Re: How does the immune system get to antigenic core of bacteria or virus?

In order to react to core antigens, the immune system has to recognize them. It seems paradoxical that something that is hidden inside of a virus can be recognized by the immune system, but the best direct evidence that such recognition happens is the presence of anti-core antigen antibodies in individuals infected with hepatitis virus (see, http://www.hbvadvocate.org/hepatitis/Basics/HEP%20B%20BASICS%20antigens% 20antibodies.pdf).

The answer comes from the way in which immune system processes and presents antigens. Basicly, antigen presenting cells ingest (or are infected by) a pathogen, process its proteins (degrade them and cut them to pieces) and present these pieces to T lymphocytes (aka, T-cells).
See, http://en.wikipedia.org/wiki/Antigen_processing, and http://en.wikipedia.org/wiki/Antigen_presentation for details.

Thus, any protein molecule of a pathogen, including its core antigens, can potentially be presented by antigen-presenting cells.