the stability of a nucleus is determined by the value of the binding energy per nucleon... the larger the value the more stable the nucleus. to investigate the nuclear force and the nature of the fundamental particles, the nucleus needs to be disrupted. to do this energy must be put into the nucleus using particle accelerators to probe inside atoms.
particle accelerators produce beams of very high-energy particles. beams of very high-energy particles are useful matter probes for two main reasons. firstly, to disrupt the nucleus and secondly, the higher the energy (and therefore velocity) of a particle, the smaller the de broglie wavelength. the smaller the de broglie wavelength, the better the resolving power of a beam of such particles.
there are many different types of particle accelerator: the van de graaff accelerator used to accelerate protons, deuterons & a-particles; the cyclotron, synchro-cyclotron, synchrotron and linear accelerator used to accelerate a variety of charged particles; and the Betatron used to accelerate electrons.
basically, that's it.