It could be said that a neutron is the first member of the periodic table, element-zero, but having no protons, it would have no electrons either, and this would make it a most unusual element, incapable of forming chemical bonds with anything, for it has no electrons. It would also be the first radioactive element! Although heavier isotopes of element zero (n-1) with 2 or 3 neutrons (n-2 and n-3) could not possibly exist, there is some speculation that n-4 with 4 bound neutrons could exist due to a possible alliance between the constituent quarks of the four neutrons. That magic number 4 again. Others are not so sure. Finding out could shed some light on the mysterious ways in which neutrons interact with other neutrons within the nucleus of much heavier elements, because here there are no protons to confuse the issue, just pure neutron matter. The stuff that neutron stars are made of, but, with neutron stars, it is the additional gravity of zillions of neutrons huddled all together which stabilise the mass against the radioactive decay that a free neutron would otherwise undergo.

Many nuclides with an excess of neutrons have a few of the neutrons circulating around the core nucleus as a neutron halo. Beryllium-14 is one such nuclide. This unstable isotope has 4 protons and 10 neutrons, with either two (or some people think four) of the ten neutrons in a neutron halo. It was whilst smashing beryllium-14 nuclei at a carbon target that researchers were surprised to find four neutrons spilling off beryllium-14 in the same direction at the same time, leaving stable beryllium-10. They were expecting the neutrons to depart in differing directions. This fuelled speculation that bound tetra-neutrons were being emitted, which would be a very novel form of radiation if correct.

It is also expected that helium-8 would have four of its six netrons orbitting the nucleus as a tetra-neutron grouping.

Because of the Pauli Exclusion Principle, no two bound entities can have the same quantum state. In a helium-4 nucleus, with two neutrons and two protons, the pairs of neutrons have different spins, up and down. The same is true of the two protons. But with tetra-neutron, this would be impossible, two of the neutrons would have to spin in the same direction, which is forbidden. But they could have the same spin-two neutrons had slightly higher energy levels that the first two, but according to calculations such an arrangement should be unstable without some un-known force holding them more tightly together. But neutrons are very poorly understood because their short halflife (887.6 seconds) allows in-sufficient time for detailed study, and tetra-neutrons cannot be ruled out entirely.