Helium-4

The helium atom is the second simplest atom (hydrogen is the simplest), but the extra electron introduces a third "body", so its wave equation becomes a "three-body problem", which has no analytic solution. However, numerical approximations of the equations of quantum mechanics have given a good estimate of the key atomic properties of helium-4, such as its size and ionization energy.

The size of the ⁴He nucleus has long been known to be in the order of magnitude of 1 fm. In an experiment involving the use of exotic helium atoms where an atomic electron was replaced by a muon, the nucleus size has been estimated to be 1.67824(83) fm.^[4]

The nucleus of the helium-4 atom has a type of stability called doubly magic. High-energy electron-scattering experiments show its charge to decrease exponentially from a maximum at a central point, exactly as does the charge density of helium's own electron cloud. This symmetry reflects similar underlying physics: the pair of neutrons and the pair of protons in helium's nucleus obey the same quantum mechanical rules as do helium's pair of electrons (although the nuclear particles are subject to a different nuclear binding potential), so that all these fermions fully occupy 1s orbitals in pairs, none of them possessing orbital angular momentum, and each canceling the other's intrinsic spin. Adding another of any of these particles would require angular momentum, and would release substantially less energy (in fact, no nucleus with five nucleons is stable). This arrangement is thus energetically extremely stable for all these particles, and this stability accounts for many crucial facts regarding helium in nature.

For example, the stability and low energy of the electron cloud of helium causes helium's chemical inertness (the most extreme of all the elements), and also the lack of interaction of helium atoms with each other (producing the lowest melting and boiling points of all the elements).

In a similar way, the particular energetic stability of the helium-4 nucleus, produced by similar effects, accounts for the ease of helium-4 production in atomic reactions involving both heavy-particle emission and fusion. Some stable helium-3 is produced in fusion reactions from hydrogen, but it is a very small fraction, compared with the highly energetically favorable production of helium-4. The stability of helium-4 is the reason that hydrogen is converted to helium-4, and not deuterium (hydrogen-2) or helium-3 or other heavier elements during fusion reactions in the Sun. It is also partly responsible for the alpha particle being by far the most common type of baryonic particle to be ejected from an atomic nucleus; in other words, alpha decay is far more common than cluster decay.

 

The unusual stability of the helium-4 nucleus is also important cosmologically. It explains the fact that, in the first few minutes after the Big Bang, as the "soup" of free protons and neutrons which had initially been created in about a 6:1 ratio cooled to the point where nuclear binding was possible, almost all atomic nuclei to form were helium-4 nuclei. The binding of the nucleons in helium-4 is so tight that its production consumed nearly all the free neutrons in a few minutes, before they could beta decay, and left very few to form heavier atoms (especially lithium, beryllium, and boron). The energy of helium-4 nuclear binding per nucleon is stronger than in any of those elements (see nucleogenesis and binding energy), and thus no energetic "drive" was available to make elements 3, 4, and 5 once helium had been formed. It is barely energetically favorable for helium to fuse into the next element with a higher energy per nucleon (carbon). However, due to the rarity of intermediate elements, and extreme instability of beryllium-8 (the product when two ⁴He nuclei fuse), this process needs three helium nuclei striking each other nearly simultaneously (see triple-alpha process). There was thus no time for significant carbon to be formed in the few minutes after the Big Bang, before the early expanding universe cooled to the temperature and pressure where helium fusion to carbon was no longer possible. This left the early universe with a very similar hydrogen–helium ratio as is observed today (3 parts hydrogen to 1 part helium-4 by mass), with nearly all the neutrons in the universe trapped in helium-4.

All heavier elements—including those necessary for rocky planets like the Earth, and for carbon-based or other life—thus had to be produced, since the Big Bang, in stars which were hot enough to fuse elements heavier than hydrogen. All elements other than hydrogen and helium today account for only 2% of the mass of atomic matter in the universe. Helium-4, by contrast, makes up about 23% of the universe's ordinary matter—nearly all the ordinary matter that is not hydrogen (¹H).

• Big Bang nucleosynthesis

• Superfluid Helium-4 Interactive Properties
• Tur, Clarisse (2009), "DEPENDENCE OF s-PROCESS NUCLEOSYNTHESIS IN MASSIVE STARS ON TRIPLE-ALPHA AND ¹²
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  REACTION RATE UNCERTAINTIES", The Astrophysical Journal, 702 (2): 1068–1077, arXiv:0809.0291, Bibcode:2009ApJ...702.1068T, doi:10.1088/0004-637x/702/2/1068, S2CID 118483505