Influence of tunneling on electron screening in low energy nuclear reactions in laboratories

Abstract

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 either by pre-tunneling transitions of the electronic state or by the symmetry of the system even if there is no essential change with the electronic state in the tunneling region.Nuclear reaction rates at low energies play the key role in energy generation in stars and the primordial and stellar nucleosynthesis. 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. This is currently a subject of great interest in nuclear physics. 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]. They also claimed that the enhancement is larger in the 3 He(d,p) 4 He reaction. 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 atom and in the target atom and is theoretically thought to provide the maximum screening energy, for all systems so far studied experimentally [2] (see ref.[3] for a recent modification). For 7 Li(p,α)α reaction, in addition to the direct measurement, an indirect measurement of the cross section using the Trojan horse method has recently been made [4]. The comparison between the two methods indicates again that the screening energy in the direct method exceeds the a...

Chaos Driven Fusion Enhancement Factor at Astrophysical Energies

“…We notice in passing that event A is a case where cylindrically symmetry is approximately satisfied, because the electron motion is practically on the xy−plane. This case gives a U e =19.5eV closest to the adiabatic limit and to the TDHF result [6,7].…”

“…The comparison between newly obtained bare cross sections, i.e., astrophysical S-factors, and the cross sections by the direct measurements gives a variety of values for the screening potential. There are already some theoretical studies performed using the time-dependent Hartree-Fock(TDHF) scheme [6,7].In this letter we examine the subject within the constrained molecular dynamics (CoMD) model [8], even in the very low incident energy region not reached experimentally yet. At such very low energies fluctuations are anticipated to play a substantial role.…”

Influence of chaos on the fusion enhancement by electron screening

“…where U (g) e = 40.7 eV and U (u) e = 0.0 eV [11,10]. If we take into account the electron capture of the projectile, i.e., in the case of D+D, the enhancement factor in the adiabatic limit is…”

“…These values are often smaller than the sudden limit or larger than the adiabatic limit. Theoretical studies performed using the time-dependent Hartree-Fock (TDHF) scheme [10,11] suggest that the screening potential is between the sudden and the adiabatic limits.…”

FUSION03, Concluding Remarks

“…44) Any enhancement of the probability due to the break-up of the nuclei is also too small. 45) In this conference Kimura showed that the screening potential may exhibit a radial variation in the tunneling region, 46) which may increase the screening energy to beyond the adiabatic limit. Unfortunately this is not a satisfactory solution since this result depend on the excited state components.…”