Nuclear Synthesis of the Elements

Overview: What “Nucleosynthesis” Means

“Nuclear synthesis of the elements” (or nucleosynthesis) describes how the chemical elements and their isotopes are built from protons and neutrons in different astrophysical and cosmological environments. In contrast to ordinary chemical reactions, these are nuclear processes: they change the composition of nuclei and therefore can create new elements.

In this chapter we focus on where and how elements form in the universe, and which processes are responsible for the observed pattern of light and heavy elements. Details of nuclear forces, nuclear stability, or generic nuclear reactions are treated in other chapters of “Nuclear Chemistry”.

Key questions here:

• Which processes create which elements?
• Under what conditions (temperature, density, time) do they occur?
• How does this explain the distribution of elements in the universe?

Primordial Nucleosynthesis: Formation of the Lightest Nuclei

Conditions in the Early Universe

Shortly after the Big Bang, the universe was extremely hot and dense. As it expanded, it cooled. There was a limited time window in which nuclear fusion could proceed before the matter became too dilute and too cool.

Important aspects:

• Main building blocks: free protons ($p$) and neutrons ($n$).
• Duration of effective nucleosynthesis: from a few seconds to a few minutes after the Big Bang.
• After that, the temperature and density dropped so much that further fusion reactions essentially ceased.

Sequence of Light Element Formation

The overall picture of Big Bang nucleosynthesis (BBN):

1. Neutron–proton ratio is set

Weak interactions kept $n$ and $p$ in equilibrium:
$$n + \nu_e \rightleftharpoons p + e^- \quad \text{and} \quad n + e^+ \rightleftharpoons p + \bar{\nu}_e$$

As the universe cooled, these reactions froze out, leaving a neutron-to-proton ratio of roughly $n/p \approx 1/6$ to $1/7$, further reduced by neutron beta decay:
$$n \rightarrow p + e^- + \bar{\nu}_e$$

2. Formation of deuterium (the “deuterium bottleneck”)

First bound nucleus with more than 1 nucleon:
$$p + n \rightarrow \, ^2\text{H} + \gamma$$
($^2\text{H}$ is deuterium; $\gamma$ is a photon.)

At very high temperatures, deuterium is quickly destroyed by energetic photons:
$$^2\text{H} + \gamma \rightarrow p + n$$

Only when the universe cooled below a critical temperature could deuterium survive long enough to act as a stepping stone to heavier nuclei. This delay is called the deuterium bottleneck.

3. Build-up to helium and a little bit of other light nuclei

Once deuterium is stable, further reactions proceed rapidly:

• $$^2\text{H} + p \rightarrow \, ^3\text{He} + \gamma$$
• $$^2\text{H} + n \rightarrow \, ^3\text{H} + \gamma$$
• $$^3\text{H} + p \rightarrow \, ^4\text{He} + \gamma$$
• $$^3\text{He} + n \rightarrow \, ^4\text{He} + \gamma$$

Result: most available neutrons are incorporated into $^4\text{He}$ (alpha particles), because $^4\text{He}$ is particularly stable.

Trace amounts of deuterium, $^3\text{He}$, and $^7\text{Li}$ (and possibly a bit of $^7\text{Be}$) are also formed via reaction chains such as:
$$^3\text{He} + ^4\text{He} \rightarrow \, ^7\text{Be} + \gamma$$
$$^3\text{H} + ^4\text{He} \rightarrow \, ^7\text{Li} + \gamma$$

4. No significant production of heavier elements

Further fusion is strongly hindered because there are no stable nuclei with mass numbers $A = 5$ or $A = 8$. For example:

• $^5\text{He}$ and $^5\text{Li}$ are unstable.
• $^8\text{Be}$ is extremely short-lived.

In the rapidly expanding and cooling universe, there is not enough time and density to bridge this “mass-5 and mass-8 gaps” efficiently.

Primordial Element Abundances

The outcome of BBN is:

• About 75 % hydrogen (by mass; mostly $^1\text{H}$).
• About 25 % helium-4 ($^4\text{He}$) by mass.
• Trace amounts of:
• Deuterium ($^2\text{H}$)
• Helium-3 ($^3\text{He}$)
• Lithium-7 ($^7\text{Li}$)

Heavier elements (with $Z > 3$) are practically absent from primordial nucleosynthesis. Their creation is dominated by processes in stars and explosive events, discussed below.

Stellar Nucleosynthesis: Element Formation in Stars

After the first generations of stars formed from primordial gas, new nucleosynthesis environments arose. Inside stars, high temperatures and pressures enable long-lasting nuclear fusion. Different stages of stellar evolution support different fusion chains.

Hydrogen Burning: Chains to Build Helium

The first main energy source of stars is the fusion of hydrogen to helium. Two main pathways are important:

Proton–Proton Chain

Dominant in stars like the Sun (relatively low core temperature compared to massive stars). Simplified net reaction:

$$4\,^1\text{H} \rightarrow \, ^4\text{He} + 2e^+ + 2\nu_e + \gamma + \text{energy}$$

The detailed path involves steps such as:

• $$^1\text{H} + ^1\text{H} \rightarrow \, ^2\text{H} + e^+ + \nu_e$$
• $$^2\text{H} + ^1\text{H} \rightarrow \, ^3\text{He} + \gamma$$
• $$^3\text{He} + ^3\text{He} \rightarrow \, ^4\text{He} + 2\,^1\text{H}$$

CNO Cycle

In hotter, more massive stars, the carbon–nitrogen–oxygen (CNO) cycle becomes the dominant hydrogen-burning process. Here, pre-existing C, N, and O nuclei act as catalysts to convert hydrogen into helium without being consumed overall.

A simplified overall reaction is still:
$$4\,^1\text{H} \rightarrow \, ^4\text{He} + 2e^+ + 2\nu_e + \gamma$$

But the cycle passes through isotopes such as $^{12}\text{C}$, $^{13}\text{N}$, $^{14}\text{N}$, $^{15}\text{O}$, etc.

The CNO cycle does not create carbon from scratch; it primarily operates once some C, N, O are already present (from earlier nucleosynthesis episodes in the universe).

Helium Burning: Creating Carbon and Oxygen

Once hydrogen is exhausted in the stellar core, the star contracts and heats up. At higher temperatures, helium fusion (helium burning) begins. The key process is the triple-alpha process:

1. Two helium-4 nuclei form beryllium-8:
   $$^4\text{He} + ^4\text{He} \rightleftharpoons \, ^8\text{Be}$$
   $^8\text{Be}$ is unstable and quickly decays back, but in a dense, hot core, it can interact before decaying.
2. A third helium-4 nucleus is captured before $^8\text{Be}$ decays, forming carbon-12:
   $$^8\text{Be} + ^4\text{He} \rightarrow \, ^{12}\text{C} + \gamma$$

This process is extremely sensitive to an excited state (resonance) in $^{12}\text{C}$, which enhances the reaction rate and is crucial for significant cosmic carbon production.

Further helium capture can produce oxygen:
$$^{12}\text{C} + ^4\text{He} \rightarrow \, ^{16}\text{O} + \gamma$$

Thus, helium burning is the main source of carbon and oxygen, two of the most important elements for life and planetary chemistry.

Advanced Burning Stages in Massive Stars

Stars significantly more massive than the Sun (roughly $>8$ solar masses) can ignite additional fusion stages after helium burning, each stage requiring higher central temperatures. These stages include:

• Carbon burning:
• $$^{12}\text{C} + ^{12}\text{C} \rightarrow \, ^{20}\text{Ne} + ^4\text{He}$$
• $$^{12}\text{C} + ^{12}\text{C} \rightarrow \, ^{23}\text{Na} + ^1\text{H}$$
• Neon burning:
• Involves photodisintegration and subsequent reactions, for example:
  $$^{20}\text{Ne} + \gamma \rightarrow \, ^{16}\text{O} + ^4\text{He}$$
• Oxygen burning:
• $$^{16}\text{O} + ^{16}\text{O} \rightarrow \, ^{28}\text{Si} + ^4\text{He}$$
• Silicon burning:
• A complex network of reactions (photodisintegration, $\alpha$-captures, proton and neutron captures) ultimately yields nuclei up to the iron group (e.g. $^{56}\text{Fe}$, $^{56}\text{Ni}$, $^{58}\text{Ni}$).

These advanced burning phases are relatively short-lived (down to years or even days) compared to the long hydrogen-burning main-sequence lifetime.

Why Fusion Stops Near Iron

Nuclear binding energy per nucleon reaches a maximum near iron and nickel. Up to iron, fusion of lighter nuclei generally releases energy. Beyond iron, further fusion would require an input of energy.

As a result:

• Normal stellar fusion processes naturally build elements up to roughly the iron group.
• Heavier elements require different mechanisms: mainly neutron-capture processes in special high-energy environments, such as supernovae or neutron-star mergers.

Neutron-Capture Processes: Building Heavy Elements

Heavier elements (beyond iron) are synthesized largely by adding neutrons to existing nuclei and then allowing some of those neutrons to beta-decay into protons. This is dominated by two main mechanisms:

• The s-process (slow neutron capture).
• The r-process (rapid neutron capture).

These processes lead to characteristic patterns of stable isotopes observed in nature.

The s-Process: Slow Neutron Capture in Evolving Stars

s-process stands for slow neutron capture relative to beta decay. Neutrons are captured at a rate such that unstable nuclei usually have time to beta decay before capturing another neutron.

Typical Sites

The s-process occurs mainly in:

• Asymptotic Giant Branch (AGB) stars – stars in a late evolutionary stage with helium-shell burning and strong convection.
• Sometimes also in helium-burning cores of massive stars.

Basic Mechanism

1. A seed nucleus (often near the iron group) captures a neutron:
   $$^{A}_{Z}\text{X} + n \rightarrow \, ^{A+1}_{Z}\text{X}$$
2. If the new nucleus is unstable, it can decay by beta decay:
   $$^{A+1}_{Z}\text{X} \rightarrow \, ^{A+1}_{Z+1}\text{Y} + e^- + \bar{\nu}_e$$
3. Repeating neutron capture + beta decay steps gradually moves nuclei along the valley of beta stability towards heavier and heavier elements.

Neutron sources in AGB stars can be reactions such as:

• $$^{13}\text{C} + ^4\text{He} \rightarrow \, ^{16}\text{O} + n$$
• $$^{22}\text{Ne} + ^4\text{He} \rightarrow \, ^{25}\text{Mg} + n$$

The s-process mainly produces stable isotopes of elements from around strontium (Sr) up to bismuth (Bi).

The r-Process: Rapid Neutron Capture in Explosive Environments

r-process stands for rapid neutron capture. Here, the neutron flux is so high that nuclei capture multiple neutrons faster than they can beta-decay.

Typical Sites

The exact astrophysical sites of the r-process were debated for a long time. Current evidence points strongly to:

• Neutron-star mergers (collisions of two neutron stars).
• Certain types of core-collapse supernovae may also contribute.

In these environments:

• Neutron densities can reach extremely high values.
• Temperatures are enormous.
• Matter is briefly in conditions where very neutron-rich nuclei can form.

Basic Mechanism

1. Seed nuclei (again often around the iron group) are bombarded with a huge flux of neutrons:
   $$^{A}_{Z}\text{X} + n \rightarrow \, ^{A+1}_{Z}\text{X} \quad (\text{repeated many times})$$
2. Nuclei move far away from the valley of stability into regions of very neutron-rich isotopes.
3. After the neutron flux subsides, these very unstable nuclei undergo a series of beta decays:
   $$^{A}_{Z}\text{X} \rightarrow \, ^{A}_{Z+1}\text{Y} + e^- + \bar{\nu}_e$$
4. Chains of decays eventually lead to stable nuclei.

The r-process is responsible for producing many of the heaviest elements, including:

• The lanthanides (rare earths).
• Much of the gold (Au), platinum (Pt), and uranium (U) in the universe.

p-Process and Other Specialized Processes

Besides the s- and r-processes, there are additional, less dominant nucleosynthesis channels:

• p-process: Produces certain rare, proton-rich isotopes (p-nuclei) that cannot be formed by neutron capture. Likely mechanisms include:
• Photodisintegration (gamma process): high-energy photons in supernovae knock out neutrons from heavy nuclei, moving them to proton-rich isotopes:
  $$^{A}_{Z}\text{X} + \gamma \rightarrow \, ^{A-1}_{Z}\text{X} + n$$
• Subsequent captures or reactions adjust the proton/neutron ratio.
• rp-process (rapid proton capture): Occurs under extreme conditions (e.g., in X-ray bursts on accreting neutron stars), where rapid proton captures and beta decays build increasingly heavier proton-rich nuclei.

These specialized processes fill in some missing isotopes not produced efficiently by s- or r-process alone.

Cosmic Recycling: How Nucleosynthesis Shapes the Universe

Element formation processes would not affect future generations of stars and planets if the products stayed locked inside stars forever. Astrophysical events act as dispersal mechanisms, spreading newly synthesized material into space:

• Stellar winds:
• Low- and intermediate-mass stars on the AGB phase lose mass via winds.
• These winds enrich the interstellar medium with carbon, nitrogen, s-process elements, and dust grains.
• Planetary nebulae:
• The outer layers ejected by dying Sun-like stars, dispersing their processed material.
• Supernova explosions:
• Massive stars end their lives in core-collapse supernovae.
• These explosions eject large amounts of elements up to iron (and some heavier) formed in the star’s core and shells.
• Supernovae also generate conditions for r-process nucleosynthesis (in some models).
• Neutron-star mergers:
• Eject neutron-rich matter which is rapidly processed by r-process reactions.
• Observational signatures (e.g., “kilonova” events) show strong production of heavy elements like gold, platinum, and lanthanides.

Over cosmic time:

1. The first stars form from nearly pure hydrogen and helium (plus traces of light elements) from Big Bang nucleosynthesis.
2. They synthesize heavier elements and expel them.
3. New generations of stars form from gas enriched with “metals” (in astronomy, all elements heavier than helium).
4. Planets, and eventually life, form from this chemically enriched material.

This ongoing cycle of formation, processing, and ejection explains why:

• Young stars in galaxies like the Milky Way contain more heavy elements than very old stars.
• The solar system contains a diverse array of elements up to uranium and beyond, each with a nucleosynthetic “origin story”.

Summary

• Primordial nucleosynthesis in the early universe produced mainly hydrogen, helium-4, and trace amounts of deuterium, helium-3, and lithium-7.
• Stellar nucleosynthesis in the interiors of stars builds elements up to the iron group through successive burning stages (H, He, C, Ne, O, Si burning).
• Neutron-capture processes extend nucleosynthesis beyond iron:
• The s-process (slow neutron capture) in AGB and other evolved stars forms many stable isotopes from Sr to Bi.
• The r-process (rapid neutron capture) in neutron-star mergers and some supernovae produces many of the heaviest elements, including gold and uranium.
• Additional processes (p-process, rp-process) account for specific proton-rich isotopes.
• Stellar winds, planetary nebulae, supernovae, and neutron-star mergers disperse these newly formed elements into space, enriching the interstellar medium and enabling subsequent generations of stars, planets, and ultimately life.