Ions are produced when an EM neutral atom gains EM charge by gaining or losing electrons, by collision with other charged particles or photons.

The study of such collisions is of fundamental importance with regard to the few-body problem (see article on few-body systems), which is one of the major unsolved problems in physics.


A fundamental difficulty in describing few-body systems is that the Schrödinger equation and the classical equations of motion are not analytically solvable for more than two mutually interacting particles even when the underlying forces are precisely known. This is known as the few-body problem.

All the underlying forces, EM, strong, weak and gravity are well known.

Therefore, any discrepancy found between experiment and theory can be directly related to the description of few-body effects. In nuclear systems, in contrast, the underlying force is much less understood. Furthermore, in atomic collisions the number of particles can be kept small enough so that complete kinematic information about every single particle in the system can be obtained experimentally. In systems with large particle numbers, in contrast, usually only statistically averaged or collective quantities about the system can be measured.


What I do not understand is, if we know the governing forces, and know the substructure of nucleons, like neutrons and protons, then why do we have this few body problem when dealing with QM systems that have large number of particles.

Yes I do understand that neutrons and protons are not only made up of three quarks, but an ever changing sea of quarks, anti-quarks, gluons, anti-gluons, that pop in and out of existence.

What I still do not understand is if we know the strong force, and QCD, then how come we cannot describe these systems.


  1. What is the few body problem really?
  • $\begingroup$ Are you asking why we don't need to consider the structure of the nucleus when calculating what happens during ionisation? $\endgroup$ – John Rennie Jul 14 at 14:16
  • $\begingroup$ @JohnRennie yes but is the few body problem about the ionization at all? it says that so. But then it says that even when we know the underlying forces, we cannot model what goes on inside. my question is more about when we try to consider the structure of the nucleus (and rather the neutrons and protons), then we can't really know what is going on inside it? Is the few body problem the same as not being able to model the inside of the neutron and the proton? $\endgroup$ – Árpád Szendrei Jul 14 at 14:32
  • $\begingroup$ @JohnRennie does the few body problem affect the ionization only? Or do we have a few body problem when we try to model the inside of a neutron or a proton, where though we know the QCD laws, we still cant model it? Or is the few body problem only for atom sized QM systems like when an atom gets ionized by a photon? $\endgroup$ – Árpád Szendrei Jul 14 at 14:35
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    $\begingroup$ I suspect the wikipedia article on ionization may be alluding to the fact that the N body problem does not have a closed form analytic solution when N>2. $\endgroup$ – David Hammen Jul 14 at 14:39

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