Basic Properties of Finite Nuclei

We begin the discussions of finite nuclei with some general remarks on the systematics of the nuclear ground state. For even-even nuclei (nuclei with an even number of both protons and neutrons) the nucleons making up the nucleus form pairs containing one spin-up and one spin-down nucleon to yield a net spin of zero and even parity. In Chapter 15 we consider elastic electron scattering from such nuclei as the paradigm for what follows. Odd-even and even-odd nuclei often, but not always, have the same spin as the last unpaired valence nucleon; we shall see examples when discussing elastic magnetic electron scattering and magnetic moments also in Chapter 15. Finally, odd-odd nuclei are somewhat unusual. There exist only four stable nuclei having unpaired protons and neutrons, namely, 2H, 6Li, and 14N with spin-parity 1+, and 10B having 3+. The basic characteristics of the known nuclei are the following: they occupy a region in the NZplane whose central valley runs roughly along the N = Z line at values of A below 40 and then bends towards the region having higher values of N than of Z, as shown in Fig. 13.1. Taking cuts across the valley at either constant Z or at constant N, one climbs out of the valley, on the average moving to less bound nuclei until reaching the so-called drip-lines where nuclei are no longer stable to proton or neutron emission. At the bottom of the valley, where the most stable nuclei reside, one finds the binding energy per nucleon to be relatively constant for nuclei beyond A = 40 at a value ̴ 8.5 MeV per nucleon, as shown in Fig. 13.2 and, as the values of N and Z where stable nuclei exist become very large, this valley of stability narrows and then disappears.

One of the key questions in studies of nuclear systematics is: Do “islands of stability” exist at even higher N, Z-values, the so-called superheavy nuclei? An island of stability, first conjectured by Seaborg in the 1960s, is a collection of heavier isotopes of transuranic elements, expected to be more stable than those closer in atomic number to uranium with radioactive decay half-lives of minutes to days.

The past one hundred years has witnessed enormous advances in human understanding of the physical universe in which we have evolved. For the past fifty years or so, the Standard Model of the subatomic world has been systematically developed to provide the quantum mechanical description of electricity and magnetism, the weak interaction, and the strong force. Symmetry principles, expressed mathematically via group theory, serve as the backbone of the Standard Model. At this time, the Standard Model has passed all tests in the laboratory. Notwithstanding this success, most of the matter available to experimental physicists is in the form of atomic nuclei. The most successful description of nuclei is in terms of the observable protons, neutrons, and other hadronic constituents, and not the fundamental quarks and gluons of the Standard Model. Thus, the professional particle or nuclear physicist should be comfortable in applying the hadronic description of nuclei to understanding the structure and properties of nuclei. Experimentally, lepton scattering has proved to be the cleanest and most effective tool for unraveling the complicated structure of hadrons. Its application over different energies and kinematics to the nucleon, fewbody nuclei, and medium- and heavy-mass nuclei has provided the solid body of precise experimental data on which the Standard Model is built.

In addition, the current understanding of the microcosm described in this book provides answers to many basic questions: How does the Sun shine? What is the origin of the elements? How old is the Earth? Further, it underscores many aspects of modern human civilization, e.g., MRI imaging uses the spin of the proton, nuclear isotopes are essential medical tools, nuclear reactions have powered the Voyager spacecraft since 1977 into interstellar space.

The purpose of the book is to allow the graduate student to understand the foundations and structure of the Standard Model, to apply the Standard Model to understanding the physical world with particular emphasis on nuclei, and to establish the frontiers of current research. There are many outstanding questions that the Standard Model cannot answer. In particular, astrophysical observation strongly supports the existence of dark matter, whose direct detection has thus far remained elusive.