Q: To what extent can I send an e-print version of the accepted paper?

Congratulations on getting accepted! As we understand it, your query deals with possible copyright issues associated with sharing e-print versions of your accepted paper that is not open access.

In general, there are two broad scenarios pertaining to copyright issues: either you have just given the publisher a license and retain the copyright, or you have assigned copyright to the publisher. In the former case, you are free to pass a copy to a third party. In the latter case, it depends what permissions the publisher has given back to you. But even if the publisher has given you no permissions, exceptions to copyright around the world usually mean you are free to pass a copy directly to a third party if it is for the purpose of non-commercial research or private study. That is, privately sharing copies of your papers with your colleagues, students, and grant reviewers who request or need a copy is typically allowed for all formats of the publication and is not subject to an embargo period.

On the contrary, "public sharing" via a depository such as Research Gate, departmental or personal websites is often subject to embargo periods and other regulations which differ from publisher to publisher. Unfortunately, each publisher has its own set of conditions and restrictions, often difficult to really understand or appreciate. For example, Elsevier's policy for Accepted Author Manuscript (AAM) says that authors retain the right to use the accepted author manuscript for personal use, internal institutional use and for permitted scholarly posting provided that these are not for purposes of commercial use or systematic distribution. Most journals, though, recommend that authors should link any preprint versions shared to the formal version in the journal through a DOI.
As a precaution, we would recommend notifying the publishing journal of any distribution and confirming with them whether sharing of the e-print version is permitted and to what extent.