Nuclear Physics The Core of Matter, The Fuel of Stars (1999) / Chapter Skim
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Pages 47-79
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From page 47... ...
THE STRUCTURE OF NUCLEI 47 47 3 The Structure of Nuclei INTRODUCTION The nucleus, the core and center of the atom, is a quantal many-body system governed by the strong interaction. Just as hadrons are composed of quarks and gluons, the nucleus is composed of the most stable of these hadrons -- neutrons and protons.
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From page 48... ...
48 NUCLEAR PHYSICS: THE CORE OF MATTER, THE FUEL OF STARS • What are the limiting conditions under which nuclei can remain bound, and what new structure features emerge near these limits? • What is the origin of the naturally occurring elements of our world?
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From page 49... ...
THE STRUCTURE OF NUCLEI 49 percent of all expected bound nuclear systems, a region where many new nuclear phenomena are anticipated. As is evident from the map of the nuclear terrain in Figure 3.1, the limits of nuclear binding are poorly known at present; often, those limits are close to the regions where the processes that form the elements in stars must proceed.
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From page 50... ...
50 NUCLEAR PHYSICS: THE CORE OF MATTER, THE FUEL OF STARS FIGURE 3.1 The bound nuclear systems are shown as a function of the proton number Z (vertical axis) and the neutron number N (horizontal axis)
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From page 51... ...
THE STRUCTURE OF NUCLEI 51 Unique information on the strong force between hadrons can be obtained by comparing the forces between two nucleons and between a nucleon and a lambda particle in which one of the quarks is a heavier strange quark. Any difference between these forces is entirely due to the change in a single quark.
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From page 52... ...
52 NUCLEAR PHYSICS: THE CORE OF MATTER, THE FUEL OF STARS BOX 3.1 A Microscope to Measure the Distributions of Protons and Neutrons in the Nucleus By bombarding nuclei with electrons from the new generation of electron accelerators and using pairs of spectrometers to detect both the scattered electron and a proton ejected from the nucleus, valuable new insight is gained into how protons and neutrons are distributed in the nucleus. The energies and angles of the electron and proton are measured with the spectrometers, and from this the energy E and the momentum k of the recoiling excited nucleus are deduced.
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From page 53... ...
THE STRUCTURE OF NUCLEI 53 FIGURE 3.1.1 Experiments in which electrons knock out protons bound in the nucleus and both are detected in coincidence are being used to probe the distributions of nucleons in the nucleus. The photograph on the left shows an example of the equipment required for these experiments at high energies -- the high-resolution spectrometers used in Hall A at CEBAF.
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From page 54... ...
54 NUCLEAR PHYSICS: THE CORE OF MATTER, THE FUEL OF STARS tering. The essentially structureless electron, possessing both an electric charge and a magnetic moment, is used as a probe to map the distribution of charge and magnetism within the nucleus.
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From page 55... ...
THE STRUCTURE OF NUCLEI 55 femtometer size, as small as a single isolated nucleon. Such shapes are formed by the joint action of the short-range repulsive force and the anisotropic pion-exchange force between nucleons.
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From page 56... ...
56 NUCLEAR PHYSICS: THE CORE OF MATTER, THE FUEL OF STARS BOX 3.2 Measuring the Shape of the Deuteron The deuteron, with just one proton and one neutron, is the simplest of nuclei beyond the proton. The nucleon density distribution in the deuteron, illustrated in Figure 3.2.1, is determined by nuclear forces; the density is large where the forces are attractive, and small where they are repulsive.
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From page 57... ...
THE STRUCTURE OF NUCLEI 57 the nucleon process is dominant at small photon energies, while at higher energies the quark process dominates. These experiments also need high-energy, highintensity electron beams.
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From page 58... ...
58 NUCLEAR PHYSICS: THE CORE OF MATTER, THE FUEL OF STARS NUCLEAR FORCES AND COMPLEX NUCLEI The work on few-body nuclei discussed above demonstrates that there is a phenomenological theory for nuclear physics: an interaction derived from nucleon-nucleon scattering, augmented by a weaker three-body force, that is used to predict the properties of the lightest nuclei with present-day computing capabilities. Thus, even though the fundamental constituents of nuclei are quarks and gluons, there exists a simpler effective theory that accurately describes nuclei in our everyday world.
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From page 59... ...
THE STRUCTURE OF NUCLEI 59 The accuracy of this correspondence -- the extent to which nucleons in a real nucleus appear to move in an average nuclear potential -- is being addressed experimentally. In a series of measurements performed in the past decade, highenergy electrons were used to knock out single protons from nuclei as described in Box 3.1.
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From page 60... ...
60 NUCLEAR PHYSICS: THE CORE OF MATTER, THE FUEL OF STARS Mean Field Methods Despite the exciting progress in shell model approaches, applications to heavy nuclei are still beyond our reach. These systems show a variety of collective motions, such as vibrations and rotations, involving many nucleons.
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From page 61... ...
THE STRUCTURE OF NUCLEI 61 Limits of Nuclear Stability One of the themes of today's nuclear science is the journey to the limits in several directions. For nuclear charge and mass this journey involves nuclei heavier than any that occur in nature or that have been produced in the laboratory; for the neutron-to-proton ratio, it involves the drip lines, the limit of binding; and for angular momentum, the journey involves the extremes of rapid rotation.
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From page 63... ...
THE STRUCTURE OF NUCLEI 63 radioactivity -- the emission of helium-4 nuclei -- just as do the naturally occurring uranium isotopes and the lighter transuranic elements. The chain of alpha particle decays that identifies the heaviest known element as A = 277 and Z = 112 is shown in Figure 3.2.
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From page 64... ...
64 NUCLEAR PHYSICS: THE CORE OF MATTER, THE FUEL OF STARS cause deviations from the periodicity of chemical properties that characterizes the periodic table for lighter elements. Toward the Limits in Neutron-to-Proton Ratio Fewer than 300 stable isotopes, shown by black squares in Figure 3.1, occur naturally.
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From page 65... ...
THE STRUCTURE OF NUCLEI 65 in this exotic territory. Such features are expected for nuclei that contain a sizable number of very weakly bound neutrons.
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THE STRUCTURE OF NUCLEI 67 While most of our knowledge of nuclei is limited to the neighborhood of the valley of stability, early experiments on far unstable nuclei have already revealed surprises. New phenomena such as halo nuclei -- with regions of nearly pure neutron matter -- and growing evidence of the fragility of shell structure far from the valley of stability are just two examples.
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From page 68... ...
68 NUCLEAR PHYSICS: THE CORE OF MATTER, THE FUEL OF STARS FIGURE 3.4 The structure of nuclei is expected to change significantly as the limit of nuclear stability is approached in neutron excess. Both the systematic variation in the shell model potential and the increased role of superconducting correlations give rise, theoretically, to the quenched neutron shell structure, characterized by a more uniform distribution of levels with dramatically reduced shell gaps.
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From page 69... ...
THE STRUCTURE OF NUCLEI 69 bands indicating very elongated, superdeformed shapes having the longer axis twice as long as the shorter (see Box 3.3)
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From page 71... ...
THE STRUCTURE OF NUCLEI 71 superconductivity, is observed at high rotational frequencies. The angular momentum behaves like an external magnetic field: it tries to align the angular momenta of nucleons along the axis of rotation, and this destroys Cooper pairs of nucleons responsible for superconductivity.
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From page 72... ...
72 NUCLEAR PHYSICS: THE CORE OF MATTER, THE FUEL OF STARS BOX 3.3 The Champion of Fast Rotation Rotation is a common phenomenon in nature -- most objects in the universe, from the very small to the very large, rotate (Figure 3.3.1)
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From page 73... ...
THE STRUCTURE OF NUCLEI 73 ed that it fissions into two fragments. Interestingly, the shape changes found in hot nuclei, where the shell effects and superconductivity can be ignored, seem to resemble this behavior.
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From page 74... ...
74 NUCLEAR PHYSICS: THE CORE OF MATTER, THE FUEL OF STARS BOX 3.4 The Nucleus: A Finite Many-Body System While the number of degrees of freedom in heavy nuclei is large, it is still very small compared to the number of electrons in a solid or atoms in a mole of gas, and as such the nucleus presents one of the most challenging many-body problems. Many fundamental concepts and tools of nuclear theory, such as the treatment of nuclear superconductivity and of nuclear collective modes, were brought to nuclear physics from other fields.
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From page 75... ...
THE STRUCTURE OF NUCLEI 75 symmetries can be attributed to the features of the effective interaction acting in the system. These dynamical symmetries can often dramatically simplify the description of otherwise complicated systems.
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From page 76... ...
76 NUCLEAR PHYSICS: THE CORE OF MATTER, THE FUEL OF STARS of the compound nucleus in the regime of neutron resonances. Today, the random matrix theory is the basic tool of the interdisciplinary field of quantum chaos, and the atomic nucleus is still a wonderful laboratory of chaotic phenomena.
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From page 77... ...
THE STRUCTURE OF NUCLEI 77 NUCLEAR MATTER While heavy and even superheavy nuclei have been discussed above, nature also provides nuclei of virtually infinite size in the dense cores of neutron stars, where hadronic matter exists as a uniform medium, rather than clumped into individual nuclei. Much of what is learned from finite nuclei -- the nature of the nucleon-nucleon force, the role of many-nucleon interactions, collective excitations, and so forth -- is crucial in explaining the properties of infinite matter.
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From page 78... ...
78 NUCLEAR PHYSICS: THE CORE OF MATTER, THE FUEL OF STARS drop, are called giant resonances. Instead of the sound waves of a bell, they emit gamma rays.
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From page 79... ...
THE STRUCTURE OF NUCLEI 79 important role in the way the universe works and how elements are synthesized in the cosmos. The properties of such nuclei are essential to a quantitative understanding of these processes.
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