Half-Life Theory: Will the Centers of Two Decaying Spheres Touch?

[AnthonyFB]

Suppose you have two similar particles that have gone through similar half life periods. They each have been reduced to practically infinitely small spheres. Within each sphere is a hollow space. They are both touching during a process in which they are constantly decaying, with two small particles remaining each reduction. The question I have is: will the center areas of the two spheres ever touch? According to modern half-life theory, and the fact that there will always be matter in between the outer shells and the shells surrounding the center spaces, the answer is no. However, my theory is that the centers will coincide due to the fact that the inner circle can never be in the exact center of each circle- it shifts to touch the outer limit.

 

[Borek]

Please describe the geometry more precisely (you can draw it and attach an image to your post). And please explain what happens to the products of decay.