Nuclear Structure and Properties

The A-values 2 and 3 are not represented by any strongly bound nuclei, and A = 5 not at all (hydrogen 5 and helium 5 immediately loosing a neutron, and lithium 5 and subsequent isotopes a proton). The binding energies (relative to protons and neutrons) are in MeV for the stable light nuclei  

It is the general consensus among nuclear physicists38) that the unsaturated behaviour of nuclei with A below 12 in Eq.(6) is atypical, in sofar the liquid drop model becomes a reasonable approximation in heavier nuclei. It may be noted that the smallest drop consisting of A identical spheres, where at least one particle is not in the surface, occurs for (both cuboctahedral and icosahedral) A = 13, related to the fact that 4 7r = 12.56637... This model was proposed by C.F. von Weiszacker in 1935, and one example 39) of the parametrization of the total atomic weight in the unit of 0.001 chemical unit is 

The sixth contribution to Eq. (7) is the Coulomb term proportional to Z2 divided by the nuclear radius. The last contribution is the even-odd term or alternating term vanishing for odd A. The alternating term represents a stabilization for even Z combined with even N, and a destabilization (of opposite sign) for odd Z combined with odd N. The parameter 6 (even A) is close40 to 13 millimassunits divided by the square-root of A. 

One of the most important uses of Eq.(7) is to predict the /Tstability line. Because of the alternating term influencing even A values, this concept is normally applied to odd A only, and for the chemical reasons outlined above, we are usually asking the question what odd A value is stable for a given Z. Actually, the odd Z values 43 and 61 have no /3-stable nuclei at all, and argon (Z = 18) and cerium (Z = 

58) have no (3-stable nuclei with odd A. These four exceptions are intimately connected with the closed neutron shells N = 50, 82, 20 and 82 discussed below. We may estimate the most stable Z, keeping A constant, by differentiating the sum of the asymmetry and Coulomb terms with respect to Z, finding the minimum energy for 

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