Gamow Peak

The optimal energy point at which most nuclear reactions occur in stars is called Gamow peak (in English Gamow peak). Its formula was calculated by George Gamow in 1928. The fusion reactions that occur in the cores of stars occur thanks to the tunnel effect, a phenomenon that allows colliding particles to jump over the strong potential barriers that separate them. The peak occurs as a result of the combination of two factors. On the one hand the Maxwellian statistical mechanical factor or Boltzmann factor. This gives us the probability that a particle found at a temperature T has an energy E. Logically, the probability decreases the higher the energy. On the other hand is the penetration factor of the Coulomb barrier.

• Boltzmann Factor: ${displaystyle expleft(-{frac {E}{kT}}right)}$

Where k It's Boltzmann's constant, E energy and T temperature.

• penetration factor: ${displaystyle expleft(-{frac {b}{E^{1/2}}}}}$

Where b is a parameter that results from the interaction between the two particles (a and x) and depends on what kind of particles they are. It is calculated as follows:

${displaystyle b=pi (2m)^{1/2}{frac {Z_{a}e^{2}{hbar }}}=31,28cdot Z_{a}Z_{x}{x}{left({frac {A_{x}}{A_{x}{A_{a_{x}{x}}{1⁄2}}}}{x}}}}{right$

Where A represents the masic number and Z the atomic number.

The Gamow curve therefore represents the total probability that two particles with energy E and temperature T fuse. This probability will logically be the result of the product of both factors whose function will have a maximum that will be the aforementioned peak.

• Gamow curve according to E (Gamow factor): ${displaystyle expleft(-{frac {E}{kT}}}}-{frac {b}{E^{1/2}}}}{right)}$

The height of Gamow's peak is very sensitive to temperature. Small increases in this cause large increases in the probability of fusion.