1.8 The atomic nucleus: The atomic nucleus contains typically fewer than 300 protons and neutrons. It is an example of a small system with both short- and long-ranged forces. The mass is given by the semi-empirical Weizscker formula (deShalit 1994): Z Al/S (Z-N). M = Zmp+Nima-aA + a2A/3+a3- + 8(A), where Z is the number of protons, N is the number of neutrons, and A=Z+N. The masses of protons and neutrons are, respectively, m, and ma, and a(i = 1,...,4) are numerical constants: +as- volume energy: a = 16MeV/c, surface energy: a2 = 19, Coulomb energy: a3 = 0.72, symmetry energy: a = 28. The symmetry energy favors A = Z. The term 8(A) is the "pairing energy" that gives small fluctuations. 12 The macroscopic view Take Z=N=A/2, manip, and neglect 8(A), so that M = (m-a)A + a24/3 + AS/3 Make a log plot of M from A = 1 to A = 104, and indicate the range in which M can be considered as extensive.