Microscopic study of the low-energy3He(3He, 2p)4He and3H(3H, 2n)4He fusion cross sections

Abstract

We have calculated the 3He(3He, 2p)4Ue and 3H(3H, 2n)eHe reaction cross sections at low energies within the microscopic multichannel resonating group method. For both reactions, we find good agreement with experiment.For the 3H(3H, 2n)4He reaction, our calculated energy dependence reproduces that of each individual low-energy experimental data set, except for a normalization constant. Using this fact, we derive at a low-energy 3H(3H, 2n)4He rate by taking the averaged mean of these fits. 25.10. +s; 25.55.e; 25.55.Ek The 3He(3He, 2p)4He reaction is an important part within the network of hydrogen burning in stars being the dominant source for the production of 4He [1 ]. This reaction as well as its mirror reaction 3H(3H, 2n)4He are believed to have also played a role within the nucleosynthesis in the early epoch of our universe [2,3]. Additionally, the fusion of two tritons via the 3H(3H, 2n)gHe reaction is one of the key nuclear reactions studied in muon-catalyzed fusion [4]. PACS:Various experimental groups have studied the 3He(3He, 2p)4He reaction at low energy [5,6]. As these measurements basically agree with each other, it is generally believed that its reaction cross section at astrophysically important energies is rather well known. However, to derive the cross section at these astrophysically most effective energies (E~20 keV for temperatures at the solar core), one has to extrapolate the measured cross section down in energy [1]. Due to the lack of reliable theoretical guidelines, this extrapolation has been performed simply using a quadratic polynomial [6]. There have been several experimental attempts to measure the low-energy 3H(3H, 2n)4He cross section. However, it has been pointed out [7] that some of these measurements might be subject to large systematic errors. The 3H(3H, 2n)4He data have been parametrized by Hale et al. within an R-matrix formulation [8] which at low energies is dominated by the Los Alamos data [9] having by far the smallest experimental uncertainties.To our knowledge there exists no theoretical study which calculates the absolute cross sections for either of the two reactions at low energies. In this paper we want to report about the first microscopic studies of the lowenergy 3He(3He, 2p)4He and 3H(3H, 2n)4He reactions performed within the framework of the coupled-channel resonating group method (RGM).A rigorous study of the two reactions requires the consideration of a 3-cluster scattering state in the outgoing channel. However, in our approach we will follow Siinkel [10] who viewed the reaction as a two-step process: After formation of the compound nucleus, the system will firstly decay into an e particle and a 2-nucleon cluster. The latter, which is energetically unbound, will then finally decay into two nucleons; this, however, is expected to occur outside the range of the nuclear forces.We will in the following neglect possible D-state admixtures in the cluster wave functions. Then, the two 3He(3H) clusters may be coupled to total spins S = 0 and 1. To fulfill the requir...

Experimental Evidence of a Variant Neutron Spectrum from the T(t,2n)α Reaction at Center-of-Mass Energies in the Range of 16–50 keV

“…range and that any resonance contributions arise from very broad states. This interpretation, which is also consistent with theoretical studies using a microscopic model [12] and R-matrix methods [13], would mean that the shape of the reaction product energy spectra would be independent of E c.m. .…”

Analysis of non-Maxwellian fusion reaction rates with electron screening

“…Regarding this particular reaction, the possible presence of a very low energy resonance is still an open problem. Recent results [5][6][7] strongly limit the effects that this resonance could have: therefore, in the following, the 3He(3He, 2p)4He reaction will be assumed non-resonant and its cross section will be approximated as [ 16]:…”

“…The first reaction is important in the design of fusion reactors [3] and its cross section shows a resonance at low energy. The second is of interest in astrophysics (solar model, neutrino problem, particle physics) and its cross section doesn't show resonances above 18 keV [4]; after the experimental work by Krauss et al [5] and the theoretical analysis by Typel et al [6] and by Winkler et al [7], it seems very unplausible the presence of a resonance below 18 keV as well. In any case future experiments have been planned at Gran Sasso Laboratory to explore this energy region [8].…”

Comment on ‘‘Shadow model for sub-barrier fusion applied to light systems’’

“…Rather than being based on the correct physical picture of barrier penetration, the energy dependence of the low-energy cross section in this model is simply assumed (Eqs. (3)(4)(5) and (8,9) in Ref. [1]).…”