Modification due to a three-body force
The two-body matrix elements are now modified in order to account for medium-modified contributions from the three-body interaction, resulting in
$$
\begin{equation}
\langle pq|\tilde{v}|rs\rangle=\langle pq|\hat{v}|rs\rangle+\sum_{i\le F} \langle pqi|\hat{w}|rsi\rangle.
\tag{19}
\end{equation}
$$
In Eq.
(19), the effective two-body interaction
\( \tilde{v} \) can contain both a standard two-nucleon interaction and a
density dependent contribution stemming from a three-body interaction
\( \hat{w} \).