ABSTRACT

Specific approximate descriptions, called models, have been developed in the case of nuclei, each of them only being appropriate for a limited range of nuclear properties. A general understanding of systematic trends found for the time-independent properties, such as mass, size, charge and energy, can be obtained from the semiclassical or particle models, which give a description in terms of energy, with no insight about details inside the nucleus. Since the nucleons are held together by strong attractive forces, it is convenient to introduce the binding energy ( )ZAB , of a nucleus that represents the energy released

in bringing the nucleons together or, conversely, the work necessary to dissociate the nucleus into separate nucleons. It is common practice to define the nuclear binding energy according to the energy-inertia relation (5.9) in terms of atomic rather than nuclear masses, as ( ) ( ) ( ) 2 2, ,H nB A Z Zm A Z m M A Z c Mc⎡ ⎤= + − − = ∆⎣ ⎦ (46.1) where is the atomic mass of the isotope, and ( ZAM , ) M∆ is the so-called mass defect. Since the state of infinite separation of the nucleons is taken to be the zero level of energy, the total energy of the ground state of a nucleus is ( )., ZAB− Nuclear energies are conveniently measured in ( )6MeV 1MeV 10 eV ,= where the electron-volt is the common atomic unit of energy. Equation (5.9) gives the energy equivalent of an atomic mass unit as ,MeV44.9311 =u so that one can work either with masses or energies as convenient. The binding energy per nucleon

( ) A

ZABf ,= (46.2) is often called the binding fraction, and its plot as a function of the mass number, given in Figure 46.1, can be used for a systematic study of nuclear binding energy.