The potential energy part includes also an external potential \( \hat{u}_{\mathrm{ext}}(x_i) \).

In a non-relativistic approach to atomic physics, this external potential is given by the attraction an electron feels from the atomic nucleus. The latter being much heavier than the involved electrons, is often used to define a natural center of mass. In nuclear physics there is no such external potential. It is the nuclear force which results in binding in nuclear systems. In a non-relativistic framework, the nuclear force contains two-body, three-body and more complicated degrees of freedom. The potential energy reads then $$ \hat{V} = \sum_{ij}^A v(x_i,x_j)+\sum_{ijk}^Av(x_i,x_j,x_k)+\dots $$