Chain Reaction

In Physics by Brian Koberlein6 Comments

It is often said that we are made of star stuff.  Except for hydrogen, the atoms in our bodies were fused in supernovae, and in the cores of stars. What’s not often talked about is just how complex fusion is, and how difficult it is to do, even in the core of a star.  Take, for example, the seemingly simple fusion of hydrogen into helium, which is the primary energy source of our Sun.

A simple calculation of the Sun’s interior puts the temperature of the Sun’s core at about 3 million Kelvin. It is actually closer to 15 million Kelvin, and has a pressure more than 300 billion times that of Earth’s atmosphere at sea level.  At such a high temperature and pressure, you can imagine that hydrogen nuclei are slamming into each other all the time.  But simply having nuclei collide is not enough to make them fuse.  Hydrogen nuclei (protons) are positively charged, so the closer they get the harder they push each other away.  This repulsive force between nuclei is so strong that most collisions aren’t strong enough to overcome it.

The most common pp-chain. Credit: ATNF

Fortunately, they don’t have to overcome all the repulsive force.  Through an effect known as quantum tunneling, nuclei that get almost close enough can rely on quantum mechanics to get the rest of the way there. Not all close collisions result in quantum tunneling, but enough do that protons can fuse into helium 2 (also known as a diproton). Unfortunately, most of these helium 2 nuclei immediately decays into two protons.  Unlike the more common helium 4, helium 2 is incredibly unstable, so simple proton collisions do not produce stable helium. However, on rare occasions helium 2 will decay into deuterium, plus a positron and neutrino.  The neutrino quickly escapes the Sun, and the positron typically collides with an electron to produce gamma rays.

A deuterium nuclei consists of a proton and neutron, and is a stable isotope of hydrogen. So even though the formation of deuterium from proton collisions is exceedingly rare, deuterium can build up in the solar core.  Usually deuterium will collide with a wandering proton to create helium 3.  Helium 3 is a stable isotope, and thus can also build up in the Sun’s core.

Because helium 3 has two protons, it is very difficult for a proton to collide with helium 3 to produce lithium 4. Lithium 4 is also extremely unstable, so such a reaction wouldn’t be very useful.  Instead, what typically happens is a helium 3 nuclei will collide with another helium 3 to produce beryllium 6, which quickly decays into helium 4 and two hydrogen nuclei.

This process of protons to deuterium to helium 3 to helium 4 is one example of what is known as the proton-proton chain (or pp-chain).  It is the primary source of energy produced within the Sun’s core. There are other pp chains that are similar, as well as other fusion processes such as the CNO cycle that contribute to solar fusion. In larger stars there are further nuclear interactions that produce heavier elements.

So it is true that we are made of star stuff, but the process of making that star stuff takes some fairly complex nuclear physics.

 

Comments

  1. Hi Brian, I just want to have one thing confirmed. You said at one stage that the positrons are created and that they usually collide with electrons and get annihilated. That would mean that the pp-chain fusion process ‘eats up’ electrons over time.

    Is my understanding right that the electron supply comes from 4 electrons orbiting those 4 initial protons of the pp-chain (well not exactly those 4, but statistically spoken) and that 2 of them end up orbiting the helium 4 core at the end while 2 of them collided with positrons?

    1. Author

      Technically it does, but it also “eats up” protons by converting them to neutrons. The total charge (0) remains the same over the course of the process.

  2. Right, understood that one. Sorry, I have 2 follow up questions.

    1) So the energy being released through the whole pp-chain process is that annihilation radiation of the positron – electron collisions plus the ejected gamma ray when deuterium uses a proton to form helium 3? Does that mean that this energy summed up is roughly the same as the mass difference between 2 neutron and 2 protons multiplied by the square of light speed? – because a helium 4 core has 2 neutrons now while 2 of the initial protons are missing. I remember from my chemistry classes that there is some kind of binding energy so that comes on top of that.

    2) You said that helium 2 is extremely unstable and decays mostly into 2 protons again. They need to capture a positron and a neutrino to do that, isn’t it?

    If the answer of those 2 questions are to hard to post here then feel free to write another post 🙂 You were asking a few months back about topics to write about so here you go … I would be interested.

    1. Author

      If you look up pp-chain on wikipedia it lists the energy released in each reaction. It is related to the mass/energy equation. Helium 2 doesn’t need to capture anything to become deuterium. What happens is that protons (stable on their own) when bound together have a chance of one proton decaying into a neutron, positron and neutrino due to the weak interaction. If that happens, then the neutron stays bound to the proton, and the positron and neutrino escape. The half-life for that to occur is much longer than the simple two-proton decay, so most of the time it doesn’t happen. But occasionally it does, and it happens often enough for fusion to occur in the Sun.

  3. Any body knows how to calculate lifetime of He3 in this PP chain?

    1. It’s highly temperature senstaive and it’s about 100,000 years at the temperatures and densities at the center of the sun. Look at a book called “Principles of Strllar Evolution and Nucleosynthesis” by Donald D Clayton. He has all the pp-chains (their are actually 4 of them, it just the one mentioned here), CNO cycles and their rates as a function of temperature, density, and nucleon fraction

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