nuklea

Nuklea is the adjective, and it covers both fields the word covers in English: the physics one, as in nuklea energio and nukleaj armiloj, and the biological one, as in the nucleus of a cell. CERN is la Eŭropa Centro de Nuklea Esploro in Esperanto, which is as good a proof as any that the register works.

Its base has no page here yet. Nukleo, the nucleus itself, is a headword in the dictionaries and simply has not reached our frequency band; the adjective did, which happens more often than you would expect with technical vocabulary that arrives through journalism rather than through textbooks.

And the dictionaries would rather you used the native word. The Reta Vortaro's own remark on nukleo recommends kerno in general, atomkerno in physics and ĉelkerno in biology, all of which are transparent compounds of roots this course has already taught. That is the whole argument of science in Esperanto in miniature: Rule 15 lets an international root in whenever the world uses one, and the language's own machinery usually offers a clearer alternative that nobody quite adopts. Nuklea won because nukleaj armiloj is what the newspapers say.

Both are correct. Write atomkerno if you want to be understood by a beginner and nukleo if you want to be understood by a physicist, and expect to meet nuklea either way.