Applying the quark model to the atomic d shell

The atomic d shell is explored from the perspective of the quark model of the atom. In this scheme, all the states are generated by four statistically independent fictitious particles (the quarks), each with angular momentum 3/2, augmented by two parity labels. The detailed quark expansions are given for the two 2D terms of d3, and the results are compared to the classic analysis of Condon and Shortley (1935). Matrix elements of single-electron tensor operators and of the Coulomb interaction are calculated in the quark scheme, and the connection to the conventional approach is made. The diagonal sum method of Slater is applied to the quark states and extensions to many-electron operators are discussed. The correspondence between the quark model and the traditional method implies relations between various n-j symbols, and this is illustrated by two special cases.