Weak-Field Yukawa Exchange and a Screened Interfacial Benchmark

This technical addendum records a post-publication weak-field calculation relevant to the contact and material-density programme in the published RFL Applications paper. A massive real mediator a, linearly sourced by the scalar density s = |psi|^2, satisfies the static weak-field limit. The Green function is exp(-mu_a r)/(4 pi r), and two localized sources generate an attractive cross-interaction. The addendum also revisits the interfacial virial expression already developed in RFL APP4 and provides a numerical quadrature benchmark with an absolute numerical-analytic pressure difference of approximately 2.7 x 10^-20. The calculation closes the Green-function reduction and the illustrative screened integral, providing a solid mathematical foundation for the RFL contact mechanics.