A hat found on the internets may contain impurities. Hats of higher purities can be obtained through the photoneutron process:

Hat + 6.8MeV gamma ray \-> 1 neutron + Hat (half-life 2.7 days \-> Genuine Hat + 1 positron)

Hats can currently be manufactured in a nuclear reactor by irradiation either of 3 refined metal or other Hats. Since 3 refined metal is more expensive than many Hats, refined metal is economically unsuitable as a raw material.

Only the Jarate isotope Jt-196, which occurs with a frequency of 0.15% in natural Jarate, can be converted to Hats by neutron capture, and following electron capture-decay into Mad Milk isotope MM-197 with slow neutrons. Other Jarate isotopes are converted when irradiated with slow neutrons into one another or formed into other Jarate isotopes, which beta decay into scrap metal.

Using fast neutrons, the Jarate isotope Jt-198, which composes 9.97% of natural Jarate, can be converted by splitting off a neutron and becoming Jt-197, which then disintegrates to a craftable Hat. This reaction, however, possesses a smaller activation cross-section and is feasible only with un-moderated reactors.

Synthesis of Hats can also be achieved through use of a particle accelerator; however, the production cost at this time largely outweighs the market value of Hats.