Resolution with Gaussian point spread function

If you have a Gaussian PSF, then how can you determine resolution
(resolvability) using the Raleigh criterion? As I understand the
Raleigh criterion says the maximum of one PSF must sit on top of the
minimum of the neighbor for them to be "just" resolved. This is OK for
a sinc-like PSF but what about a Gaussian PSF which doesn't even have
a minimum?

.