Undergrad Calculating conditions necessary for nuclear fusion

[PlanetGazer8350]

I would like to know if there is any formula for calculating the necessary conditions for certain elements to undergo nuclear fusion. I know that before the quantum tunnel effect was proposed, theoretically nuclear fusion reactions shouldn't occur in the Sun; with the increasing energy (affected by pressure, etc.), is there a way to find out the probability of x number of atoms crossing the 'barrier', to undergo nuclear fusion, given, i.e: z number of atoms?

For example, can you find out the conditions (pressure, temperature, etc.) necessary for having (this is just an example) 5 atoms of carbon-12, from 100 of them, of fusing with 5 atoms of hydrogen-1, from another 100?

 

[mfb]

theoretically nuclear fusion reactions shouldn't occur in the Sun

That is only true if you use wrong theories.

is there a way to find out the probability of x number of atoms crossing the 'barrier', to undergo nuclear fusion, given, i.e: z number of atoms?

Sure. Gamow factor is the keyword here.