3d heat profile with opacity I would like to define a 3d, spherically symmetric, profile for objects that changes colour and loses opacity as move away from the centre. Essentially I want a 3d heat map centred on the object. The idea is that if I place many of these objects near each other, than they will blend seamlessly, i.e. that instead of overlapping, the space in between them will get the colour and opacity that is the sum of the two. 

Is this possible in blender? 

Edit for some figures:

So, firstly what I'd like to is paste a 3d profile on to all my objects. Something like this but in 3d:

I'd like the opacity to follow the same or a similar gradient as the colour in the above image. So that you can kind of see through the edges of the objects, but not the centre.

Then I'd like to add many objects but I'd like them to combine like this:

Notice how one object doesn't overlap the other, rather they blend seamlessly, and the brightness at points between them is the sum of the brightnesses from each individually.
First, give each of your objects a white volumetric emission shader.  The strength doesn't really matter that much as long as you use the same material on every object so the relative density is consistent.

For the objects themselves I am using a collection of Metaballs.  Meta-objects will "blend" into each other similarly to what you are describing.



Now set set your background color to black and render.  This will result in the following black and white map.



Next jump over to the compositor to remap this to the color gradient you want.  First plug the render into a Normalize node to remap the range of the render to [0,1].  Now run that output through a Color Ramp node and set up whatever gradient you want.

I also found that it gives a result closer to your reference images if you also add a small amount of blur.



The result looks like this: