redirecting after domain change

[chrisuk]

I have a pr6 site that has changed its name and domain name, the new name and site is pr5 now.

Both domains, old and new resolve to the same place in the browser and are on the same ip. The old domain name is not using any redirects, it is running as it always has been.

Thus the new domain name is not directly benefiting from the Pr6 and inbound links that the old domain had. What therefore is the best way to say to Google that the old site and domain is actually the new.

I guess a redirect but what kind would do the best job in this situation? Or is there any benefit to leaving things exactly as they are?

Thanks