A very straight forward way to do that is to have a world environment node with bloom enabled. You will most likely need to tweak the settings so that it looks great along with the scene. A little bit of bloom goes a long way.
If that's not working out for you, you can give the particle system a second mesh. This second one shall be a billboard which is either unshaded or emissive, has an add blend mode, and has some sort of halo texture that shall be you glow. It's main advantage over a bloom effect is that it has more artistic freedom, and you can customize the halo glow as you wish.