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OCR for page 67
Funciamental Forces in the
Nucleus
Since the early days of nuclear physics, researchers have had
considerable success in accounting for the measured properties of
nuclei by assuming that the only constituents of nuclei are protons and
neutrons. The effects of the other constituents, such as virtual mesons,
are present in the strong forces that act between nucleons. However,
the mesons and more fundamental constituents are usually hidden from
view in experimental measurements. The situation is analogous to the
role of the core electrons in the chemical bonding of atoms. The core
electrons certainly affect the chemical bonding forces but can for the
most part be ignored in describing the chemical bond. In the same way,
nucleons are viewed as composite objects made up of quarks, but only
a few kinds of experiments are decisive in revealing this underlying
structure.
Experiments measuring the electromagnetic properties of nuclei are
particularly informative. Many of the constituents are charged and thus
produce measurable electromagnetic currents. Another kind of exper-
iment is to measure violations of symmetry in nuclear transitions.
Nuclear states have symmetries that are easy to classify and measure,
and any violations can be attributed to fundamental particles that
mediate the nuclear forces. In the next two sections, some of the
studies that connect nuclear properties with the fundamental particles
and interactions are described in more detail.
67
OCR for page 68
68 NUCLEAR PHYSICS
NONNUCLEONIC CONSTITUENTS OF NUCLEI
The lightest hadron, the pion, has a prominent role in both nuclear
and elementary-particle physics. In nuclear physics, the strong inter-
action is mediated at large internucleon distances by virtual pions. The
charged virtual pions found in the nucleus make their presence known
by the magnetic effects of their currents. The pionic aspects of nuclear
states can be studied in many other ways as well, such as the scattering
of high-energy nucleons from nuclei. In a grazing collision, the
projectile nucleon hardly disturbs the target except for the fleeting
effect of the pionic cloud of the projectile, as well as the effects of the
other forces. Measurement of the scattering and absorption of pions by
nuclei has provided knowledge of the hadronic interactions, supporting
the idea that the symmetries embodied in the quark physics apply to
the pions in the nuclear medium.
The realization that the nucleus contains virtual mesons suggests
that it may contain other virtual particles as well. To complicate even
further this sharp departure from the simple proton-neutron model of
the nucleus, it is now widely accepted that nucleons and mesons are
themselves composite objects made up of quarks. The quarks that
constitute a nucleon interact strongly by exchanging gluons among
themselves. The quarks are strongly bound in the nucleon and have a
spectrum of energy states analogous to those of bound electrons in an
atom. From this viewpoint, a particular nucleon is only one possible
quark state; other excited states correspond to more massive, non-
nucleonic members of the baryon family, so that a nucleon changes to
a different kind of baryon when the quarks change state. In the five
decades since the discovery of the neutron, the picture of the nucleus
has changed from a simple cluster of proton and neutron "billiard
balls" to a seething mass of nucleons, other baryons, and mesons, all
consisting of quarks and gluons.
It is natural to ask whether the new, nonnucleonic features in the
present model of the nucleus have observable consequences. The
success of the proton-neutron model of the nucleus at low to moderate
energies implies that nonnucleonic contributions must be looked for in
higher energy ranges or in interactions different from the nucleon-
nucleon scattering used so widely in the past. In recent years,
experimenters have probed nonnucleonic effects in nuclei by going to
higher energies, by deliberately creating nonnucleonic constituents in
nuclei, and by studying directly the interactions of more exotic
particles.
OCR for page 69
FUNDAMENTAL FORCES IN THE NUCLEUS 69
Scientists have long known that an object is difficult to see unless the
wavelength of light is small compared with the object's dimensions;
this fundamental wave property limits the useful magnification of
optical microscopes, for example. It is one of the stranger aspects of
quantum mechanics (also called wave mechanics) that any particle of
atomic dimensions or smaller exhibits distinctly wavelike as well as
particlelike behavior and has a definite wavelength that is inversely
proportional to the particle's momentum. Exploring small structures in
the nucleus therefore requires a particle probe with high momentum
(and correspondingly high energy) to give a wavelength small enough
to enable inner structures to be distinguished clearly. High-energy
electrons are a good choice for this type of experiment, because they
interact with nuclei through the well-understood electromagnetic force
and because they seem to be pointlike particles having no dimensions
or inner structure themselves.
Another recent approach is to implant nonnucleonic baryon impuri-
ties into a nucleus and to study the subsequent response of the system.
Using advanced experimental techniques, one can replace a single
nucleon in a nucleus by a strange lambda or sigma hyperon (a baryon
that differs from nucleons in having a strange quark rather than up and
down quarks only) with hardly any disturbance of the nucleon orbits.
The result is a hypernucleus, in which a nucleon-nucleon interaction is
replaced by the somewhat different hyperon-nucleon interaction. Be-
cause the internal motions in the hypernucleus are closely related to
known motions in the original nucleus, properties of the nucleon-
hyperon interactions can be inferred from the measured hypernuclear
structure.
A new class of experiments still being developed uses proton-
antiproton collisions at moderate energies to bridge the gap between
nuclear physics and particle physics. On the one hand, the proton-
antiproton system represents a familiar interaction mediated by the
exchange of mesons, but from the viewpoint of the quark model it is a
system of three quarks and three antiquarks whose interactions are
mediated by the exchange of gluons. These experiments should pro-
vide challenging tests of both meson-exchange theories and quark
models.
The three types of experiments outlined here are discussed in further
detail below, to bring out the kinds of information that they can provide
and to mention some of the exciting surprises that have already been
found.
OCR for page 70
70 NUCLEAR PHYSICS
Probing Quark Structure with Leptons
Leptons-electrons, muons, tauons, and their associated neutri-
nos interact with nucleons through the electroweak force rather than
the strong force. Thus a lepton interacting with a nucleus does not
usually exert enough force on the nucleons to perturb them signifi-
cantly from their internal motions, even if the lepton passes directly
through the nuclear matter. Leptons are therefore excellent probes for
observing the nucleus essentially in its natural state. Moreover,
because the electromagnetic force is well understood, the measured
scattering of leptons from nuclei can be related to the properties of the
scatterers without much uncertainty.
Over the past three decades, the scattering of high-energy electrons
by nuclei has been the most successful method for providing detailed
information on the distribution of electric charge, and also of magne-
tism, in nuclei. This charge does not reside in the protons alone,
however. Many of the virtual mesons existing momentarily in a nucleus
are electrically charged, and even the neutrons and neutral mesons can
exert magnetic forces. The technique of high-energy electron scattering
is therefore a natural choice in looking for the effects of these me sonic
constituents.
Relatively high bombarding energies (in the GeV range) are needed
to make the electron's wavelength short enough to be able to 'isee" the
fine details inside a nucleus. The experimental results of scattering
high-energy electrons from the very light nucleus helium-3 cannot be
explained satisfactorily using theoretical models that take into account
only the ejects of the charge and magnetism of the two protons and
one neutron; one must also include the electromagnetic effects arising
from the exchange of a pion or rho meson between nucleons. The
meson-exchange model gives a strikingly better account of the data
(see Figure 3.1~. Such tantalizing results obtained over the past decade
have created intense scientific interest. The 4-GeV Continuous Elec-
tron Beam Accelerator Facility (CEBAF) proposed for construction by
the Southeastern Universities Research Association (SURA) would
allow much-improved investigation of meson-exchange contributions
in experiments of the kind described above.
Electrons, muons, and neutrinos have all been used to investigate
the quark structure of hadrons (baryons and mesons). The usual
method of studying new particles bombarding a target with sufficient
energy to create or release the desired particle~oes not apply here,
however. Because of the phenomenon of quark confinement, it is
OCR for page 71
10°
10-2
o
Cal
o
c' 10-4
._
-
a'
ct
10-6
10-8
FUNDAMENTAL FORCES IN THE NUCLEUS 71
1 1 1
\\
_ \\
o
0 MlT-Bates
· CEN Saclay
Nucleons only
\ \2 - Nucleons plus meson
\ ~ exchange
\ \
I /~- ``
1
b
20 30
Squared momentum transfer (fm~2)
FIGURE 3. l Data obtained by the high-energy elastic scattering of electrons from the
helium-3 nucleus reveal the superiority of the meson-exchange model in describing the
distribution of magnetism in nuclei, compared with the model that considers only the
nucleons. All three curves represent theoretical calculations; the two solid ones are
based on somewhat different assumptions. [From J. M. Cavedon et al., Physical Review
Letters 49, 986 (1982).]
apparently impossible to liberate quarks from their hadrons with the
means currently at hand.
To describe this unique situation, quark models are based on the
assumption that the constituent quarks of a hadron are confined in an
impenetrable bag or tied together by unbreakable strings, so that they
cannot escape. This aspect of quark behavior is based on an astonish-
ing characteristic of the strength of their color interaction: it is nearly
zero when they are very close together (a condition called asymptotic
freedom) and grows stronger as they move apart! This is just the
opposite of the gravitational, electromagnetic, and strong interactions
OCR for page 72
72 NUCLEAR PHYSICS
between hadrons, all of which grow weaker as the interacting particles
move apart. The size of a quark bag (i.e., the size of a hadron)
represents the limit beyond which the quarks are unable to move apart.
The standard quark model was developed in order to account
concisely for the variety of known hadrons. The model requires quarks
to have the spin quantum number 1/2 so that their spins can combine
properly to yield the observed spins of the hadrons. Electron-scattering
and muon-scattering experiments have yielded results consistent with
this requirement. These experiments make use of the magnetism that
spinning charged particles inherently possess. Comparison of the
fraction of projectiles scattered through small angles with the fraction
scattered through large angles allows the erect of electric forces to be
eliminated, leaving only the scattering due to magnetism. At the
energies where the theoretical model is most accurate, the magnetic
erects are consistent with the scattering from pointlike particles (the
quarks) having spin 1/2.
The standard quark model also assumes that quarks have fractional
electric charge (compared with the unit charge of the electron), to make
the net charge of a given combination of quarks equal to the observed
charge of the hadron that they constitute. The existence of a free
fractional electric charge has never been convincingly demonstrated
for any macroscopic object; this is explained on the basis of quark
confinement. However, electron scattering from hydrogen and deute-
rium at the Stanford Linear Accelerator Center and neutrino scattering
from a fluorinated hydrocarbon at CERN in Geneva have both pro-
duced results consistent with those predicted by a quark model based
on pointlike particles having charges of -1/3 and + 2/3 (in units of the
electron charge). Furthermore, the experimental results are in excel-
lent agreement with each other. Taken as a whole, the lepton-scattering
experiments provide strong support for the quark model.
Nuclei provide the only available system for hunting for complex
multiquark states, in which more than three quarks are confined in the
same bag. Finding multiquark states would be of great interest in
developing our understanding of quark confinement. The European
Muon Collaboration at CERN has recently obtained exciting results in
collisions between muon projectiles and deuterium or iron targets. The
experiments have been interpreted to show that the distribution of
quarks in iron nuclei is slightly, but significantly, different from the
distribution in isolated nucleons (see Figure 3.21. (The deuteron is so
loosely bound as to be essentially two free nucleons.)
Possible explanations based on the notion that quarks are less
strongly confined within the environment of a nucleus have been
OCR for page 73
FUNDAMENTAL FORCES IN THE NUCLEUS 73
1.2
._
0 4 ~
_ 1. 1
Q
._
.° 1.0
Cal
to
C'
~ 0.9
en
CO
o
C) '
O.8
~ ~ ~ ~ ~ ~ I
_ ~
- ~ ~
~ ~ _
~ I I I ~ I 1 1 ~ I I I _
o European Muon Collaboration, CERN
· Stanford
-~-~-- ~--~! T~
0 0.2 0.4
, , 1 , , , 1 1 1 1
0.6
Momentum fraction, x
1,,,
0.8 1.0
FIGURE 3.2 Inelastic scattering data from experiments with high-energy muons and
electrons can be interpreted as showing that the distributions of quarks in iron nuclei and
deuterium nuclei are substantially different, as discussed in the text. If they were not
different, the data points would be expected to fall along the dashed line. (New electron
data courtesy of R. G. Arnold, American University, Washington, D.C.)
advanced. The nucleons may expand as a result of their mutual
interactions, or the quarks may "percolate" from one nucleon to
another. An alternative explanation is that the additional quarks are
part of the virtual pions in the nucleus; the lepton scattering, in eject,
provides a "snapshot" of the nuclear constituents. The progress of
these experiments is being closely watched by nuclear physicists and
elementary-particle physicists, all of whom have much to gain from a
deeper understanding of the role of quarks in nuclear structure.
The Physics of Hypernuclei
The presence of surrounding nuclear matter can drastically modify
the properties of a particle. A free neutron, for example, has a half-life
of about 10 minutes for decaying into a proton, but the neutrons in
ordinary atomic nuclei have existed throughout the age of the universe.
In turn, the interactions of an embedded particle can modify the
properties of nuclear matter. The possibility of studying nonnucleonic
particles and nuclear matter in the same system has stimulated both
OCR for page 74
74 NUCLEAR PHYSICS
experimenters and theorists alike since the discovery of the first
hypernucleus about three decades ago.
For several reasons, much of the work in hypernuclear physics has
concentrated on the lambda-nucleus interaction. A lambda hyperon
implanted in a nucleus does not modify the nucleus drastically, because
a lambda is very much like a neutron: it has zero charge, about 20
percent greater mass, and only somewhat weaker interactions with
nucleons. Thus a lambda hypernucleus is different from the original
nucleus, but not so different as to preclude understanding. Another
useful property of this hyperon is that, compared with other unstable
particles, it has the enormously long lifetime (on the nuclear time scale)
of about 10-~° second. The lambda's lifetime is long enough for the
details of its interaction with nucleons to be studied precisely.
The general technique for making hypernuclei is to produce the
hyperon in situ by allowing a suitable projectile to react with a nucleon
in the target nucleus. The usual projectile is the negative kaon, which
is produced in accelerators at such institutions as CERN (Switzerland),
Brookhaven National Laboratory, and KKK (Japan). The kaon reacts
with a neutron to produce a lambda and a negative pion; the pion is
ejected from the system and provides a signal that a hypernucleus has
been formed.
For the cleanest experiments, the nonnucleonic baryon should be
created nearly at rest in the nucleus, to avoid depositing a burst of
energy that could boil nucleons out of their orbits or even out of the
nucleus entirely. With the appropriate choice of experimental param-
eters, this condition can be achieved in the kaon-induced reactions,
and the created baryon will be moving not much more rapidly than the
nucleons already present in the target nucleus. The baryon will be left
in essentially the same state as the nucleon it replaced; this is called a
substitutional state of the nucleus. Experimentally, substitutional
states can be studied by programming the measuring equipment to
accumulate data only when the detectors spot an exiting pion moving
nearly parallel to the projectile beam direction.
The kaon beams required for producing substitutional states are
difficult to produce with high quality. Kaons, which are unstable, are
generated as a secondary beam in a multi-GeV proton accelerator. The
kaons produced in the initial proton reaction with a selected target have
a wide spread in energy and angle and are mixed with a large
proportion of pions. Considerable sorting is necessary before the kaons
can be isolated for the production of substitutional states in
hypernuclei. The research is greatly hampered at present by the lack of
intense kaon beams having a narrow energy spread.
OCR for page 75
FUNDAMENTAL FORCES IN THE NUCLEUS 75
About two dozen distinct types of lambda hypernuclei have been
produced, mainly from among the light elements (up to oxygen).
Analysis of the binding energy data of the lambda in the nuclear ground
state (i.e., the amount of energy required to break the lambda free)
shows that the spin-independent part of the lambda-nucleon interaction
is only about two thirds as strong as the nucleon-nucleon interaction
and that the spin-dependent interaction is much weaker for the lambda.
If an excited state of a lambda hypernucleus is produced, it may
decay to a lower state by emitting a gamma ray. Measurement of the
gamma-ray energy therefore gives the energy spacing between the
states the same method commonly used to study the energy levels of
ordinary nuclei and thereby to test theories of nuclear structure.
Researchers at Brookhaven National Laboratory have been especially
active in this field, and they are currently performing experiments with
high-resolution gamma-ray detectors to measure the energies more
precisely.
The sigma hypernucleus has also been studied to a small extent. The
sigma is a hyperon that decays to the lambda a process that is
expected to be very fast. Workers at CERN and at Brookhaven were
therefore surprised recently to discover quite long-lived substitutional
states in sigma hypernuclei. The data are sparse, and it is not yet
known whether the slow decay of a sigma to a lambda in hypernuclei
represents a special inhibiting effect limited to light nuclei or a general
property of nuclear matter.
Quantum Chromodynamics at Low Energies
It is now widely believed that quantum chromodynamics will be-
come established as the correct theory of the strong interaction. For
the region of asymptotic freedom, where the quarks are close together
and interact very weakly, QCD calculations produce results in good
agreement with experiment. At larger distances, however, where the
confined quarks interact strongly, the calculations become so compli-
cated that reliable results are difficult to obtain, although considerable
progress is being made through the use of lattice gauge theory (see page
142 for an explanation of this term). Because the region of asymptotic
freedom can be probed in the laboratory only in experiments at very
high energies, theory and high energy have gone hand in hand in the
development of QCD. At lower energies, however, the experiments
performed so far do not seem to bear on QCD in a way that would
facilitate extending the theory to the domain of strong quark interac
OCR for page 76
76 NUCLEAR PHYSICS
Proton
Antiproton
Virtual
muon
Lambda
+
~ Antilambda
FIGURE 3.3 Annihilation of a u quark and a u antiquary in a proton-antiproton
collision. The annihilation produces a high-energy virtual gluon, which disappears with
the creation of an s quark and an s antiquary in the respective nuclei, which have thus
become a lambda hyperon and an antilambda hyperon.
lions. Physicists have therefore tried to conceive lower-energy exper-
iments directly relevant to QCD.
Prime candidates for studying quark properties at lower energies
(less than 1 GeV) are the proton-antiproton interaction or the proton-
kaon interaction. According to the quark model, a proton has the quark
structure uad (two up quarks and one down quark). An antiproton has
the analogous structure uad, made with antiquarks instead of quarks.
During a proton-antiproton collision, one u quark may annihilate its
antiquark u to form, for example, the strange quark s and its antiquark
s (see Figure 3.31. After the collision, the system separates into two
three-quark hyperons: uds (a lambda) and uds (an antilambda). The
precise study of such processes over a range of energies is expected to
provide important data for guiding the development of QCD.
Studies of proton-antiproton interactions are already under way at
CERN's new Low-Energy Antiproton Ring (LEAR), an accelerator
facility that is a nearly ideal source of low-energy antiprotons. It
provides a copious, essentially pure beam of antiprotons over a wide
energy range, with a very small energy spread. Although it could profit
from the additional ability to produce polarized (spin-aligned)
antiprotons for the investigation of spin-dependent forces, the LEAR
facility offers opportunities for exciting research that make it singularly
attractive to many user groups from the United States.
OCR for page 77
FUNDAMENTAL FORCES IN THE NUCLEUS 77
THE NUCLEUS AS A LABORATORY FOR FUNDAMENTAL
SYMMETRIES
Much of our physical understanding of nature is embodied in
conservation laws and in the symmetry principles from which they
stem. Conservation laws make powerful statements of great generality
that apply even if the details of a system are unknown. The classical
laws of electric-charge conservation, energy conservation, and mo-
mentum conservation are routinely applied to the analysis of nuclear
reactions because of their complete reliability. From the opposite
viewpoint, the fact that conservation laws inferred from everyday
physics can be applied to nuclear systems represents a great extension
of these laws to new realms of size and energy. The study of nuclear
systems has also revealed new symmetries and conservation laws not
apparent in the behavior of macroscopic objects. As theory pushes on
to examine the nature of the fundamental forces at energies far beyond
the reach of the largest manmade accelerators, searches for symmetry
violations in the precisely calibrated environment of the nucleus may
be the only viable approach for seeing the subtle residual effects
predicted to occur at energies that are accessible.
There are several reasons why the nucleus is an excellent laboratory
for the study of fundamental symmetries. The nucleus readily displays
the effects of both the strong and electroweak forces, and the dimen-
sions of the nucleus place it only one or two steps away from what we
believe is the ultimate structure of matter. Furthermore, the wide range
of proton and neutron numbers available in nuclei helps to illuminate
differences and distinguish the general from the specific. Strange
particles such as the lambda hyperon can be implanted to form
hypernuclei, thereby extending the variety of nuclei even further.
Finally, nuclei have definite quantum states, so that the systems
studied have well-defined properties. An added advantage is the large
amplification of small effects that can occur when two nuclear states
with specific properties happen to have nearly the same energy; as
physics has advanced to more and more comprehensive theories,
experimental sensitivity to small effects has become increasingly
important.
The weak force has been an extraordinarily fruitful source of
information about the underlying symmetries of nature. It is exposed
for convenient study in the more than 2000 known nuclei that undergo
beta decay a manifestation of this force. The attention of physicists
was refocused on the question of symmetry laws by a famous experi-
ment carried out in 1956 at the National Bureau of Standards. The beta
OCR for page 78
78 NUCLEAR PHYSICS
decay of parallel-spin (magnetically oriented) cobalt-60 nuclei was
shown not to give the same result as the corresponding mirror-image
experiment- a most astounding result at the time. In terms of symme-
try, this result is described by saying that the weak force does not
behave symmetrically under reflection; in terms of conservation laws,
it is described by saying that weak-force interactions do not conserve
parity. The strong, electromagnetic, and gravitational forces do not
appear to violate parity; why the weak force does is not understood.
In familiar examples of the phenomena of classical physics-collid-
ing billiard balls, for example the physical laws that govern the
interactions of objects appear always to be the same, regardless of
whether one considers time to be running forward or backward. This
independence of the direction of time's arrow is a symmetry principle
called time-reversal invariance, which was long thought to be abso-
lutely valid in all physical systems. In 1964, however, a violation of
time-reversal invariance was discovered in a decay process involving
the weak force. The particle in question was the neutral K meson
(kaon), which can undergo beta decay by two modes, to give in part
either positive electrons (positrons) or negative electrons. If time-
reversal invariance held, the two rates of decay would be exactly
equal; instead, their ratio is found to be 1.0067.
Although the effect is small and occurs in an obscure submicroscopic
system, it may have important cosmological implications: it may be
related to the preponderance of matter over antimatter in the known
universe or to the preponderance of radiation over matter. Along with
other cases of symmetry-principle violations, time-reversal-invariance
violation has forged unexpected links between nuclear physics and
cosmology, connecting the unimaginably small with the unimaginably
large.
Finding other examples of time-reversal-invariance violation in
processes simpler than that of kaon decay would help greatly in
understanding the origin of this surprising phenomenon. Theorists have
therefore tried to predict observable effects of such a violation in
nucleons and nuclei for instance, a nonzero electric dipole moment
(slight separation of internal positive and negative charges) for the
neutron. Searches for such effects are being conducted in phenome-
nally precise studies that are a tribute to the ingenuity of experimen-
talists.
Because symmetry principles can apply even when the detailed
interactions in a system are unknown, modern theory building often
starts by postulating certain symmetries suggested either by experi-
mental data or by beauty of design in the theory. Some symmetries can
OCR for page 79
FUNDAMENTAL FORCES IN THE NUCLEUS 79
be readily visualized, such as the symmetries of space and time that
underly the conservation laws for momentum, angular momentum,
parity, and energy. But symmetries can also apply to abstract quanti-
ties such as the isospin concept that merges individual proton and
neutron identities into the more general nucleon description.
Present-day theorists have set themselves the ambitious task of
unifying the "fundamental'' forces of nature into one comprehensive
description from which everything else can be rigorously derived.
Their achievements to date have been impressive. The theory showing
that electromagnetism and the weak force both spring from a com-
mon electroweak force has been a triumph of successful predic-
tions, including the existence of the charm quark and the recently
discovered W+, W-, and Z° bosons. These last three particles are
crucial because their exchange (as virtual particles) is at the origin of
the weak force.
Despite these triumphs, the new electroweak theory-which, to-
gether with QCD, is now referred to as the Standard Model-is
incomplete. It does not explain (but does allow) the violations of parity
and time-reversal invariance, it does not unify the strong force or the
gravitational force with the electroweak force, and it does not predict,
a priori, the observed relative strengths of the electromagnetic and
weak forces. Theorists are still striving for a Grand Unified Theory that
would unite all the forces and that would include all the symmetry laws
and their violations. The following sections give some examples of how
nuclear physics is providing guideposts along the dimly outlined road
to grand unification.
Right-Handed Bosons in Beta Decay
Parity is found to be violated to the maximum possible extent by
nuclear beta decay; i.e., the mirror-image decays are never observed.
Suppose that the neutrino emitted in a beta decay is represented by a
partially closed left hand, with the thumb in the direction of the
neutrino's motion. The curl of the fingers represents the direction of
the classical rotation analogous to the neutrino's spin. If this model is
viewed in a mirror parallel to the thumb, the direction of motion is
unchanged, but the mirror-image spin is in the opposite direction.
Mirror reflection changes a left hand to a right hand, a complete
reversal of parity. The hypothesis that neutrinos are strictly left-
handed therefore successfully accounts for parity violation.
The Standard Model assumes that the W+ and W- bosons are
left-handed (strictly speaking, it is their interactions that are left
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80 NUCLEAR PHYSICS
handed) and that the Z° boson is partly left-handed, which leads
automatically to the left-handedness of neutrinos. Other theories
consider the more symmetric possibility that there are right-handed as
well as left-handed W and Z bosons. If the right-handed bosons were
significantly more massive than the left-handed ones, their force would
have a shorter range, and left-handed neutrinos would dominate in
present experiments. The situation is somewhat like that of the
electroweak force, where the constituent electromagnetic and weak
forces are fundamentally the same yet manifest themselves to us with
very different strengths.
Several different kinds of experiments have shown that if right-
handed W and Z bosons do exist, they must be extremely massive.
Some experiments have searched for small right-handed effects in
muon decay or in the beta decay of neon-19 nuclei; other experiments
infer the properties of neutrinos from the measured spin and motion of
the much more easily observed decay electrons. It will be some time
before accelerators large enough to permit a direct search for the
massive right-handed bosons themselves can be constructed.
The Mass of the Neutrino
If an observer could overtake and pass a left-handed neutrino, the
neutrino's direction of motion (but not its spin direction) would appear
to reverse, the way cars seem to fall behind when we pass them. The
observer's motion alone could thus change a left-handed neutrino into
a right-handed one, so that left-handedness would no longer be an
intrinsic oronertv of the neutrino. The way out of this paradox is to
r - - ~ - - - ~
assume that neutrinos move with the speed of light, too fast for any
observer to overtake. The theory of relativity shows that particles
moving with the speed of light must have zero mass. The Standard
Model admits only massless neutrinos, but in most proposed Grand
Unified Theories, electron neutrinos, for example, can have a very
small mass, typically between 10-8 and 1 eV. (By comparison, the
mass of the electron is 511,000 eV.)
Whether a neutrino has zero or nonzero mass bears directly on
neutrino handedness and parity, and on the structure of Grand Unified
Theories. The neutrino mass also has important implications for
cosmology. The universe still contains so many neutrinos formed
during the big bang that if the neutrinos have even a very small mass,
their gravitational force could eventually brake and reverse the
universe's current outward expansion. Because the density of ob-
served stars and galaxies appears to be too low to accomplish this, the
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FUNDAMENTAL FORCES IN THE NUCLEUS 81
neutrinos could represent the additional "missing mass" needed to
hold the universe together. Indeed, arguments from cosmology have
set a rough upper limit of 30 eV on the electron neutrino mass, based
on the observation that the universe is still expanding at present.
In 1980, researchers in the Soviet Union reported that the electron
neutrino from nuclear beta decay probably has a mass between 15 and
50 eV, just within the interesting range for cosmology. Their experi-
mental method was to study the beta decay of hydrogen-3. The decay
electron and the neutrino (actually an antineutrino in this case) are
emitted simultaneously and share the available decay energy between
them, so that in different decays, the electron may receive anywhere
from nearly zero energy to the maximum. The probability of the
electron's receiving a particular energy within this range is a charac-
teristic of the decay and is called the shape of the electron spectrum.
The object of the Soviet experiment was to determine the shape (by
measuring the energies of the decay electrons), because it depends on
the neutrino mass in a known way.
The experiment is far from easy, and certain systematic effects can
distort the shape in a way that mimics the effect due to neutrino mass.
Conclusions from this experiment are not universally accepted, and
refined versions are now being carried out in the United States and
other countries.
Neutrino Oscillations
A mass hanging from a spring is a favorite demonstration in physics
lectures. The system has two modes of oscillation: the mass can vibrate
up and down, or the whole system can swing like a pendulum. With
proper design, the system can pass alternately from one mode to the
other, with swinging changing gradually to springing, and back again.
A quantum-mechanical system may exhibit a similar alternation of
mode, as a kind of swelling and ebbing "beat" of the quantum-
mechanical wave oscillations. In some cases, the beats can even
manifest themselves as alternations in the identity of a particle.
There are three apparently distinct neutrinos emitted during beta
decays: a different neutrino is associated with electrons, muons
(essentially, heavy electrons), and tauons (very heavy electrons). The
Standard Model strictly maintains the separate identities of electron
neutrinos, muon neutrinos, and tauon neutrinos, in accord with the
currently accepted lepton-family-number conservation laws: the total
number of electrons and electron neutrinos in the universe minus the
total number of antielectrons (positrons) and electron antineutrinos is
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82 NUCLEAR PHYSICS
constant. Similar laws hold separately for the muon family and for the
tauon family.
However, Grand Unified Theories generally allow a neutrino of one
kind to transform gradually into another kind. An electron neutrino
from a nuclear decay, for example, could gradually become a muon
neutrino or a tauon neutrino as it sped along its way. The rate of change
as the quantum-mechanical beats ebb and swell depends on the mass
differences between the various neutrinos; equal-mass or zero-mass
neutrinos retain their identities. If neutrino oscillations were observed
experimentally, it would imply that at least one kind of neutrino has
nonzero mass. Also, an observed change in identity would be the first
known violation of the lepton-family-number conservation laws. The
beta decay of fission products in a nuclear reactor produces a copious
flux of antineutrinos, and experimenters at the Savannah River,
Grenoble (France), and Gosgen (Switzerland) reactors have set up
detectors to see if the number of electron antineutrinos diminishes
along their flight path. The most sensitive experiments to date have
produced no evidence of the disappearance of electron antineutrinos.
Similarly, accelerator experiments at Fermilab, Brookhaven, and
CERN have not revealed any oscillation of muon neutrinos to other
kinds, or any oscillation of electron neutrinos or muon neutrinos to
tauon neutrinos.
The sensitivity of the reactor experiments to small neutrino-mass
differences increases as the flight path is lengthened; small mass
differences make the oscillations very slow, so that neutrinos could
travel great distances before undergoing observable transformations.
The flight paths in the reactor experiments so far have extended up to
46 m, which sets an upper limit on the possible neutrino oscillations.
Using neutrinos produced in the Sun would give a flight path of 1.5 x
108 km, increasing the sensitivity dramatically. As discussed in Chap-
ter 5, the counting rate in present solar-neutrino detectors is roughly
one fourth the theoretically expected value. One proposed solution to
this vexing disparity is that oscillation decreases the number of
solar-electron neutrinos arriving at the Earth. However, present neu-
trino detectors are sensitive only to the small fraction of the Sun's
neutrinos that result from a rather minor nuclear-energy-generating
process, so the theoretical uncertainties in the expected number may
be large.
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FUNDAMENTAL FORCES IN THE NUCLEUS 83
Double Beta Decay
The energy for the decay of a radioactive nucleus comes from the
mass difference between the initial nucleus and the decay products.
Accurate mass data are available from many different experimental
methods, so the energy available for decay can be predicted quite well.
Study of these mass data shows that certain nuclides for example,
selenium-82 and tellurium-13~are stable against ordinary beta decay
but are allowed by energy considerations to undergo double beta
decay. In this process, the decaying nucleus simultaneously emits two
electrons instead of one, thereby raising the proton number of the
nucleus by 2; double beta decay would therefore change selenium to
krypton, and tellurium to xenon.
In ordinary beta decay, the decaying nucleus emits an electron and
an antineutrino, a process that conserves lepton family number, as
discussed earlier. The analogous process for double beta decay would
be the emission of two electrons and two antineutrinos, again conserv-
ing lepton family number. The more particles that are to be emitted in
a given decay process, the smaller the probability that the decay will
occur. Because four particles are emitted in this two-neutrino mode of
double beta decay, the half-lives are expected to be extremely long,
typically 102° to 1025 years.
On the other hand, double beta decay might possibly proceed by
emitting only the two electrons and no antineutrinos. This neutrinoless
mode of double beta decay would be expected to have a shorter
half-life than the two-neutrino mode, because only two particles need
be emitted, instead of four. However, the neutrinoless mode is
opposed by the conservation law for lepton number it involves the
creation of two leptons (the two electrons) uncompensated by
antileptons (the two antineutrinos). If neutrinoless double beta decay
were observed, it would imply a violation of lepton-number conserva-
tion.
Certain conditions in addition to the violation of lepton-number
conservation must also be satisfied to allow neutrinoless double beta
decay to occur. The neutrinoless mode is described as a two-step
process: the decaying nucleus first emits one electron and a virtual
antineutrino, a reaction analogous to ordinary beta decay. In the
second step, the daughter nucleus instantaneously absorbs this
antineutrino and emits the second electron. The second step is analo-
gous to a known process, except that nuclei absorb neutrinos, rather
than antineutrinos, to emit electrons. For neutrinoless double beta
decay to occur, therefore, the antineutrino and the neutrino must in
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84 NUCLEAR PHYSICS
·~
~ Electron
- ~ tracks
1 MeV
FIGURE 3.4 Computer simulation of the two-neutrino double beta decay of a sele-
nium-82 nucleus in a particle detector called a time projection chamber. In this
hypothetical event, the strong magnetic field in the detector causes the two emitted
electrons to spiral away from the nucleus along separate paths. The computer-generated
helical tracks of the electrons have been projected onto a plane in this cross-sectional
view, producing a figure-8 pattern. (The energy scale gives the track diameter of a 1-MeV
electron emitted in the plane of the figure.) Finding such a pattern in an actual experiment
might signal the occurrence of this extremely rare event. (Courtesy of M. K. Moe,
University of California, Irvine.)
fact be one and the same particle. Furthermore, the neutrinoless mode
requires the virtual neutrino to be partially right-handed.
Although the necessary conditions described above stack the cards
heavily against the neutrinoless mode, a single observed instance
would shatter many currently held ideas. Meanwhile, considerable
effort has been put into the search for two-neutrino double beta decay,
despite the experimental difficulties imposed by the very long half-lives
and the consequent low rates of decay. Such difficulties make the
computer simulation of possible events a valuable design tool (see
Figure 3.4~.
The search for the presumably even rarer neutrinoless double beta
decay is made extremely difficult by cosmic rays, which can create
background ejects in the experimental apparatus that mask the true
signal. For increased sensitivity, therefore, the experiments must be
moved deep into the Earth, under a thick shield of rock. The Soviet
Union has recently completed a large underground laboratory at
Baksan for physicists who require very high sensitivity in such
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FUNDAMENTAL FORCES IN THE NUCLEUS 85
experiments as the search for neutrinoless double beta decay, the
search for decay of the proton, and the measurement of the solar-
neutrino flux. A similar dedicated facility, the National Underground
Science Facility, has been proposed in the United States. Several
experiments are already under way in deep mines and mountain
tunnels in the United States and Europe.
Parity Violation in Nuclei
According to the Standard Model, nucleons are made of two
different combinations of three up and down quarks. In this picture, all
the properties of nuclei spring ultimately from quark interactions, but
only recently have the first attempts been made to relate nuclear
properties to quark behavior. The strong quark interaction (and the
resulting strong force) is believed to conserve parity strictly, but
quarks also take part in the parity-nonconserving weak force, in which
charged W+ or W- bosons or neutral Z° bosons are exchanged. The
quark model predicts that the exchange of charged W+ or W- bosons
will add to the nucleon-nucleon force a small weak-force component
that does not conserve parity and that chiefly causes the isospin of a
pair of interacting nucleons either to remain the same or to change by
two units. The neutral Z° exchange gives rise to a weak-force compo-
nent that also does not conserve parity and that changes the isospin of
a pair of nucleons by zero, one, or two units. A great many states of
different parities and isospins are available among the known nuclei,
and careful selection of the test nuclei allows the two different
weak-force components (from W and Z exchange) to be distinguished
experimentally.
The strong force in nuclei conserves parity, so that each nuclear
state can be assigned a definite parity value (even or odd). However,
the parity-nonconserving weak force mixes the parities of the states, so
that they are actually neither purely even nor purely odd. The nuclei
fluorine-19 and neon-21 both exhibit the favorable circumstance of
having two closely spaced energy levels of the same angular momen-
tum but opposite parity; this close proximity increases the usually tiny
effects of the weak force in mixing the parities of these states.
Furthermore, the isospins of the states in question are such that both
the charged and neutral boson-exchange components are able to
influence the mixing in fluorine-l9 and in neon-21.
Experimentally, the parity-nonconserving mixing is observed in
fluorine-19, where the charged and neutral components add. However,
it is not seen in neon-21, where the charged and neutral components
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86 NUCLEAR PHYSICS
tend to cancel. Higher sensitivity should soon allow the pure neutral-
component contribution in a nearby nucleus, Huorine-18, to be mea-
sured. Comparing the experimental results with theory allows two
important conclusions to be drawn. First, the Z° boson exchange
between nucleons is definitely present (the Z° boson has recently been
detected directly as a free particle). Second, the dynamic masses of the
up and down quarks in a nucleon are very close to the values originally
predicted.
Representative terms from entire chapter:
nuclear physics
