The existence of neutral nuclei has been a long-standing question in nuclear physics. Over the last forty years very different techniques have been employed in various laboratories for the search of multineutrons, mainly 3,4n, without success. All the techniques consisted of two stages, the formation and the detection of the multi-neutron, and the negative results were always interpreted as due to the extremely low cross-section of the reaction used to form the multineutron. Theoretically, ab initio calculations suggest that neutral nuclei are unbound. However, the uncertainties in many-body forces, the already relatively poor knowledge of the two-body n-n interaction, and in general the lack of predictive power of these calculations, do not exclude the possible existence of a very weakly bound 4n.“
Source : The European Physical Journal A - Hadrons and Nuclei volume 25, pages311–313(2005) (paywalled)
The 4n , cited above, is also known as the 'TetraNeutron'. A grouping of four neutrons, similar to the nucleus of helium, but with two neutrons replacing the two protons.
According to some research groups it cannot theoretically exist, and does not exist in the real world. Other groups maintain the opposite.
Several recent experiments have claimed to have detected (extremely short-lived) tetraneutrons - but the results are disputed by some researchers.
More details at Wikipedia
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