Gamow peak in thermonuclear reactions at high temperatures

The Gamow peak represents one of the most important concepts in the study of thermonuclear reactions in stars. It is widely used in order to determine, at a given plasma temperature, the effective stellar energy region in which most charged-particle induced nuclear reactions occur. It is of importance in the design of nuclear astrophysics measurements, including those involving radioactive ion beams, and for the determination of stellar reaction rates. We demonstrate that the Gamow peak concept breaks down under certain conditions if a nuclear reaction proceeds through narrow resonances at elevated temperatures. It is shown that an effective stellar energy window does indeed exist in which most thermonuclear reactions take place at a given temperature, but that this energy window can differ significantly from the commonly used Gamow peak. We expect that these findings are especially important for thermonuclear reactions in the advanced burning stages of massive stars and in explosive stellar environments.

Figure 1

Fractional contributions of narrow resonances to the total reaction rate versus resonance energy for (a) ${}^{27}\mathrm{Al}$(p,γ)${}^{28}\mathrm{Si}$ at $T=3.5$ GK and (b) ${}^{24}\mathrm{Mg}$($\alpha ,\gamma$)${}^{28}\mathrm{Si}$ at $T=2.5$ GK. The Gamow peak is shown as dotted line. Resonance energies and strengths are adopted from Ref. [3].

Figure 2

Gamow peak (region between black lines) and effective thermonuclear energy range (region between red lines) versus stellar temperature for the ${}^{35}\mathrm{Cl}$(p,γ)${}^{36}\mathrm{Ar}$ reaction. Resonance energies and strengths are adopted from Ref. [3].

Figure 3

Gamow peak (black bars) and effective thermonuclear energy range (red bars) versus target mass number for the proton-capture reactions on ${}^{21,22}\mathrm{Ne}$, ${}^{23}\mathrm{Na}$, ${}^{25,26}\mathrm{Mg}$, ${}^{27}\mathrm{Al}$, ${}^{29,30}\mathrm{Si}$, ${}^{31}\mathrm{P}$ and ${}^{35}\mathrm{Cl}$ at two different temperatures: $T=0.6$ GK (top panel) and $T=2.5$ GK (bottom panel). Resonance energies and strengths are adopted from Ref. [3].