tvöfrafernd (double magic foursome, alpha particle)

A name for the alpha particle could be fjóreind, fereind or even simply fernd in the same fashion as tvennd was mentioned in the additional meaning of "deuteron" (heavy-water hydrogen nucleus) (Arngrímur Sigurðsson, Íslensk orðabók til að hafa við höndina).
But there's a better one: tvöfrafernd, consisting of tvöfra- (double magic, a contraction of tvö- and töfra- (magic) and fernd (foursome). http://en.wikipedia.org/wiki/Magic_number_(physics)
The term tvöfrungur (double magic one, a magic nucleus) can be used to designate "alpha-radiation" since the other magic nuclei oxygen-16 (16O), calcium-40 (40Ca), calcium-48 (48Ca), nickel-48 (48Ni) and lead-208 (208Pb) don't form a "type of radiation".  "Alfageislun" could become more purely icelandic "tvöfrungageislun",  "ferndagaislun", tvennageislun (tvenna- is the genitive plural of tvennur and stands for "of two pair", which indicates the two protons and two neutrons in the alpha particle).

alpha particle: fereind, fjóreind, emblukjarni (helium is the femine part, the "embla" (first woman in Scandinavian mythology) of the two original gases because it is the central element in the most important nucleosynthesis processes, it is a mother-element. The chemically vigourous hydrogen could be viewed as "askur"), tvöfrafernd, tvöfratvennur.

alpha radiation: tvöfrungageislun (radiation of the double magic particle, which can here only refer to alpha-radiation, there is no O-16 or Ca-48 radiation), ferndageislun (radiation of foursomes),
The oxygen-burning process is the last nuclear reaction in the star's core which does not proceed via the alpha process.

triple-alpha process (formation of carbon-12 by 3 alpha particles): þvöfrungaþreföldun, þrjálfun (þrí + alfa = þrjálfa (verb denoting the fusion of three alfa particles, þrja- is not one of the declension forms of þrír so it sounds akward an unnatural and for that reason I umlauted the "a": þrjálfa, the noun derivation of which is þrjálfun)

helium-3:
1) þrjórloft (þrjór- from þrí- (refering amount of nuclons) + fjór- (four, the amount of nucleons in normal, much more abundant He-4.  This contraction of two numeral derivations is an Icelandic answer to the alternatively used term "trialphium", tri- (three) + alpha-particle (which consists of four nucleons + -ium (suffix denoting chemical elements).  See http://en.wikipedia.org/wiki/Helium-3
2) valeðalvetni (strange noble hydrogen)
3) þrenndareðalloft (threesome noble gas)

helion (helium-3 nucleus): þrjóreind (þrjór- from þrí (refering amount of nuclons) + fjór- (four, the amount of nucleons in normal, much more abundant He-4)