How does quantum tunneling enable nuclear fusion in the Sun?

[Positron137]

I know that the Sun radiates vast amounts of energy partly due to nuclear fusion. I've also heard that nuclear fusion can occur in the Sun due to quantum tunneling. I'd like to know how the process of quantum tunneling in the Sun allows nuclear fusion to take place. Thanks!

 

[Bill_K]

This is because the thermal energy of the protons in the solar interior is not enough (by a factor of 1000) to overcome their Coulomb repulsion. Consequently in order to fuse they must tunnel through the barrier. See for example http://www.astro.soton.ac.uk/~pac/PH112/notes/notes/node111.html and the next pages after.

 

[Positron137]

Thanks! I know this is a naive question, but I just wanted to clarify, what exactly is the "barrier"?

 

[Bill_K]

Sure, as the reference I cited explains, the two protons being both positively charged repel each other. This means the potential energy between then is positive and gets larger and larger as they get closer together. This is the potential barrier. But the total energy PE + KE remains the same, and eventually they get so close that KE = 0.

If they were classical particles that would be as close as they could get, but quantum particles can tunnel into the region even where KE < 0, and come out the other side (the well). This only happens with a certain small probability, but when it does it let's them get close enough together to fuse and make a nucleus of deuterium.

 

[Positron137]

Ah ok. I understand that on Earth, to create nuclear fusion, we have to attain temperatures much higher than the interior of the Sun (if I am correct). But the Sun can achieve nuclear fusion at its temperature probably because it contains a much larger mass of hydrogen under high pressures, and can sustain that amount for a long time. SO with that much mass of hydrogen, the small probability becomes a very likely event. Is that a correct interpretation?

 

[ThereIam]

Yeah, it's probably better language to word it as a "greater number of hydrogen atoms" rather than a "larger mass of hydrogen", but that is the gist of it.

 

[Crazymechanic]

Pretty much accurate yes , basically you can go two ways , either you have extremely high temperature which assures that each of the particles has a kinetic energy high enough to fuse with other particle upon a collision, or you can go with a lower more "humane" temperature but a lot of pressure.
Now in the more pressure less temperature case the tunneling effect is more often.

 

[IttyBittyBit]

The sun has a very low ratio of surface area to volume, hence energy loss by radiation is limited. Thus temperatures in the interior of the sun can reach millions of degrees even though the rate of heat production is very slow (the rate of heat production in the human body, for instance, is much higher).

 

[Positron137]

Ah ok. Thanks guys!