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OCR for page 107
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Nuclear Astrophysics
When astrophysicists first realized, in the 1920s, that processes
producing enormous amounts of heat and outward radiation pressure
must be occurring deep inside the Sun to prevent it from collapsing
under its own gravitational field, the study of nuclear physics had only
barely begun. The neutron itself was not discovered until 1932, and it
was another 6 years before a plausible explanation for the Sun's energy
was advanced by nuclear physicists: in a type of reaction called nuclear
fusion, four hydrogen nuclei combine to form one helium nucleus, with
the release (on a stellar scale) of vast amounts of energy. Since that
time, a fruitful symbiosis has arisen between nuclear physics and
astrophysics, with progress in each field spurring progress in the other.
Studies of nuclear reactions in laboratories on Earth tell us a great deal
about the birth, evolution, and death of stars, while astrophysical
measurements tell us much about nuclear processes that are difficult or
impossible to produce on Earth.
Nuclear astrophysics is concerned with the mechanisms of stellar
nuclear reactions that generate energy and that lead to the formation of
the chemical elements in the process of nucleosynthesis. Some of the
most active areas of nuclear astrophysics today are concerned with the
mechanisms of supernova explosions, where nucleosynthesis of the
heavy elements occurs, and the formation of neutron stars. The latter
represent nuclear matter under conditions of high temperature and
density, from which a unique insight can be gained on the fundamen
107
OCR for page 108
108 NUCLEAR PHYSICS
tally important nuclear-matter equation of state. Perhaps most inter-
esting of all, however, is the neutron stars' status as a kind of ultimate
nuclear laboratory: they are the only known "nuclei" in which the
effects of all three of the fundamental forces-the strong force, the
electroweak force, and gravitation are intimately interwoven.
In this chapter we look at a few of the most active current topics in
nuclear astrophysics research, which epitomize the ways in which
progress in basic nuclear physics benefits the development of other
sciences and, ultimately, of our technological society as a whole.
NUCLEI UNDER EXTREME ASTROPHYSICAL CONDITIONS
The most extreme condition of matter imaginable existed for only an
instant at the beginning of our universe, but a plausible account of this
awesome event and its aftermath has been reconstructed from data
available today. Among the most important of these data are the known
abundances of the chemical elements in the stars and nebulas and in
the Earth itself because these values impose certain constraints on
the theoretical mechanisms by which nucleosynthesis could have
occurred. These constraints are based not only on the nature of nuclear
reactions as we know them from terrestrial studies but also on the
conceivable dynamical processes by which stars can undergo a spec-
tacular death by supernova explosion.
Nucleosynthesis of Light Elements
In the first seconds after the big bang, there were no nuclei just
elementary particles and hadrons. The latter were primarily nucleons,
and it was only after about 3 minutes when the temperature of the
nascent universe had cooled to about 109 K that these particles could
begin to coalesce to form deuterons (2H) and nuclei of helium-3 and
helium-4 (3He and 4He); it now seems possible that nuclei of the isotope
lithium-7 may also have formed at that time. These four nuclides are
thus the big bang nuclides. It took at least half a million years more for
the universe to cool sufficiently for these nuclei to capture electrons
and become atoms, and a few billion years for stars to form. Only when
the stare nuclear fires began to burn did nuclei of the remaining
elements begin to form. In the universe today, hydrogen and helium
constitute roughly 93 and 7 percent, respectively, of the nuclei, while
all the heavier elements make up only about 0.1 percent.
Although most of the lighter elements are believed to be produced in
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NUCLEAR ASTROPHYSICS 109
the stellar interiors, a few are too fragile to survive the intense heat and
must be formed at cooler sites. These elements are the ones that lie
between helium and carbon in the periodic table: lithium, beryllium,
and boron. The nuclides in question are 6Li, 9Be, LOB, and SIB, and
their observed abundances in the universe can now be accounted for
fairly well in terms of a model based on the bombardment of heavier
nuclei in the interstellar medium by cosmic rays. In these spallation
reactions, a very energetic projectile breaks the target nucleus up into
several fragments. Measurements of nuclear spallation reactions at
cosmic-ray energies have recently become sufficiently extensive to
allow a meaningful test of the astrophysical model, and it has been
found that these cosmic-ray nuclides are produced in roughly their
observed relative cosmological abundances.
The four big bang nuclides mentioned above are the only four that
can be attributed to that stage of the evolution of the universe.
Remarkably, the modern theory of nucleosynthesis can account for the
observed abundances of these four nuclides in terms of a single
assumed value of the baryon density of the early universe. In terms of
the expanding universe, this primordial density would give rise to a
present density between 0.6 x 10-3~ and 11 x 10-3~ gram per cubic
centimeter (g/cm3), a range that neatly brackets the observed density of
visible matter, 3 x 10-3i g/cm3 (see Figure 5.11. For the universe to be
closed i.e., for its own gravitational self-attraction to be sufficient to
stop the expansion eventually this density would have to be about 10
times greater. Whether the universe is closed is not known, nor is it
known where the missing mass, if any, is to be found.
A possible source of the missing mass may be neutrinos if they turn
out to have some mass after all. Neutrinos exist in enormous numbers
throughout the universe, but a limit can be set on the number of kinds
of neutrinos (the three now known correspond to electrons, muons,
and tauons) from the observed abundance of 4He produced in the early
universe. If there were still another (as yet undetected) kind of
neutrino-and if it were present in great numbers it would have added
substantially to the overall energy density of the universe during the
first 3 minutes, and the universe would therefore have expanded more
rapidly. Among other things, this more rapid expansion would have
increased the neutron-to-proton ratio, and because most of the neu-
trons were eventually incorporated into helium nuclei, the result would
have been a greater abundance of 4He than is actually observed.
It could be, therefore, that we have already discovered all the kinds
of neutrinos that exist in the universe, although a fourth kind cannot be
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110 NUCLEAR PHYSICS
' ~' 1
Closed
universe
Open
universe
Astronomy
2H
3He
7Li
. 1 1 , 1 ; 1 ,
1
10-32 10-31 10-3° 10-29 10-28
Baryon density (9/cm3)
FIGURE 5.1 From the observed abundances of the four big bang nuclides, it is possible
to infer the present baryon density of the universe. The shaded bar for each nuclide
represents the range of values calculated from its abundance, and the solid vertical line
represents the best fit to these data. The inferred baryon density of about 5 x 10-3' g/cm3
is about 10 times less than that which would be required for the universe to be
gravitationally closed (dashed vertical line). Thus, this evidence is consistent with an
open universe. (After S. M. Austin, in Progress in Particle and Nuclear Physics, Vol. 7,
D. Wilkinson, ea., Pergamon Press, Oxford, 1981.)
entirely ruled out. Uncertainties in the observed abundances of the
nuclides, as well as certain assumptions in the big bang model that
have not yet been validated, make various details of the picture
unclear. What is clear is that the nucleosynthesis of the light elements
is closely connected to fundamental questions of particle physics and
cosmology.
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NUCLEAR ASTROPHYSICS 111
Supernova Explosions and Neutron-Star Formation
The study of supernovas and neutron stars has opened up a new area
of nuclear astrophysics and has motivated theoretical and experimental
research leading to a deeper understanding of the rich properties of
nuclei and nuclear matter, especially at high densities. In ordinary
stars, such as our Sun, the inward force of gravity is balanced by the
outward hydrodynamic pressure of the hot gases and, to a lesser
extent, by the radiation pressure of photons. When their nuclear fuel is
exhausted, however, some stars undergo gravitational collapse and
then explode as a supernova (see Figure 5.21; a small, extremely dense
neutron star may be left as a remnant of this stupendous event. The
physics of neutron-star formation and the establishment of a new
equilibrium against gravity are intimately tied to the behavior of
nuclear matter under extreme conditions. In particular, it now appears
that neutrinos play an important role in the mechanism of supernova
collapse.
The hydrogen fusion reaction in stars produces two positrons and
two neutrinos. Most nuclear matter is almost perfectly transparent to
neutrinos, so most of them depart the star, headed for deep space.
(Experiments to detect solar neutrinos passing through the Earth are
described later in this chapter.) The escaping neutrinos cool the star by
carrying away some of its fusion energy, but this energy loss is slight
during the middle period of a star's life.
As the star reaches old age and the hydrogen in its interior is
consumed, its central temperature will rise, causing the outer layers to
expand to form a red giant as our Sun is most likely to do. In later
stages of its evolution, the star's interior may collapse, with the release
of huge amounts of gravitational energy. As the collapse progresses,
the heated nuclei are reformed into much heavier, more neutron-rich
species than are normally found in stars. Changing a proton into a
neutron, however, requires the capture of an electron, a process that
releases a neutrino. (The competing reverse reaction of neutrino
capture raises new problems in the study of weak-interaction pro-
cesses.) The increased neutrino flux produced by the collapsing star
increases the rate of energy loss by the star; this, in turn, decreases its
internal pressure and hastens the collapse. At a later stage of the
collapse, however, neutrinos will become trapped inside the star
because of the greatly increased mass density of the star, which
decreases its transparency to neutrinos; this trapping inhibits further
electron capture and halts the synthesis of heavy elements.
As the nuclei become crushed together by the colossal gravitational
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1 12 NUCLEAR PHYSICS
FIGURE 5.2 The Crab nebula, about 5 light-years in diameter with a neutron star at its
center, is believed to be the remnant of a supernova explosion that was observed and
recorded by Chinese and Japanese astronomers and also, perhaps, by North American
Indians July 4, 1054. It remained visible.to the naked eye, in the constellation
Taurus, for almost two years. Why there is little evidence of its having been chronicled
by European or Arabic astronomers is a matter of conjecture. (Courtesy of the Lick
Observatory, University of California.)
field, the supernova collapse is eventually halted by the repulsive part
of the strong force at very short internucleon distances. One effect of
this compression to about twice normal nuclear density is an intense,
rebounding pressure wave that forms a gigantic, outward-moving
shock wave. The shock wave is believed to be principally responsible
for the supernova explosion that blasts the outer mantle and envelope
of the star into space. Understanding the propagation of the shock
OCR for page 113
NUCLEAR ASTROPHYSICS 113
wave is complicated, however, by the dissociation of nuclei as the
shock passes through them a process that dissipates some of its
energy.
Many other aspects of this model are not yet clear. The ability of the
shock wave to blast away the outer layers, for example, depends
critically on the temperature, density, and composition of the original
star; these factors are, in turn, highly sensitive to the rates of electron
capture by the various nuclei present and to the rate of cooling by the
accompanying neutrino emission. Refining the model is hampered by
inadequate knowledge of the properties of nuclei and of the equation of
state of hot, dense nuclear matter. Predicting the amount of energy
transmitted to the outer layers, for instance, requires an accurate
equation of state. A key parameter, the compressibility of nuclear
matter, is letdown for ordinary nuclear density (2.5 x 10'4 g/cm3) from
observations of the giant monopole resonance, as discussed in Chapter
2. Relativistic heavy-ion collisions can reach the regime of densities (up
to BOOS g/cm3) existing in supernova collapse, but such experiments
have only recently begun (see Chapter 41.
The supernova shock wave forms outside a central core of about one
solar mass, so the explosion of a very massive star leaves behind only
a small fraction of its mass as a remnant. If the mass of the remnant is
less than about 2.5 solar masses, the remnant becomes a small, dense,
rapidly rotating neutron star, of the order of 10 km in diameter; more
massive remnants become black holes and disappear from direct view.
A neutron star can make its presence known to us by electromag-
netic radiation as a pulsar or compact x-ray source. Neutron stars can
also be detected indirectly, if they perturb the motions of a visible star
with which they are associated in a binary system. To date, well over
300 neutron stars have been identified in our neighborhood of the
galaxy, and some black holes may also have been detected indirectly.
Weak-Interaction Processes in Supernovas
As far as we know, the conditions required for the nucleosynthesis
of heavy elements occur only in supernovas. All the gold and uranium
found on the Earth today, for example, may have come from a single
supernova whose cast-off outer layers were swept up into the interstel-
lar gas cloud that eventually evolved into our solar system. Although
the nuclear reactions in supernovas are dominated, as in all other forms
of nuclear matter, by the strong force, it is also crucial to a description
of supernova dynamics to understand the key weak-interaction pro
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114 NUCLEAR PHYSICS
cesses that occur there. One such process is electron capture, or
inverse beta decay.
Electron-capture rates by nuclei under conditions of high tempera-
ture and density appear to be dominated by excitation of the Gamow-
Teller giant resonance (see Chapter 2) in the product nucleus; here the
values of both the spin and the isospin of the nucleus are simulta-
neously flipped as a proton is transformed to a neutron upon capturing
the electron. Calculated rates based on this picture provide not only
information necessary for constructing supernova models, but also a
self-consistent analysis of the electron-capture process through the
region of moderate atomic mass numbers from 21 to 60. To supplement
this work experimentally will require high-energy neutron beams
having a narrow spread in energy. The purpose of such beams would be
to excite and study the Gamow-Teller resonance in those nuclei that
result from electron capture in the corresponding stellar reactions.
The extremely neutron-rich nuclei produced in supernovas can be far
from the relatively narrow valley of nuclear stability described in
Chapter 4; indeed, the last neutron may be bound so weakly that it is
almost ready to "drip" from the nucleus. Recent theoretical work on
beta decay of nuclei far from stability has emphasized the role of the
spacing of highly excited energy levels in the product nucleus. The
half-life for beta decay is quite sensitive to this quantity, and the
half-lives are a crucial ingredient for calculating the production of
heavy elements in supernovas.
Recently refined beta-decay calculations lead to relative nuclear
mass abundances that match measured values extremely well. The
abundances of these heavy elements and their decay products can also
be used to estimate the age of the universe (actually, the age at which
heavy-element production began), using the calculated beta-decay
half-lives and updated beta-delayed fission rates. The result obtained is
about 20 billion years, which is not inconsistent with the value of 15
billion to 18 billion years, derived for the age of the oldest globular
clusters (using the theory of stellar evolution), or with the value of 13
billion to 18 billion years, derived from the rate of expansion of the
universe.
NUCLEAR REACTIONS IN STARS
Modern experimental and theoretical techniques have provided a
great deal of information on many of the nuclear reactions that generate
energy and synthesize elements in the stars. In our own Sun, for
example, the main path to hydrogen fusion starts with the pep reaction,
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NUCLEAR ASTROPHYSICS 115
in which two protons react to form a deuteron by emitting a positron
and a neutrino. Our Sun, being the nearest star, is naturally the most
thoroughly studied. An indirect way of checking the validity of models
of solar structure and dynamics is to compare calculated results with
measured physical properties of the Sun or with measured abundances
of the elements.
The Solar-Neutrino Problem
About 25 years ago, an improved understanding of neutrino interac-
tions led to the suggestion of a relatively direct way of observing
nuclear reactions taking place in the Sun's core: use an earthbound
detector to measure the flux of neutrinos released by these reactions.
Because neutrinos interact only via the weak force, they stream
relatively unimpeded from the Sun's center and offer us a glimpse of
the processes occurring there. Photons, by contrast, undergo the much
stronger electromagnetic interaction with the solar material, and it
takes them about 107 years to wend their way from the Sun's center to
its surface.
In 1970 a solar-neutrino detector built by Brookhaven National
Laboratory began operating in a South Dakota gold mine, a mile
underground to help shield against cosmic-ray background counts. In
experiments carried out during the past 14 years, the average counting
rate has been about three neutrino captures per week, roughly one
fourth the rate predicted by solar models. The discrepancy, which is
still unresolved, is called the solar-neutrino problem.
Solar-neutrino detectors are based on a nuclear process, related to
beta decay, in which a nucleus absorbs a neutrino and transforms to a
daughter nucleus by emitting an electron. In the Brookhaven
radiochemical detector (see Figure 5.3), the target nucleus is
chlorine-37 (37Cl), in the form of 100,000 gallons of perchloroethylene
cleaning fluid. The daughter nucleus, argon-37 (37Ar), is a gas, which is
relatively easy to sweep out of the liquid and measure. The reaction in
question, however, requires a minimum neutrino energy of 0.81 MeV.
Unfortunately, this restriction makes the detector insensitive to the pep
reaction, which provides 90 percent of the total solar-neutrino flux but
whose neutrinos have a maximum energy of only 0.42 MeV.
An analysis of relevant nuclear reactions shows that 80 percent of all
the neutrinos that should be detected by the 37Cl come from a minor
solar reaction (about 0.01 percent of the total) in which a proton reacts
with beryllium-7 to produce boron-8, which then decays to beryllium-8
by emitting a positron and a neutrino with a maximum energy of 14
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1 16 NUCLEAR PHYSICS
3.8 x 108 cm3C2CI4
2 2 x 103° 37CI atoms
~ ..
=-q
l
3.86 x 1026 watts
1.8 x 1038 neutrinos/sec
-
-
-
6.6 x 101° neutrinos/sec~cm2
_
__.
_ .
\ /_
\\
\
( 037CI
~ ~37Ar/week
l
FIGURE 5.3 The solar-neutrino experiment being conducted in a South Dakota gold
mine (see the text for details). Of every 1022 neutrinos that pass through the 100,000-
gallon tank of perchloroethylene, fewer than one interacts with a 37C1 nucleus. Each such
interaction produces a 37Ar atom, which can be extracted and counted. The counting rate
of about three neutrino-produced events per week is about one fourth the expected rate.
OCR for page 117
NUCLEAR ASTROPHYSICS 117
MeV. The selectivity of the 37C1 detector for this minor reaction is
actually an advantage for solar diagnostics, however, because the
reaction (unlike the pep reaction) sensitively reflects conditions at the
core of the Sun.
The solar-neutrino problem represents the only major failure of the
otherwise extremely successful standard solar model, and this discrep-
ancy between the predicted and measured neutrino counting rates has
prompted critical re-examinations of various aspects of solar physics
and nuclear physics. The nuclear-reaction rates in question have been
substantiated by new results in many laboratories. It has also been
suggested that the electron neutrinos, on their way to the Earth from
the Sun, may undergo neutrino oscillations to their muon or tauon
counterparts, as discussed in Chapter 3. There is no real evidence for
this, however, and the problem remains under investigation.
The next logical step would seem to be the construction of detectors
having target nuclei that could respond to other parts of the predicted
solar-neutrino spectrum. The proposed detector currently receiving the
most attention is based on gallium-71 (alga), which produces germa-
nium-71 (age) upon reacting with a neutrino. The 7'Ga detector has the
advantage that most of its counts (63 percent of the total) would be due
to neutrinos from the pep reaction, which is the basic reaction
responsible for the Sun's luminosity.
The neutrino flux from the pep reaction is relatively insensitive to
detailed conditions inside the Sun. Therefore, if the measured counting
rate in the Olga detector were still less than the predicted rate, we
would be left with only two possible explanations: either (1) some form
of neutrino oscillation or decay occurs between the center of the Sun
and the Earth, or (2) the Sun is producing energy through some
nonequilibrium process (so that it is currently producing less energy
than it is radiating). Conversely, if the measured and predicted
counting rates were in agreement, we could infer a limit on the neutrino
mass differences of approximately 10-6 eV or less, and we could verify
that the Sun is currently producing energy at a rate consistent with its
observed luminosity, although this fact alone could not rule out the
possibility of nonequilibrium processes.
Tests on a pilot detector made with 1.8 tons of gallium have shown
an efficiency of 95 percent or better for collecting the age reaction
product; at present, it is estimated that a full-scale detector would
require between 15 and 30 tons of gallium. Meanwhile, various other
possible detectors are under consideration, including two that would be
able to measure the solar neutrinos directly. One of these would be able
to measure both the energy and time of interaction of a given neutrino,
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118 NUCLEAR PHYSICS
and the other would be able to measure these quantities as well as the
direction of arrival of the neutrino.
Stellar Evolution
As a star evolves from youth to old age, its primary energy-
generating reactions shift from hydrogen fusion to other processes
involving progressively heavier elements. An understanding of stellar
evolution therefore requires a thorough study of the corresponding
nuclear reactions. Recent interest in stellar energy generation and
nucleosynthesis has been focused on these later stages of stellar
evolution. In a red giant star, for example, a primary process is the
fusion of three 4He nuclei (alpha particles) to form carbon-12 (TIC), a
process called helium burning. Some of the '2C nuclei can react further
with 4He to form oxygen-16 (~60), so that the ratio of ~60 to ~2C from
nucleosynthesis depends on the reaction rate of '2C with 4He relative to
its rate of formation through helium burning. There is currently a
discrepancy by a factor of 2 between different laboratory measure-
ments of the 4He plus '2C reaction, which needs to be resolved by
further experiments.
Considerable work has been done recently on stellar nuclear reac-
tions involving aluminum and magnesium, triggered by the discovery in
1976 that aluminum mineral inclusions in the Allende meteorite contain
an excessive proportion of 26Mg relative to the other magnesium
isotopes. The excess 26Mg is directly proportional to the amount of
aluminum present; this leaves little doubt that the excess 26Mg is the
decay product of radioactive 26Al, which has a half-life of only 7.2 x
1Os years. Recently, gamma rays from the decay of 26Al in the
interstellar medium have been identified with high-resolution detectors
in orbiting satellites. These observations point to the presence of a
substantial amount of 26Al distributed in the plane of our galaxy and
suggest that the most likely source of this material is from nova
explosions. This is consistent with recent nuclear-physics measure-
ments that suggest that red giant stars and novas are more likely
sources of 26Al than are supernovas.
Another example of the value of nuclear physics in furthering our
understanding of stellar evolution is that of very hot stars, such as
white dwarfs. Here certain radioactive nuclear species both ground
states and long-lived excited states are important in nucleosynthetic
reaction cycles even though their half-lives are relatively short. For
example, the reaction of a proton with nitrogen-13 (half-life 9.97
minutes) to give oxygen-14 (half-life 70.6 seconds) forms part of the
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NUCLEAR ASTROPHYSICS 119
rp process /
/
2sSj ~ 27sf
is, ~`
JUDAIC 24AI-
20N~;
, ~
Hot CNO cycle
/~, . O , O
IN
FIGURE 5.4 Series of nuclear reactions such as the hot CNO cycle and the rp (rapid
proton capture) process occur on time scales that are short compared with the half-lives
of nuclides such as '3N (10 minutes) and i9Ne (17 seconds). These explosive phases of
nucleosynthesis are thought to occur on the surfaces of white dwarfs and neutron stars
that are accreting fresh hydrogen on their surfaces. They may be responsible for novas,
which occur at a rate of about 25 per year in our galaxy.
so-called hot CNO cycle (carbon, nitrogen, oxygen; see Figure 5.41.
Studying such reactions experimentally is technically very challenging,
requiring the production of intense secondary beams of radioactive
nuclides. At least four different methods have been proposed for
producing the required beams. This technical capability would provide
important information for astrophysical processes, and it would also
open up the possibility of investigating otherwise inaccessible nuclear
reactions.
Representative terms from entire chapter:
nuclear physics
