Approaching someone outside my department for work experience I am a masters student at my university within the school of mathematical and science. 
Within this school there are two departments, the maths department and physics department.
These two departments are very close and tight knit especially at the postgraduate level. 
I am within the mathematical department. 
Within the physics department there are many professors that are part of a world leading research group at a top experiment and research centre in the world.

This research centre offers work experience/ internships.

I want to ask these professors for work experience at this research facility.

How can I approach them and ask them for this? 
How long shall I wait after the start of term to ask them?
Why not? Worst case, they tell you "no".

Just make sure you are able to prove you have the requisite skills and background, and willingness to come up to speed fast.