neutrons and protons imply filling higher energy levels for one type of particle, while leaving lower energy levels vacant for the other type. Pairing energy, which accounts for the tendency of proton pairs and neutron pairs to occur. An even number of particles is more stable than an odd number due to spin coupling. The formula The mass of an atomic nucleus, for neutrons, protons, and therefore nucleons, is given by where and are the rest mass of a proton and a neutron respectively, and is the binding energy of the nucleus. The semi-empirical mass formula states the binding energy is The term is either zero or , depending on the parity of and , where for some exponent . Note that as , the numerator of the term can be rewritten as . Each of the terms in this formula has a theoretical basis. The coefficients , , , , and are determined empirically; while they may be derived from experiment, they are typically derived from least-squares fit to contemporary data. While typically expressed by its basic five terms, further terms exist to explain additional phenomena. Akin to how changing a polynomial fit will change its coefficients, the interplay between these coefficients as new phenomena are introduced is complex; some terms influence each other, whereas the term is largely independent. Volume term The term is known as the volume term. The volume of the nucleus is proportional to A, so this term is proportional to the volume, hence the name. The basis for this term is the strong nuclear force. The strong force affects both protons and neutrons, and as expected, this term is independent of Z. Because the number of pairs that can be taken from A particles is , one might expect a term proportional to . However, the strong force has a very limited range, and a given nucleon may only interact strongly with its nearest neighbors and next nearest neighbors. Therefore, the number of pairs of particles that actually interact is roughly proportional to A, giving the volume term its form. The coefficient is smaller than the binding energy possessed by the nucleons with respect to their neighbors (), which is of order of 40 MeV. This is because the larger the number of nucleons in the nucleus, the larger their kinetic energy is, due to the Pauli exclusion principle. If one treats the nucleus