Hey Knobbynobbes -
So I have reproduced you Material and Particle system and I can see a little bit of a fuzzy edge, but it is honestly not extreme and seems more to be caused by the refresh rate and animation on my screen than a problem with the system or material.
That being said, I did try the same particle system using a White Dot texture as opposed to the Radial Gradient function and it got a marginally sharper result, but not enough to be of significant note. My white dot texture was 256x256 which is still huge for a particle system, I normally work in much smaller texture sizes. If it is a concern though you could try to test the results with a much larger texture, but it will be a performance hit which may make it not worth it.
Thanks
Eric Ketchum