Nuclear Physics (1986) / Chapter Skim
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2 Nuclear Structure and Dynamics
2 Nuclear Structure and Dynamics
Pages 37-66
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From page 37... ...
This is the conceptual basis of the shell model, which is the foundation for much of our quantitative understanding of nuclear energy levels and their properties. In this model, individual nucleons are considered to fill energy states successively, forming a series of nuclear shells that are analogous to the shells formed by electrons in the atom.
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From page 38... ...
For many of these models, it is possible to make the connection with the more fundamental but more complicated shell-model description. Experimentalists study nuclear structure by determining what energy states appear in a given nucleus and what states play a role in particular nuclear reactions.
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From page 39... ...
ELEMENTARY MODES OF EXCITATION Extreme limiting cases, in which one type of behavior overshadows all competing effects, are often the easiest to deal with in physics. Nuclear physicists have therefore concentrated much of their attention on excited states corresponding either to the shell model, at one extreme, or to the liquid-drop model, at the other.
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From page 40... ...
The observed probability for absorption of the gamma rays at resonance energies is nearly equal to the theoretical maximum from the sum rule for electric dipole oscillations strong evidence that essentially all of the protons take part in the collective motion. The giant electric dipole resonance peak extends over a width of 3 to 7 MeV in energy, depending on the nucleus.
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From page 41... ...
In the early 1970s, a group in Darmstadt, West Germany, using inelastic electron scattering, and a group at Oak Ridge National Laboratory, using inelastic proton scattering, both found clear evidence for a giant electric quadrupole resonance. Here the protons and neutrons move together in a quadrupole vibration, in which the center
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From page 42... ...
Unlike gamma-ray absorption, which excites dipole vibrations selectively, the inelastic scattering of charged particles can excite several vibrational modes. To disentangle the individual vibrational patterns from the measured angular intensities of the scattered particles, physicists exploit the fact that each multipole is associated with a definite integer value L of angular momentum (L = 1 for dipole, L = 2 for quadrupole)
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From page 43... ...
Heavy ions might be especially suitable projectiles for exciting vibrations with large L values, because such massive ions can transfer a large amount of angular momentum to a target nucleus. Also, variations on monopole or quadrupole vibrations are possible in which the neutrons and protons move in opposition rather than together.
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From page 44... ...
Even when the differences between the target protons and neutrons are much smaller, as in the giant quadrupole vibrations in heavy nuclei, they can be detected through positive and negative pion scattering. This technique thus provides a sensitive test of the microscopic theory of nuclear vibrations.
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From page 45... ...
Deltas are high-energy excited states of the baryon. The first (lowest-level)
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From page 46... ...
(By contrast, it is often difficult to separate the reaction mechanism from the target structure in hadronic scattering of strongly interacting particles.) Of course, these comments also apply to photon scattering, but a second great advantage of electron scattering is that, for afixed nuclear excitation energy, one can vary the momentum transferred by the scattered electron to the nucleus and map out the charge and current densities, even in the deep interior of the nucleus.
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From page 47... ...
Furthermore, because the interaction of the electron with the intrinsic magnetization is enhanced at high momentum transfer and large electron scattering angles, it is possible to examine high-spin states of a magnetic character. Finally, at the very high energy and momentum transfers that are obtainable at the Stanford Linear Accelerator Center (SLAC)
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From page 48... ...
4 FIGURE 2.3 A nuclear diffraction pattern obtained by the elastic scattering of 500-MeV electrons from calcium-40 nuclei. Note that the measurements were made over the enormous range of about 12 orders of magnitude.
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From page 49... ...
Since neutrons possess a small intrinsic magnetic moment, they will also contribute to elastic magnetic scattering. By measuring the scattered electrons' diffraction pattern to high values of momentum transfer, one can see the spatial distribution of the last valence particle proton or Nuclear charge density IS Nuclear FIGURE 2.4 A perspective view of the electric charge distribution in the nucleus of ytterbium-174.
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From page 50... ...
All of these particles are now used as precision probes, bringing together complementary interactions with which the whole of nuclear matter can be mapped. The Interacting Boson Model Geometrical symmetries are used to describe special, simple properties of otherwise complex structures.
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From page 51... ...
. This interacting boson model is characterized by a particular pattern of nuclear energy levels (and their decays)
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From page 52... ...
A major program effort in heavy-ion physics is to utilize these effects to study macroscopic nuclear properties involving the cooperative motion of many nucleons. Heavy-ion collisions can give rise to new phenomena not seen when the projectile is a single particle: they can split off chunks of nuclear matter, they can completely disintegrate nuclei in a burst of nucleons, and they can transfer large amounts of angular momentum, leading to instability and breakup.
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From page 53... ...
At intermediate impact parameters, the nuclei graze just closely enough to bring the nuclear forces into play. A likely event during a grazing collision is the transfer of one or more nucleons between the collision partners, or perhaps the excitation of collective modes.
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From page 54... ...
occur with lower probability, however, because of the smaller cross-sectional area presented. Given sufficient projectile energy to overcome the repulsive Coulomb forces, all the reaction types described above can occur, and great skill is needed to single out the particular reaction of interest.
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From page 55... ...
of one or a few nucleons from the normally occupied ground level to normally unoccupied excited levels. A general result from the quantum mechanics of many-body systems is that the energy levels allowed for the nucleus become more closely spaced as the energy above the ground level increases.
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From page 56... ...
56 '_ I_ _ _ _, _ _, _ _r _ ~,_I _ ~_ ~ _ __ _I hi_ an,.
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From page 57... ...
They involve some of the same reaction mechanisms that occur in fission, but in deep-inelastic collisions, these can be studied in a controlled way by the suitable choice of projectile, target, and energy, for example. In a deep-inelastic collision, the projectile nucleus can lose most of its energy as it plows into the target nucleus; the energy loss is often so great that the emerging reaction fragments are initially nearly at rest, and they fly apart mainly because of the repulsive Coulomb force between them.
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From page 58... ...
The nuclear matter in a low-energy, deep-inelastic collision is not highly excited, and relatively few excited states are accessible to the nucleons. Under these conditions, the Pauli exclusion principle still diminishes the effects of the nuclear force, and a given nucleon can move fairly freely through the nuclear interiors.
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From page 59... ...
Great progress has nevertheless been made in microscopic nuclear theory during the past decade, thanks to the steadily increasing knowledge of the NN force, improved calculational techniques, and more precise data on nuclear structure and interactions. A broad conclusion from this work is that the traditional picture of interacting nucleons alone cannot explain the detailed behavior of nuclear matter.
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From page 60... ...
The Three-Nucleon Nucleus and Infinite Nuclear Matter Advances in many-body calculations are usually tested first on two limiting cases, to see if an extension to more complicated systems is warranted. Two such cases often employed are the three-nucleon nucleus and an infinite nuclear matter consisting of neutrons and protons filling all space uniformly at a given density.
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From page 61... ...
A third property, the compressibility, has recently been derived from giant monopole resonances in real nuclei, as described earlier; the compressibility tells how the binding energy per nucleon changes when the nucleon density is varied. During the 1970s, major advances in mathematical techniques and in the development of powerful computers spurred a vast amount of theoretical work that largely eliminated earlier inconsistencies among various techniques for calculating the properties of nuclear matter.
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From page 62... ...
Calculations of finite nuclei can now also be tested in favorable cases by the measured distribution of an individual nucleon in atnucleus a major advance in the field during the past decade. One method makes use of electron scattering to measure the proton distributions in nuclei differing by only one proton for example, thallium-205 (81 protons, 124 neutrons)
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From page 63... ...
With so many factors involved at once, it would obviously benefit the development of nuclear theory to have experiments that significantly test only one specific factor at a time. A suitable type of experiment for this purpose is the reaction that involves the interaction of a projectile nucleon with only one nucleon in the target nucleus.
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From page 64... ...
The NN force between free nucleons displays a similar trend in the relative strengths, but predictions based on it are not in quantitative agreement with these experiments; the nuclear environment can dramatically modify pion-exchange processes, as various many-body calculations have suggested. The results to date have demonstrated that nucleon-induced transitions at intermediate bombarding energies can indeed act as a selective filter for various components of the nucleon-nucleon force in nuclei.
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From page 65... ...
A quantum field theory of the hadronic interactions in nuclei combines relativity and quantum mechanics. These are essential features of any reliable extrapolation of the properties of nuclear matter to extreme conditions of temperature (average nuclear energy)
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From page 66... ...
The central issues for understanding the nuclear many-body problem are thus to identify unambiguously the quark and color contributions to the description of nuclear systems, to establish the theoretical relationship between the quantum chromodynamic and quantum hadrodynamic pictures of nuclear structure, and to develop a description of nuclei entirely within the framework of quantum chromodynamics.
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