Improve Narrative

[evanberkowitz]

The authors should improve the narrative, particularly the introduction.

The authors should give particular care to formulating a coherent introduction. For instance, in the first paragraph of the paper, the authors should clarify that it is only at threshold (zero energy) that scattering is characterized by the scattering length. Should the intended meaning of the third paragraph be readily apparent? (It was not apparent to me.)

Another example is the first sentence of the fourth paragraph: "Such scale-free results must result from peculiar potentials". I for one would need a clearer description of the intended meaning.

[ckoerber]

Current draft (PR #43) made significant changes to the intro:

For example, addressing the referee comments, it now adds:

The effective range expansion (ERE), which depends on details of the interaction, describes the scattering of fermions at low energies.
The leading term of the ERE, the scattering length, dominates the scattering description of fermions close to the zero-energy threshold.
In three dimensions, if the range of the interaction becomes negligible compared to this scattering length, scattering details are energy independent, and it is possible to produce any amplitude unless otherwise restricted by the Wigner bound\cite{Wigner:1955zz, Phillips:1996ae, Hammer:2010fw}.

and

Even though scattering details of unitary systems are scale-independent, interactions describing such systems must fulfill specific requirements.