Diagonalization of the spin part of the exchange hamiltonian in the second-quantization method for composite particles

Using the atomic second-quantization procedure an explicit expression is derived for the operator of exchange interaction between two atoms a and b in a state of any value of their atomic orbital and spin momenta, in the approximation of one and two pairs of exchanging electrons and without assuming the orthogonality between the orbitals of a and b. The obtained exchange interaction operator diagonalized in spin space is a second-order polynomial in the scalar product Ŝa · Ŝb. The coefficients of the polynomial are given operators operating in orbital space only. The possible physical implications are discussed.