The s-Process

We have seen how the elements up to iron can be produced by fusion reactions and by nuclear statistical equilibrium in stars. But what of the elements beyond iron? They cannot be produced in the same way because the Coulomb barriers become so large that extremely high temperatures would be required to force heavier nuclei to react. These high temperatures would produce a bath of photons having such high energy that they would disintegrate any heavier nuclei that were formed.

Neutron Capture
Thus, another mechanism must be responsible for producing heavier elements. The key is the capture of neutrons on nuclei to build heavier nuclei. Because neutrons are electrically neutral, they do not have a Coulomb barrier to overcome, permitting reactions to take place at low enough temperatures that the newly formed heavy nuclei will not be dissociated immediately by high energy photons. There are two basic neutron capture processes that can produce heavy elements, the s-process and the r-process. We discuss the s-process first.

Beta Decay
Neutron capture by itself cannot produce all the heavy elements because adding neutrons to a nucleus increases its mass number, but not its atomic number. That is, the isotope changes, but the element remains the same. But many nuclear isotopes are unstable to beta decay: either β+ decay, which converts a proton to a neutron, or β- decay, which converts a neutron to a proton (we discussed beta decay in conjunction with the PP chain in Chapter 18). Thus, we can build up heavy elements by neutron capture if we intersperse the neutron captures with beta decays to convert some of the neutrons to protons and increase the atomic number.

Segrè Charts
Two important concepts in understanding element production in stars are the Segrè chart (also called the chart of the nuclides) and the valley of beta stability. The Segrè chart is named in honor of Italian-American physicist Emilio Segrè, who made important contributions to the early development of both nuclear physics and elementary particle physics. It is an array of all possible isotopes of the elements with a little box for each isotope and with the boxes arranged in a 2-dimensional array so that proton number (atomic number) increases vertically and neutron number increases horizontally. A small part of a Segrè chart is shown in the figure adjacent right.

Thus, in such a chart each horizontal row corresponds to all possible isotopes of an element, while each vertical row corresponds to all different elements having the same number of neutrons. Because of this arrangement, isotopes of different elements having the same mass number occur on lines slanting downward diagonally from left to right. For example, note the diagonal line of isotopes in the adjacent figure having mass number 58.

The Valley of Beta Stability
The valley of beta stability is the region of the Segrè chart where the nuclei that are stable against radioactive decay reside. It is termed a "valley" because these nuclei have lower masses than their neighbors, so if one plots the masses the most stable nuclei lie in a valley. The following figure is a chart of the nuclides that marks the stability valley in orange.

For low masses, the stability valley corresponds approximately to equal numbers of protons and neutrons, but for heavier isotopes the number of neutrons becomes larger than the number of protons for the most stable isotopes. For example, we see from the above figure that for proton number 80 the most stable nuclei have neutron number around 120.

Drip Lines
Also marked on this graph are the proton and neutron drip lines. Isotopes that are not in the stability valley but that lie between the drip lines are unstable to radioactive decay, but they have half-lives such that they can at least exist for short periods of time before they decay. For nuclei outside the neutron drip line, the binding is so weak that neutrons can be emitted spontaneously. That is, neutrons appear to "drip" out of nuclei (the term "drip" is inspired by the jagged shape of the drip line, which looks like paint dripping on a vertical surface). Likewise, for nuclei outside the proton drip line, protons can "drip" out of the nuclei. Thus, for the most part, only nuclei lying between the drip lines are stable enough to be important in element production processes.