Charged-particle thermonuclear reactions

An overview is presented on the subject of the theory of charged-particle thermonuclear reactions in the context of astrophysical nuclear reactions and in particular those processes occurring in stellar interiors. The authors discuss the energy dependence of charged-particle reaction cross sections for low energies which are governed by the Coulomb penetration factor and the de Broglie wavelength. Therefore it is common to transform the cross section into the so called astrophysical S-factor: S(E)= sigma (E).E.exp(2 pi eta ), where eta is the Sommerfeld parameter ( eta =Z₁Z₂e²/h(cross)v). The low energy tail of broad resonances or non-resonant processes can be studied experimentally down to a limiting energy E_l. However, the most interesting region for astrophysics is the vicinity of the Gamow peak, which arises at the overlap region of the Maxwell-Boltzmann distribution of the stellar plasma and the exponentially decreasing cross section. It is this region where the reaction rate is needed, but it is also the region which is hardly accessible by experiments. Therefore, the non-resonant contributions have to be extrapolated and the properties of the subthreshold resonances as well as other resonances located near the Gamow energy have to be investigated by other means. Possible techniques to approach reliable reaction rates are sketched. The most critical reactions for the solar v-problem are also discussed.