Answer to Question #112386 in Atomic and Nuclear Physics for DEEPAK SINGH

Question

obtain the semi-empirical mass formula for a nuclide of mass number A and atomic C number Z.

Answer 1

The mass of an atomic nucleus, for N neutrons, Z protons and therefore A = N + Z nucleons, is given by

m = Zm_p + N m_n − E_B ( N , Z ) / c²

where m_p and m_n are the rest mass of a proton and a neutron, respectively and E_B is the binding energy of the nucleus. The semi-empirical mass formula states the binding energy is:

E_B = a_VA − a_SA^{2 / 3} − a_C * Z ( Z − 1 ) / A^{1 / 3} − a_A * ( A − 2 Z) ²/ A − δ ( N , Z )

The δ ( N , Z ) term, depending on N and δ₀ = a_PA^kp , is either zero or ± δ₀, where δ₀  =  a_PA^kp for some exponent k_P .

Each of the terms in this formula has a theoretical basis. The coefficients a_V, a_{S ,}a_{C ,} a_A are determined empirically; while they may be derived from experiment, they are typically derived from least squares fit to contemporary data.