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Making the heavy elements

Iron captures neutrons. Slowly, in giant stars, each capture waits for the β decay and the flow hugs the valley of stability (s process). In a neutron flood the captures run far to the neutron-rich side until photodisintegration stops them (r process). Both stall at the closed neutron shells N = 50, 82, 126, but the r process meets them at lower Z, so after the decay back to stability its abundance peaks sit about ten mass units below those of the s process.

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r-process conditions

T₉

n_n

Waiting points (path nucleus at a closed shell)

Rendering

Why the r peaks sit lower

A closed neutron shell is a step down in S_n: in AME2020 the 83rd neutron is bound by 3.2 to 5.0 MeV less than the 82nd (pairing included); at N = 50 the step is 3.1 to 4.8 MeV and at N = 126 2.4 to 3.4 MeV (differences of measured S_n, every element where both are measured). Near stability the s process meets N = 82 at Xe to Sm (¹³⁶Xe to ¹⁴⁴Sm are stable), and its flow piles up there: the s peak at A ≈ 138.

The r process works where S_n ≈ S_a⁰, 2.9 MeV at the default setting (0.2 to 11 MeV over the full range of the sliders); at a few MeV no nucleus near stability is that weakly bound. There N = 82 is met by Z ≈ 40 to 50, and a run of elements waits at the same N while successive β decays raise Z (the vertical stretch of the path). At freeze-out each waiting point decays at fixed A, so the peak lands at A = Z + 82 ≈ 122 to 132, about ten units below the s peak. The same happens at N = 50 (A ≈ 76 to 80 against 86 to 92) and N = 126 (A ≈ 190 to 200 against 208).

What this page does not compute

The heights of the r columns are isotope shares: the Saha distribution inside each element, normalized to one per element. They are not element abundances. How much of each element there is depends on how long each chain waits for its β decays, and so on β-decay rates of nuclei that have mostly never been measured; without them the page does not predict the r-process abundance pattern, only where the path runs and where its waiting points decay to (Arnould, Goriely and Takahashi 2007, Sect. 4.1, Eqs. (26) and (27)).

The s path is drawn by a rule, not computed: a radioactive nucleus on it either decays or captures, never both. Real s-process branchings, where decay and capture compete, the exposure distribution and the abundances along the path are not modelled. The solar s/r split in the abundance panel is the published one.

Also left out: β-delayed neutron emission (it shifts the decayed mass down by one or two units), fission recycling beyond the actinides, neutron captures after freeze-out, excited states and ground-state spins in the partition functions.

Model and sources

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