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Nucleosysthesis is usually broken into the following stages:

p-p chains: these are used to make helium-4 in the early universe. It relies on a proton being able to beta+ decay into a neutron and make a deuteron (proton + neutron), which picks up another proton to make helium-3... two helium-3's merge to and emit 2 protons and make helium 4. This takes billions of years. A proton has never been seen to decay this way in a lab.

Making of carbon: mass 5 and 8 are unstable so He4 + p or He4 + He4 occur but break up instantly. So we have something called the triple alpha process where 3 4He nuclei fuse into a resonant state (Fred Hoyle's Nobel prize circa 1960). This is a very difficult reaction. If you look at elemental abundances there is 100 times less carbon compared to Hydrogen and Helium.

After we have carbon we begin fusing stuff.. so we get protons added to stuff, as well as 4He's added. This is known as the 'burning stage'. This continues to about mass 56 (Iron, Nickel, Cobalt) where we break off to a new process because the nuclei are too positively charged to add more protons. The only option is to add neutrons. These occur in two processes.

The slow-capture process: A neutron is added every 1000 years or so, if the new nucleus is stable it will capture another neutron in another 1000 or so years, otherwise it will decay to something stable.. they decay is usually much faster than the time to capture a new neutron. The nuclei follow a very fixed path. This continues until just after lead at mass 208 where there is a gap of unstable elements... this where the s-process ends.

The rapid capture process: this is my thesis work... if there is a very high neutron density it is possible to capture many neutrons very quickly... Having lots of neutrons makes it unstable so it will decay every once in a while by converting a neutron to a proton (beta - decay) then it will add more neutrons and cycle between these steps. This produces elements up to the Uranium group (very heavy). The r-process is thought to occur over about 5 seconds.

There are three more processes using photo-disintegration, CNO cycle and rapid proton capture that i won't go into.

Methods used: Experimental nuclear physics measure the probabilities of these reactions occurring, and how they effect current ideas of nuclear theory. These reactions have tell-tale characteristics which need to be better understood. We can detect energy peaks in the suns light spectrum which are characteristic of certain reactions. So we can indirectly see reactions occurring. However, the more interesting stuff occurs in dying stars like red giants, white dwarves and supernovae.

Also, as we can only experiment relatively near the stable elements many scientists use computer models to predict what is going on using well defined statistics... these generally work well, but they are usually based on some assumptions. These are in a constantly state of flux as new theories occur frequently and old ones are corrected.

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