the foundations of nuclear physics lie.
THE ELEMENTARY PARTICLES
The experimental study of elementary-particle physics also known
by the inexact name high-energy physics~iverged from that of
nuclear physics around 1950, when developing accelerator technology
made it relatively easy to search for other and ultimately more
basic "elementary" particles than the proton or the neutron. An
enormous variety of subnuclear particles has by now been discovered
and characterized, some of which are truly elementary (as far as we can
tell in 1984), but most of which are not.
Along with the discovery of these particles came major theoretical
advances, such as the electroweak synthesis mentioned above, and
mathematical theories attempting to classify and explain the seemingly
arbitrary proliferation of particles (several hundred by now) as accel-
erator energies were pushed ever higher. Chief among these theories,
because of their great power and generality, are the quantum field
theories of the fundamental interactions. All such theories are relativ-
istic, i.e., they incorporate relativity into a quantum-mechanical frame-
work suitable to the problem at hand. They thus represent the deepest
level of understanding of which we are currently capable.
We will return to these theories shortly, but first let us see what
classes of particles have emerged from the seeming chaos. This is
essential for two reasons. First, the nucleus as we now perceive it does
not consist of just protons and neutrons, and these are not even
elementary particles to begin with. To understand the atomic nucleus
properly, therefore, we must take into account all the other particles
that exist there under various conditions, as well as the compositions
of the nucleons and of these other particles. Second, the theoretical
framework for much of nuclear physics is now deeply rooted in the
quantum field theories of the fundamental interactions, which are the
domain of particle physics. Aspects of the two fields are rapidly
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INTRODUCTION TO NUCLEAR PHYSICS 17
converging, after their long separation, and it is no longer possible to
investigate many fundamental problems of nuclear physics except in
the context of the elementary particles. Much of the material in this
book, in fact, deals with the ways in which this new view of nuclear
physics has come about and the ways in which it will accelerate in the
future.
Physicists now believe that there are three classes of elementary
particles leptons, quarks, and elementary vector bosons and that
every particle, elementary or not, has a corresponding antiparticle.
Here we must make a short digression into the subject of antimatter.
An antiparticle differs from its ordinary particle only in having some
opposite elementary properties, such as electric charge. Thus, the
antiparticle of the electron is the positively charged positron; the
antinucleons are the negatively charged antiproton and the neutral
antineutron. The antiparticle of an antiparticle is the original particle;
some neutral particles, such as the photon, are considered to be their
own antiparticles. In general, when a particle and its corresponding
antiparticle meet, they can annihilate each other (vanish completely) in
a burst of pure energy, in accord with the Einstein mass-energy
equivalence formula, E = mc2. Antiparticles are routinely observed
and used in many kinds of nuclear- and particle-physics experiments,
so they are by no means hypothetical. In the ensuing discussions of the
various classes of particles, it should be remembered that for every
particle mentioned there is also an antiparticle.
Leptons
Leptons are weakly interacting particles, i.e., they experience the
weak interaction but not the strong interaction; they are considered to
be pointlike, structureless entities. The most familiar lepton is the
electron, a very light particle (about 1/1800 the mass of a nucleon) with
unit negative charge; it therefore also experiences the electromagnetic
interaction. The muon is identical to the electron, as far as we know,
except for being about 200 times heavier.* The tan particle, or taNon,
is a recently discovered lepton that is also identical to the electron
except for being about 3500 times heavier (making it almost twice as
*The muon is still occasionally called a mu meson its original name which can be
confusing because the term "meson" is now restricted to a very different kind of
particle; thus a "mu meson" is not a meson in the modern sense.
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18 NUCLEAR PHYSICS
heavy as a nucleon). The very existence of these "heavy electrons"
and "very heavy electrons" is a major puzzle for physicists.
Associated with each of the three charged leptons is a lepton called
a neutrino: thus there is an electron neutrino, a muon neutrino, and a
tauon neutrino. Neutrinos are electrically neutral and therefore do not
experience the electromagnetic interaction. They have generally been
assumed to have zero rest mass (see page 31 for an explanation of this
term) and must therefore move at the speed of light, according to
relativity, but the question of their mass is currently controversial. If
the electron neutrino, in particular, does have any mass, it is very slight
indeed. The possible existence of such a mass, however, has great
cosmological significance: because there are so many neutrinos in the
universe, left over from the big bang, their combined mass might exert
a gravitational effect great enough to slow down and perhaps halt the
present outward expansion of the universe.
Neutrinos and antineutrinos are commonly produced in the radioac-
tive process called beta decay (a weak-interaction process). Here a
neutron in a nucleus emits an electron (often called a beta particle) and
an antineutrino, becoming a proton in the process. Similarly, a proton
in a nucleus may beta-decay to emit a positron and a neutrino,
becoming a neutron in the process. Neutrinos and antineutrinos thus
play an important role in nuclear physics. Unfortunately, they are
extremely difficult to detect, because in addition to being neutral, they
have the capability of passing through immense distances of solid
matter without being stopped. With extremely large detectors and
much patience, however, it is possible to observe small numbers of
them.
We have now seen that there are three pairs, or families, of charged
and neutral weakly interacting leptons, for a total of six; there are
therefore also six antileptons. Let us next look at the quarks, of which
there are also three pairs-but there the similarity ends.
Quarks
Quarks are particles that interact both strongly and weakly. They
were postulated theoretically in 1964 in an effort to unscramble the
profusion of known particles, but experimental confirmation of their
existence was relatively slow in coming. This difficulty was due to the
quarks' most striking single characteristic: they apparently cannot be
produced as free particles under any ordinary conditions. They seem
instead always to exist as bound combinations of three quarks, three
antiquarks, or a quark-antiquark pair. Thus, although they are believed
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INTRODUCTION TO NUCLEAR PHYSICS 19
to be truly elementary particles, they can be studied-so far-only
within the confines of composite particles (which are themselves often
inside a nucleus). This apparent inability of quarks, under ordinary
conditions, to escape from their bound state is called quark confine-
ment.
There are six basic kinds of quarks, classified in three pairs, or
families; their names are up and down, strange and charm, and top and
bottom. Only the top quark has not yet been shown to exist, but
preliminary evidence for it was reported in the summer of 1984. The six
varieties named above are called the quark flavors, and each flavor is
believed-to exist in any of three possible states called colors. (None of
these names have any connection with their usual meanings in every-
day life; they are all fanciful and arbitrary.) Flavor is a property similar
to that which distinguishes the three families of leptons (electron,
muon, and tauon), whereas color is a property more analogous to
electric charge.
Another odd property of quarks is that they have fractional electric
charge; unlike all other charged particles, which have an integral value
of charge, quarks have a charge of either -1/3 or + 2/3. Because free
quarks have never been observed, these fractional charges have never
been observed either-only inferred. They are consistent, however,
with everything we know about quarks and the composite particles
they constitute. These relatively large composite particles are the
hadrons, all of which experience the strong interaction as well as the
weak interaction. Although all quarks are charged, not all hadrons are
charged; some are neutral, owing to cancellation of quark charges.
There are two distinctly different classes of hadrons: baryons and
mesons. Baryons which represent by far the largest single category of
subnuclear particles-consist of three quarks (antibaryons consist of
three antiquarks) bound together inside what is referred to as a bag.
This is just a simple model (not a real explanation) to account for the
not yet understood phenomenon of quark confinement: the quarks are
assumed to be "trapped" in the bag and cannot get out.
Now, finally, we can say what nucleons really are: they are baryons,
and they consist of up (u) and down (d) quarks. Protons have the quark
structure bud, and neutrons have the quark structure add. A larger
class of baryons is that of the hyperons, unstable particles whose
distinguishing characteristic is strangeness, i.e., they all contain at
least one strange (s) quark. In addition, there are dozens of baryon
resonances, which are massive, extremely unstable baryons with
lifetimes so short (about 10-23 second) that they are not considered to
be true particles.
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26 \~ ~3
~ -a
FIGURE 1.3 a, ~ woodcut by M. C. Escher, provides an example of complex
geomethca1 symmetries, which underDe many aspects of nuclear structure. Equally
impotent are dynamical symmetries Lund in the physical laws governing aN natural
phenomena. (By permission of the Escher Foundation, Hags Cemeentemuseum The
ague. Reproduction rights arranged courtesy of the Vows OaDer~s, New York San
Franc~co, and Laguna Beach.)
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INTRODUCTION TO NUCLEAR PHYSICS 27
many years, it was believed that parity was an exact (universal)
symmetry of nature. In 1956, however, it was discovered by nuclear
and particle physicists that this is not so; parity is not conserved in
weak interactions, such as beta decay. However, it is conserved, as far
as we know, in all the other fundamental interactions and thus
represents a simplifying principle of great value in constructing math-
ematical theories of nature.
A similar, albeit isolated, example of symmetry violation has been
found for the equally fundamental and useful principle called time-
reversal invariance, which is analogous to parity except that it entails
a mirror imaging with respect to the direction of time rather than to the
orientation of particles in space. This symmetry has been found to be
violated in the decays of the neutral kaon. No other instances of the
breakdown of time-reversal invariance are known yet but physi-
cists are searching carefully for other cases in the hope of gaining a
better insight into the underlying reason for this astonishing flaw in an
otherwise perfect symmetry of nature.
The implications of such discoveries extend far beyond nuclear or
particle physics; they are connected to basic questions of cosmology,
such as the ways in which the primordial symmetry that is believed to
have existed among the fundamental interactions at the instant of the
big bang was then "broken" to yield the dramatically different inter-
actions as we know them now. The efforts of theoretical physicists to
construct Grand Unified Theories of the fundamental interactions, in
which these interactions are seen merely as different manifestations of
a single unifying force of nature, depend strongly on experimental
observations pertaining to symmetries, conservation laws, and their
violations.
A most important observation in this regard would be any evidence
of a violation of the conservation of baryon number, which may not be
a universal law after all. Certain of the proposed Grand Unified
Theories predict, in fact, that such a violation should occur, in the form
of spontaneous proton decay not in the sense of a radioactive beta
decay, in which a proton would be converted to a neutron (thus
conserving baryon number) but rather as an outright disappearance of
a baryon (the proton) as such. Extensive searches have been mounted
to find evidence for proton decay, so far without success.
Also of great importance would be any violation of the conservation
of lepton number. This law, which is also obeyed in all currently known
cases, is analogous to the conservation of baryon number, but with an
added twist: lepton number ~ + 1 for leptons, -1 for antileptons)
appears to be conserved not only for leptons as a class but also for each
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28 NUCLEAR PHYSICS
of the three families of leptons individually (the electron, muon, and
tauon, with their respective neutrinos). Any violation of lepton-number
conservation would mean that neutrinos are not, in fact, massless and
that they can oscillate (change from one family to another) during their
flight through space. Exactly these properties are also predicted by
certain of the proposed Grand Unified Theories, and this provides the
impetus for searching for them in various types of nuclear processes.
Such searches for violations of conservation laws represent an impor-
tant current frontier of nuclear physics as well as of particle physics.
ACCELERATORS AND DETECTORS
The principal research tools used in nuclear physics are accelera-
tors- complex machines that act as powerful microscopes with which
to probe the structure of nuclear matter. Equally indispensable are the
sophisticated detectors that record and measure the many kinds of
particles and the gamma rays emerging from the nuclear collisions
produced by the accelerator beams.'
There are several different kinds of accelerators, differing mainly in
the ways in which they provide energy to the particles, in the energy
ranges that they can span, and in the trajectories followed by the
accelerated particles. The most common kinds are Van de Graaff
electrostatic accelerators, linear accelerators, cyclotrons, and syn-
chrotrons; an example of a modern cyclotron is shown in Figure 1.4.
Most of the details of these machines need not concern us here, but a
survey of some basic ideas is necessary for an appreciation of how
nuclear physics research is actually done. Additional information on
accelerators in general and on several important accelerators of the
future can be found in Chapter 10, and a survey of the major operating
accelerators in the United States is given in Appendix A.
Projectiles and Targets
The basic principle of all accelerators is the same: a beam of
electrically charged projectile particles is given a number of pulses of
energy in the form of an electric or electromagnetic field to boost
the particles' velocity (and hence kinetic energy) to some desired value
before they collide with a specified target. Typically, the projectiles are
electrons, protons, or nuclei. The latter are often called ions, because
they are generally not bare nuclei, i.e., they still retain one or more of
the orbital electrons from the atoms from which they came. Nuclei of
the two lightest elements, hydrogen and helium, are called the light
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INTRODUCTION TO NUCLEAR PHYSICS 29
FIGURE 1.4 Top view of the main cyclotron of the Indiana University Cyclotron
Facility, a modern accelerator used for basic nuclear-physics research. The field
produced by the four large magnets (note the physicist standing between two of them)
confines the projectile particles light ions up to mass number 7 to a series of roughly
circular orbits of ever-increasing size as they are accelerated to energies in the range of
40 to 210 MeV. After about 300 orbits, the beam is extracted and directed at targets in
nearby experimental areas. (Courtesy of the Indiana University Cyclotron Facility.)
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30 NUCLEAR PHYSICS
ions; they include the often-used alpha particle, which is just the
nuclide helium-4 (Z = 2, N = 21. Nuclei from those of lithium (A = 6
or 7) to those with a mass number of about 40 can be called medium
ions, and those with a mass number from about 40 on up through the
rest of the periodic table are called heavy ions. (This classification is
useful but necessarily somewhat arbitrary; the definition of heavy ion,
for example, is sometimes extended all the way down to lithium.)
Accelerators can also produce beams of exotic or unstable charged
projectiles such as muons, mesons, antiprotons, and radioactive
nuclides. These are made in reactions occurring at the target of a
primary beam and are then focused into a secondary beam. Even
neutral particles, such as neutrons and neutrinos, can be produced and
used as secondary beams.
The target struck by the accelerated projectile in a typical nuclear-
physics experiment is a small piece of some solid chemical element of
particular interest, although liquid and gaseous targets can also be
used. The objective may be to use the projectiles to raise nuclei in the
target substance from their lowest-energy ground state to higher-
energy excited states in order to gain insight into the structures and
dynamics of intact nuclei; in this way one studies nuclear spectros-
copy. Alternatively, the objective may be to bombard the target nuclei
in such a way that they undergo a nuclear reaction of some kind,
possibly disintegrating in the process.
The above descriptions pertain to the traditional fixed-target ma-
chines (a stationary target being bombarded by a projectile beam), but
accelerators can also be constructed as colliding-beam machines, or
colliders. Here two beams collide violently with each other, nearly
head-on, in a reaction zone where the beams intersect. Colliders have
been pioneered by elementary-particle physicists because of the huge
amounts of energy that can be deposited in the collision zone when
both beams have been accelerated to high velocities. Their use is
becoming increasingly important to nuclear physicists for the same
reason, as described in Chapter 7.
Energies
The kinetic energies to which particles or nuclei are accelerated are
expressed in terms of large multiples of a unit called the electron volt
(eV), which is the amount of energy acquired by a single electron (or
any other particle with unit electric charge, such as a proton) when it
is accelerated through a potential difference of 1 volt (V) as in a 1-V
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INTRODUCTION TO NUCLEAR PHYSICS 31
battery. The characteristic particle beam energies in modern nuclear-
physics accelerators are of the order of mega-electron volts (1 MeV =
106 eV) and giga-electron volts (1 GeV = 109 eV). When dealing with
accelerated nuclei, which contain more than one nucleon, it is custom-
ary to give the energy per nucleon rather than the total energy of the
nucleus.
For convenience, not only the energies of particles but also their
masses are customarily given in terms of electron volts. Any mass can
be expressed in terms of an equivalent energy, in accord with E = mc2.
Thus the mass of an electron is 0.511 MeV, and the mass of a proton
is 938 MeV. These are the rest masses of these particles, i.e., the
masses that they have when they are not moving with respect to some
frame of reference (such as the laboratory). When they are moving,
however, their kinetic energy is equivalent to additional mass. This
effect becomes significant only when their velocity is very close to the
speed of light; then their kinetic energy becomes comparable to or
greater than their rest mass, and they are said to be relativistic particles
(or nuclei), because the dynamics of their reactions cannot be accu-
rately described without invoking relativity theory.
It is convenient to classify nuclear processes in terms of different
energy regimes of the projectiles, although any such classification, like
that of the projectile masses, is somewhat arbitrary and not likely to
find universal acceptance. Bombarding energies of less than about 10
MeV per nucleon, for example, produce a rich variety of low-energy
phenomena. It is in this regime (at about 5 MeV per nucleon) that the
effects due to the Coulomb barrier are particularly important; the
Coulomb barrier is a manifestation of the electrostatic repulsive force
between the positively charged target nucleus and any positively
charged projectile. For a collision involving the effects of the strong
force to occur, the projectile must be energetic enough to overcome the
Coulomb barrier and approach the target closely.
Between about 10 and 100 MeV per nucleon is the medium-energy
regime, where many studies of nuclear spectroscopy and nuclear
reactions are carried out; these are the energies characteristic of the
motions of nucleons within a nucleus. In the high-energy regime,
between about 100 MeV per nucleon and 1 GeV per nucleon, high
temperatures are produced in the interacting nuclei; also, some of the
collision energy is converted to mass, usually in the form of created
pions, which have a rest mass of 140 MeV. Above about l GeV per
nucleon is the relativistic regime, where extreme conditions, such as
the formation of exotic states of nuclear matter, are explored. [It is
worth noting here that for electrons the transition to relativistic
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32 NUCLEAR PHYSICS
behavior occurs at much lower energies (about 0.5 MeV), owing to the
electron's small rest mass.]
Nuclear Interactions
The principal kinds of nuclear interactions in collisions are scatter-
ing, in which the projectile and target nuclei are unchanged except for
their energy states; transfer, in which nucleons pass from one nucleus
to the other; fusion, in which the two nuclei coalesce to form a
compound nucleus; spallation, in which nucleons or nucleon clusters
are knocked out of the target nucleus; and disintegration, in which one
or both nuclei are essentially completely torn apart.
Not all interactions that occur in collisions are equally probable, so
it is important to know what does occur to an appreciable extent and
what does not-and why. The probability of occurrence of a given
interaction is expressed by a quantity called its cross section, which
can be measured experimentally and compared with theoretical pre-
dictions.
Another quantity whose experimental measurement is important is
the half-life of a radioactive species the time it takes for half of all the
nuclei of this nuclide in a sample to decay to some other form or state.
Normally, this decay is by the emission of alpha or beta particles or
gamma rays; less commonly, it is by spontaneousission, in which a
nucleus simply splits in two, with the emission of one or more
neutrons. After half of the nuclei have decayed, it will take the same
length of time for half of the remaining nuclei to decay, and so on. The
characteristic half-lives of radioactive nuclides vary over an enormous
range of values: from a small fraction of a second to billions of years.
Particle Detectors
Accelerators would be useless if there were no way to record and
measure the particles and gamma rays produced in nuclear interac-
tions. The detectors that have been invented for this purpose represent
a dazzling array of ingenious devices, many of which have pushed high
technology to new limits. Some are designed to detect only a specific
particle whose presence may constitute a signature of a particular kind
of event in the experiment in question. They may be designed to detect
this particle only within a certain limited range of angles of emission
with respect to the beam direction or over all possible angles of
. .
emission.
Other detectors are designed to detect as many kinds of particles as
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INTRODUCTION TO NUCLEAR PHYSICS 33
possible, simultaneously again either for limited angles or for all
angles. This kind of detector is necessarily complex, owing to the many
kinds of particles that must be observed and to the number of particles
actually produced. This latter number, called the multiplicity, is as
small as one or two for many kinds of events, but in the catastrophic
collisions of relativistic heavy ions, it may be several hundred. Yet
another consideration in the design of detectors is whether they are to
be used at a fixed-target accelerator or a collider; the requirements are
often very different.
Among the simplest detectors are those in which a visible track is left
in some medium by the passage of a particle. Examples of such visual
detectors are the streamer chamber (in which the medium is a gas), the
bubble chamber (liquid), and photographic emulsions (solid). Most
detectors, however, rely on indirect means for recording the particles,
whose properties must be inferred from the data. The operating
principles of the great majority of such detectors are based on the
interactions of charged particles with externally applied magnetic fields
or on the ionization phenomena resulting from their interactions with
the materials in the detectors themselves. The largest of these detector
systems may consist of thousands of individual modules and are used
in the study of very complex events. Sophisticated, dedicated comput-
ers are required to store and analyze the torrents of data from such
instruments.
At the largest accelerators, the efforts of many physicists, engineers,
and technicians may be required for many months to plan and execute
one major experiment, and months more of intensive effort may be
required to process and analyze the data and interpret their meaning.
This is the "big-science" approach to nuclear-physics research. A
highly noteworthy feature of nuclear physics, however, is that much
research of outstanding value is still done by individuals or small
groups working with more modest but nonetheless state-of-the-art
facilities in many universities and laboratories throughout the world. It
is the cumulative effort of all these scientists and their colleagues
working at the accelerators together with that of the nuclear theo-
rists that advances our knowledge of nuclear physics.
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I
Major Advances In
Nuclear Physics
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Representative terms from entire chapter:
strong force
