Within a cluster expansion of the correlated operator $$\tilde{O} = C^{\dagger} O C = \tilde{O}^{[1]} + \tilde{O}^{[2]} + \cdots + \tilde{O}^{[A]}, 
\label{cexpansion}$$ where $\tilde{O}^{[n]}$ denotes the irreducible $n$-body contribution, we usually employ a two-body approximation, i.e., three-body and higher-order terms of the expansion are neglected. Starting from the uncorrelated Hamiltonian $H$ for the $A$-body system, consisting of the kinetic energy operator $T$ and a two-body potential $V$, the formalism of the UCOM is used to construct the correlated Hamiltonian in two-body approximation $$H^{C2} = {\tilde{T}}^{[1]} + {\tilde{T}}^{[2]} + {\tilde{V}}^{[2]}
  = T + V_{\text{UCOM}},$$ where the one-body contribution comes only from the uncorrelated kinetic energy ${\tilde{T}}^{[1]} = T$. Two-body contributions arise from the correlated kinetic energy ${\tilde{T}}^{[2]}$ and the correlated potential ${\tilde{V}}^{[2]}$, which together constitute the phase-shift equivalent correlated interaction $V_{\text{UCOM}}$.

It has been verified that higher-order contributions due to short-range central correlations can be neglected in the description of nuclear structure properties [@RNH2004]. The tensor interaction, on the other hand, is long-ranged and thus generates long-range correlations in an isolated two-nucleon system. However, the long-range tensor correlations between two nucleons embedded in a many-nucleon system are suppressed by the presence of other nucleons, leading to a screening of the tensor 