In a recent work, we derived a formula for the elastic
s-wave phase shifts for deep potentials with attractive tails vanishing faster than
1/r2 asymptotically [Phys. Rev. A 84, 032701 (2011)]. As an addendum to that work, we reformulate its key result, i.e., the formula for the scattering phase shift ${\ensuremath{\delta}}_{0}$, in such a way that the contributions independent of the short-range influence of the full potential are explicitly expressed in terms of the amplitudes for transmission through and quantum reflection by the nonclassical region of the potential tail.