The s-process: from iron to lead

Nuclei with 50, 82 or 126 neutrons have closed neutron shells, the magic numbers of nuclear physics. They are reluctant to capture one more neutron: their capture cross sections are far smaller than those of their neighbours. Matter flowing along the path piles up in front of them like traffic at a narrowing. That is why the solar abundances show s-process peaks at strontium, yttrium and zirconium (N = 50), at barium, lanthanum and cerium (N = 82) and at lead (N = 126) [1]. On the chart above the three shells are the shaded columns.

In 1961 Clayton, Fowler, Hull and Zimmerman worked out how abundances build up along such a chain of captures [7]. Where the flow is steady, a nucleus that captures easily is used up quickly and stays rare, and one that captures reluctantly accumulates: the product of the cross section and the abundance changes only slowly between the closed shells, and drops in steps at them. Measured cross sections and the solar abundances of nuclei made only by the s-process test this picture, which is why the cross sections have to be known well.

Two kinds of stars run the s-process. Most of it happens in stars of one to three times the mass of the Sun near the end of their lives, when they have swollen into red giants; the rest in stars of more than about ten solar masses, before they explode. The first build nuclei all the way to lead, the second mostly up to strontium.

In the r-process, in a neutron-star merger or a similar explosion, nuclei capture neutrons far faster than they decay, and are pushed far to the neutron-rich side of the chart. When the neutrons run out they decay back, along lines of constant mass number, until each chain meets the first stable nucleus on its way. A stable nucleus that has a stable neighbour of the same mass and lower charge is therefore shielded: the r-process decays stop at the neighbour. If the s-process path passes through it, it is an s-only nucleus, made by the s-process alone. Examples are ¹⁴⁸Sm and ¹⁵⁰Sm, shielded by ¹⁴⁸Nd and ¹⁵⁰Nd, and ²⁰⁴Pb, shielded by ²⁰⁴Hg [1]. Their solar abundances measure the s-process directly, without the r-process mixed in.

Conversely, the most neutron-rich stable isotopes of an element are often bypassed by the s-process, because the isotope before them decays before it can capture. They are r-only nuclei, such as ¹⁵⁰Nd and ¹⁷⁶Yb. The rarest, proton-rich stable isotopes are reached by neither; they belong to the p-process. On the chart the s-only nuclei found by the rule are filled in orange.

In 1952 Paul Merrill found lines of technetium in the spectra of red giants of class S [9]. Technetium has no stable isotope, and even its longest-lived ones last a few million years, far less than the age of these stars: it had been made inside them, recently. It was the first direct sign that stars make elements, and the s-process makes ⁹⁹Tc on its way [1].

In 1987 grains of silicon carbide less than a micrometre across were found in the Murray meteorite, with isotopic compositions unlike anything formed in the Solar System [10]. They condensed in the winds of AGB stars before the Sun was born, and the krypton, strontium and barium trapped in them carry the s-process pattern of a single star, measured atom by atom in the laboratory [1].

In a star poor in iron the same neutrons fall on fewer seeds, so each seed captures more of them and the flow runs through to lead. Classical analyses of the solar abundances needed a third, strong component to make about half of the ²⁰⁸Pb; AGB stars of low metallicity supply it [1]. In 2001 three such stars were found that are more enriched in lead than in any other element heavier than iron, as the models predicted [11].

Some old stars show a mixture that neither the s- nor the r-process explains. When hydrogen is mixed into a hot helium layer, ¹³C forms and burns at once, and the neutron density climbs to about 10¹⁵ per cubic centimetre, between the s and the r values: the intermediate or i-process, first suggested by Cowan and Rose in 1977 [12, 13].

A few radioactive nuclei on the path live about as long as the wait for the next neutron: years to centuries. There the path forks. Some nuclei decay, some capture another neutron, and the share depends on the neutron density and, where the decay itself changes with the heat of the star, on the temperature. The abundances of the isotopes beyond such a branch point record the conditions inside the star that made them [1]. Three classic examples are marked A, B and C on the chart.

Radioactive branch points can now be measured directly, on samples made in reactors. ¹⁷¹Tm(n,γ)¹⁷²Tm, on thulium that lives two years, was measured at n_TOF and at SARAF; it captures 2.6 times less readily than the general-purpose libraries JEFF-3.3 and ENDF/B-VIII said [23]. ²⁰⁴Tl(n,γ)²⁰⁵Tl, on nine milligrams of thallium that lives almost four years, decides how much of the s-only ²⁰⁴Pb is made, and was measured for the first time in 2024 [24]. ⁹³Zr lives 1.6 million years: in the star it captures like a stable nucleus, and what is left of it decays later to niobium; ⁹³Zr(n,γ)⁹⁴Zr has been measured at n_TOF up to 8 keV [25].

Everything on this page rests on laboratory measurements of how readily each nucleus captures a neutron at the energies neutrons have inside a star, around 30 keV, the energy of a gas at about 350 million kelvin. Two kinds of experiment measure it: one times the flight of each neutron, the other irradiates a sample and counts what it has become.