Introductory Nuclear Physics

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PHY431 Lecture 3 1 2/11/2000 5.1. The Measured Nuclear Binding Energy The binding energy per nucleon, derived from the measurement of the atomic masses, is shown as function of the atomic number A in the figure. Clearly, for atomic num- ber below about 30, a smooth curve is not ob- served, and the peaks and dips indicate more struc- ture than the naive liquid drop model can explain. The distribution peaks around A =59 for Co and Fe, and drops off on either side of that. Indeed Fe is the most stable element around. Of course, for a given atomic number A , a variety of stable and radioactive elements with N+Z=A ex- ist. This is the so-called valley of stability, be- cause in the neutron number N versus proton number Z plot, the stable elements form a nar- row valley somewhat above the line N=Z ; see the figure beside. The further one departs from the center of the valley, the more unstable the elements encountered. From this figure, and for the detailed study of the binding energies, it appears that at certain values for N or Z nuclei are particularly stable. These numbers have been historically known as magic numbers , and are N or Z = 2, 8, 20, 28, 50, 82, and 126. The existence of the magic numbers was finally explained in the frame- work of the nuclear shell model: at certain fill- ings the low lying set of shells are fully filled, and the next lowest empty energy level is sepa- rated from the filled shell by a relatively large energy gap. The details of the energy level structure depend crucially on the details of the (strong) nuclear potential. A naive harmonic potential of square-well potential are unable to explain the existence of the magic numbers. The existence Binding energy per nucleon, for all stable nuclei up to A=21, and for a stable nu- cleus of A=29, 39, 49 etc. above. Data from Wapstra and Audi (1985). The β -stability valley. Black squares are the natural stable nuclei, and neighbors between the drip lines are radioactive, often artificial. Data: Chart of Nuclides , 1977, GE Company. proton drip line neutron drip line 28.3 / 4 MeV+6.25 keV × A
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PHY431 Lecture 3 2 2/11/2000 of angular momentum and strong spin-orbit coupling are necessary to explain the observed energy structure. The nuclear shell structure has been studied using the measurement of de-excitation gamma rays in many unstable nuclei. The approximate level pattern for nucleons is shown in the figure below; The number of nucleons in each level and the cumulative number is shown on the right. The oscillator grouping (a dis- torted harmonic oscillator poten- tial is used) is shown at left. Neu- trons and Protons have essentially the same level structure up to to- tals of about 50, thereafter some deviations occur: low neutron an- gular momenta are more favored than low proton angular mo- menta. 5.2. Example: Nickel-48 48 Ni is much too far below the N=Z line to occur naturally. However, because it would be doubly magic, N =20 and Z =28, it might be (is) long-lived enough to be observed close to an accelerator. In the following pages we reproduce a recent article from Physics Today (Feb 2000) on its discovery.
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