Abstract
The {}^{5}He({}^{3}He,{}^{4}He){}^{4}He reaction involving the unstable {}^{5}He nucleus is a possible process in primordial nucleosynthesis to convert {}^{3}He into {}^{4}He in a neutron transfer reaction. Since experimental data for the reaction cross section are not available, a theoretical prediction is needed to estimate the relevance of this process in comparison to other reactions, e.g., {}^{3}He({}^{2}H,p){}^{4}He or {}^{3}H({}^{2}H,n){}^{4}He. In this work the cross section and the Maxwellian-averaged transition rate of the {}^{5}He({}^{3}He,{}^{4}He){}^{4}He reaction are calculated using a post-form distorted-wave Born approximation in a simple cluster model. For that purpose the reaction is treated as a genuine process with three particles, text{ n }+{}^{4}text{ He }+{}^{3}text{ He }, in the entrance channel proceeding through the 3/2^{-} resonance in the n-{}^{4}He scattering continuum.
Highlights
The study of nuclear reactions was one of the most prominent topics in the work of Mahir S
In a scattering reaction with two particles in the entrance channel, the direction of the initial momentum is usually fixed and an integration over the scattering angles in the exit channel has to be performed to arrive at the total cross section
Since there are no experimental data available for the cross section of this reaction, a theoretical estimate is necessary to judge its importance in comparison to other nuclear reactions that synthesize 4He in astrophysical environments
Summary
The study of nuclear reactions was one of the most prominent topics in the work of Mahir S. The most prominent example is probably the triple-α reaction that proceeds through a sharp 0+ state at 7.654 MeV excitation energy in 12C, the so-called Hoyle state, just above the 3α breakup threshold [9,10,11,12] It is essential for the nucleosynthesis of carbon in read giant stars that burn 4He. For recent theoretical works see, e.g., [13,14] and references therein. (DWBA) is used to find the relevant T-matrix element that enters in the calculation of the transition rate of this neutrontransfer reaction This approach shares some similarities with the reaction theory applied in the Trojan-Horse method where transfer reactions to the continuum are employed to extract cross sections of a certain sub-process in an indirect approach [21,22,23,24]. The connection of transition rates and cross sections with the T-matrix elements describing the process is established for general cases in Sect.
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