Interacting particles in one orbit, ch. 4

Methods are discussed that can be used to reduce the matrix elements of the residual interaction between many-particle states to sums over two-body matrix elements. A pictorial notation is introduced for the many-particle states that are angular-momentum coupled and antisymmetrized. Coefficients of fractional parentage are also introduced. The interaction energy of more than two particles in one orbit is calculated. Double-parentage coefficients are introduced and applied. The various quantum numbers such as total spin and isospin, seniority and reduced isospin, which are necessary to specify a system of n particles in one orbit are discussed. The excitation energies in the nucleus 51V are calculated as an example