Validity of single- and two-nucleon matrix-element equality with dynamical mesons

Determine whether the equality between the two-nucleon scattering matrix elements of the single-nucleon operator \(\Omega(\mathbf{k})\) and the two-nucleon operator \(\Pi(\mathbf{k})\) remains valid when the underlying nuclear theory includes dynamical mesons or other non-nucleon degrees of freedom.

Background

For nuclear potentials such as AV18, which contain only nucleonic degrees of freedom, the paper finds that the matrix elements of the single-nucleon momentum operator $\Omega(\mathbf{k})$ and the two-nucleon momentum operator $\Pi(\mathbf{k})$ are identical up to an overall constant. This relation underlies the proportionality between their Wilson coefficients and the approximate relation between single- and two-nucleon momentum distributions at large momentum.

The authors explain that dynamical mesons would introduce nontrivial integrations over mesonic intermediate states and could alter the structure of the single-nucleon matrix element. Whether the equality survives in such theories is therefore left unresolved.