Tips and Techniques/Soft Particle Regions
From VFXPedia
To soften the borders of a particle region, used for emission or for defining a particle force in space, you can apply a high-frequency animation to its size.
For instance, you can assign a Shake modifier with extremely low Softness parameter to a Cube region's Width, Height and Depth:example composition
Or alternatively, shake the Cube's X/Y/Z Offset parameters.
Similarly, you can soften a Sphere, Rectangle or Bezier region.
But animating it's shape with a modifier may give you more freedom.
A Mesh region can be smoothed either by shaking its position with an additional Transform3D or by applying a shaky Displacement3D with an arbitrary map.