Many-particle correlations of fermion clusters in the method of transition density operators

Exact wave function of the $N$-fermion system is divided into the parts corresponding to $s$-particle fermion clusters formed by one-particle states of the self-consistent wave function. Transition density operators involving all virtual transitions between the particle and hole clusters are defined. Using these transition operators, the exact two-particle density matrix is found and the equation of motion describing correlation interaction of the clusters is suggested. It is shown that the expression for the energy dispersion derived with the aid of these equations makes it possible to obtain the estimate for particle correlation of the excited state in the Tamm–Dankoff approximation.