Progress of Theoretical Physics Supplement No. 154, 2004 317 Influence of Tunneling on Electron Screening in Low Energy Nuclear Reactions Sachie Kimura, 1 Noboru Takigawa, 2 Masanori Abe, 3 D. M. Brink 4 and A. Bonasera 1 1 Laboratorio Nazionale del Sud, INFN, via Santa Sofia, 62, 95123 Catania, Italy 2 Department of Physics, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan 3 Department of Basic Science, Ishinomaki Senshu University, Ishinomaki 986-8580, Japan 4 Theoretical Physics, University of Oxford,1 Keble Road, Oxford OX1 3NP, UK Using a semiclassical mean field theory, we show that the screening potential exhibits a characteristic radial variation in the tunneling region in sharp contrast to the assumption of the constant shift in all previous works. Also, we show that the explicit treatment of the tunneling region gives a larger screening energy than that in the conventional approach, which studies the time evolution only in the classical region and estimates the screening energy from the screening potential at the external classical turning point. This modification becomes important if the electronic state is not a single adiabatic state at the external turning point. Furthermore, as an alternative solution of the screening problem, we give the estimation for the effect of extra electrons which are caught into the ground state of the projectile by using constraint molecular dynamics. §1. Introduction Nuclear reaction rates at astrophysical energies are interesting quantities for their own sake and also in connection with nucleosynthesis in stars. The bare reaction rates are modified in stars by the screening effects of free and bound electrons. The knowledge of the bare nuclear reaction rates at low energies is important not only for the understanding of various astrophysical nuclear problems, but also for assessing the effects of host material in low energy nuclear fusion reactions in matter. Rolfs and his colleagues have reported that the experimental cross sections of the 3 He(d, p) 4 He and of D( 3 He, p) 4 He reactions with gas target show an increasing enhancement with decreasing bombarding energy with respect to the values obtained by extrapolating from the data at high energies. 1) Since then similar enhancement has been reported for many systems with not only gas targets, but also with metal targets such as the 6 Li(p, α) 3 He reaction. These observations have motivated many theoretical as well as experimental studies. Many of them attempted to attribute the enhancement of the reaction rate to the screening effects by bound target electrons. A simple approach is to assume that the screening effects can be well represented by a constant, i.e. radially independent, decrease of the barrier height in the tunneling region. This decrease is named the screening energy. It is determined by making a fit to the data. A puzzle is that the screening energy obtained by this procedure exceeds the value in the so called adiabatic limit, which is given by the difference of the binding energies in the united Downloaded from https://academic.oup.com/ptps/article-abstract/doi/10.1143/PTPS.154.317/1845754 by guest on 26 May 2020