Analyzing the results in terms of the nuclear force components

Our Hamiltonian contains one-body, two-body and three-body contributions and in the equations below, we label states below the Fermi level \( F \) as \( i,j,\ldots \) while states above the Fermi level are defined by \( a,b,\ldots \). General single-particle states are given by the letters \( p,q \dots \). The quantities \( pq\dots \) represent the quantum numbers of various single-particle states, namely \( p=(n_p,l_p,j_p,m_{j_p},t_{z_p}) \). The commutation relations for creation and annihilations operators with respect to a given reference state are then given by $$ \begin{equation*} \left\{a_p^\dagger, a_q \right\}= \delta_{pq}, p, q \leq F \hspace{0.5cm} \left\{a_p, a_q^\dagger \right\} = \delta_{pq}, p, q > F. \end{equation*} $$