  High energy collision of massive bodies is investigated without fine tuning.
We study multiple collisions of two spherical concentric shells in a
gravitationally bound system and calculate the center of mass energy between
the shells. We solve the equation of motions for two shells without imposing
any fine tuning of the initial parameters. In this bound system, the shells
collide many times and these motions are highly nontrivial due to chaotic
behavior of the shells. Consequently, the center of mass energy for each
collision varies nontrivially and even reach almost its theoretical upper
limit. We confirm that a significant proportion of the theoretical limit is
automatically achieved during multiple collisions without fine tuning. At the
same time, we also study shell ejection from the system after some collisions.
If the initial shell's energy is large enough, multiple collisions may cause
one shell to accumulate energy so that it escapes to infinity, even though two
shells are initially confined in the system. The ejection is caused by multiple
collisions inducing nontrivial energy transfer between the shells. The relation
between the maximum center of mass energy and the energy transfer causing the
shell ejection is also discussed.
