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Theoretical prediction of surface stellar abundances of light elements–lithium, beryllium, and boron–represents one of the most interesting open problems in astrophysics. As well known, several measurements of 7Li abundances in stellar atmospheres point out a disagreement between predictions and observations in different stellar evolutionary phases, rising doubts about the capability of present stellar models to precisely reproduce stellar envelope characteristics. The problem takes different aspects in the various evolutionary phases; the present analysis is restricted to protostellar and pre-Main Sequence phases. Light elements are burned at relatively low temperatures (T from ≈2 to ≈5 million degrees) and thus in the early evolutionary stages of a star they are gradually destroyed at different depths of stellar interior mainly by (p, α) burning reactions, in dependence on the stellar mass. Their surface abundances are strongly influenced by the nuclear cross sections, as well as by the extension toward the stellar interior of the convective envelope and by the temperature at its bottom, which depend on the characteristics of the star (mass and chemical composition) as well as on the energy transport in the convective stellar envelope. In recent years, a great effort has been made to improve the precision of light element burning cross sections. However, theoretical predictions surface light element abundance are challenging because they are also influenced by the uncertainties in the input physics adopted in the calculations as well as the efficiency of several standard and non-standard physical processes active in young stars (i.e. diffusion, radiative levitation, magnetic fields, rotation). Moreover, it is still not completely clear how much the previous protostellar evolution affects the pre-Main Sequence characteristics and thus the light element depletion. This paper presents the state-of-the-art of theoretical predictions for protostars and pre-Main Sequence stars and their light element surface abundances, discussing the role of (p, α) nuclear reaction rates and other input physics on the stellar evolution and on the temporal evolution of the predicted surface abundances.

Light elements offer a unique opportunity for studying several astrophysical scenarios from Big Bang Nucleosynthesis to stellar physics. Understanding the stellar abundances of light elements is key to obtaining information on internal stellar structures and mixing phenomena in different evolutionary phases, such as the pre-main-sequence, main-sequence or red-giant branch. In such a case, light elements, i.e., lithium, beryllium and boron, are usually burnt at temperatures of the order of 2–5 × 106 K. Consequently, the astrophysical S(E)-factor and the reaction rate of the nuclear reactions responsible for the burning of such elements must be measured and evaluated at ultra-low energies (between 0 and 10 keV). The Trojan Horse Method (THM) is an experimental technique that allows us to perform this kind of measurements avoiding uncertainties due to the extrapolation and electron screening effects on direct data. A long Trojan Horse Method research program has been devoted to the measurement of light element burning cross sections at astrophysical energies. In addition, dedicated direct measurements have been performed using both in-beam spectroscopy and the activation technique. In this review we will report the details of these experimental measurements and the results in terms of S(E)-factor, reaction rate and electron screening potential. A comparison between astrophysical reaction rates evaluated here and the literature will also be given.