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The anti-particle corresponding to a proton or an electron is a particle with an equal mass, but an opposite charge. So what is the anti-particle corresponding to a neutron (which does not possess a charge)? And if it is just another neutron, will its collision with the original neutron be as destructive as the collision of a proton with an anti-proton or an electron with an anti-electron?

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Charges come in many different forms, not just electric/magnetic. At least one has the weak isospin and hypercharges (which encompasses the usual electromagnetic ones) and colour charges. All these must be reversed for particles and their antiparticles. –  genneth Jun 2 '12 at 14:29
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The anti-particle corresponding to a neutron is an anti neutron!

The neutron is made up of one up quark and two down quarks. The anti-neutron is made up of an anti-up quark and two anti-down quarks. Both have zero charge because the charges of the quarks within them balance out.

You are correct that elementary particles with no charge are often their own anti-particles. These tend to be vector bosons; for example the photon and the Z boson are their own anti-particles. The W$^-$ and W$^+$ are each other's anti-particles. It's a bit more complicated with the gluons because they carry a colour charge.

Amongst the fermions there are no particles known that are their own anti-particles. If such particles exist they would obey the Majorana equation and these theoretical particles are known as Majorana fermions.

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sorry, you have to edit this, there are antineutrinos after all, whole experiments have been run with antineutrino beams! en.wikipedia.org/wiki/Antineutrino#Antineutrinos –  anna v Jun 2 '12 at 14:15
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@annav: the Wikipedia article says: "Because antineutrinos and neutrinos are neutral particles it is possible that they are actually the same particle. Particles which have this property are known as Majorana particles. If neutrinos are indeed Majorana particles then the neutrinoless double beta decay process is allowed. Several experiments have been proposed to search for this process." –  John Rennie Jun 2 '12 at 14:18
    
Good answer. I think you missed a couple "anti-" towards the end there. –  Colin K Jun 2 '12 at 14:18
    
@ColinK: oops, thanks :-) –  John Rennie Jun 2 '12 at 14:21
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Antineutron neutron annihilation is similar to antiproton proton annihilation as far as the end products are concerned . Since there is about 2 GeV of energy from rest masses ( quarks have very small masses) there is energy available even with annihilation at rest to create pions and kaons with recombining the quarks to the appropriate format and getting strange antistrange quarks from the gluon sea. If a quark meets an antiquark head on it is more probable to go into gluons than gammas, as the strong constant is orders of magnitude larger than the electromagnetic one. –  anna v Jun 2 '12 at 19:38
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