The study of d(d,p)t reaction is very important for the nucleosynthesis in both standard Big Bang and stellar evolution, as well as for the future fusion reactors planning of energy production. The d(d,p)t bare nucleus astrophysical S(E) factor has been measured indirectly at energies from about 400 keV down to several keV by means of the Trojan horse method applied to the quasi-free process $\rm {}^2H({}^6Li,pt){}^4He$ induced at a lithium beam energy of 9.5 MeV, which is closer to the zero quasi-free energy point. An accurate analysis leads to the determination of the $\rm S_{bare}(0)=56.7 \pm 2.0 keV \cdot b$ and of the corresponding electron screening potential $\rm U_e = 13.2 \pm 4.3 eV$. In addition, this work gives an updated test for the Trojan horse nucleus invariance comparing with previous indirect investigations using $\rm {}^3He=(d+p)$ breakup.
To explore a possible indirect method for $\rm ^8Be$ induced astrophysical reactions, the $\rm ^9Be=({}^8Be+\it n)$ cluster structure was studied via the Trojan Horse Method. It is the first time to study a super short life nucleus $\rm ^8Be$ via the Trojan Horse Method, and it is the first time to make a valid test for $l=1$ Trojan-horse nucleus. The $\rm ^9Be$ nucleus is assumed to have a ($\rm {}^8Be+\it n$) cluster structure and used as the Trojan-horse nucleus. The $\rm ^8Be$ nucleus acts as a participant, while the neutron is a spectator to the virtual $\rm ^8Be +{\it d}\rightarrow α+ {}…
The $\mathrm{^2H}(d,p)\mathrm{^3H}$ bare nucleus astrophysical S(E) factor has been measured indirectly at energies from about 500 keV down to several keV by means of the Trojan-horse method applied to the quasi-free process $\mathrm{^2H({}^6Li},pt)\mathrm{^4He}$ induced at the lithium beam energy of 11 and 9.5 MeV, which makes the virtual binary process incident energy $\mathrm {E}_{dd}^{qf}$ go much closer to the zero-quasi-free-energy point than that in the previous similar experiment. The obtained results are compared with direct data as well as with previous indirect investigation of the …
We discuss the foundation of the Trojan Horse Method (THM) within the Inclusive Non-Elastic Breakup (INEB) theory. We demonstrate that the direct part of the INEB cross section, which is of two-step character, becomes, in the DWBA limit of the three-body theory with appropriate approximations and redefinitions, similar in structure to the one-step THM cross section. We also discuss the connection of the THM to the Surrogate Method (SM), which is a genuine two-step process.
In this Letter I argue that the Surrogate Method, used to extract the fast neutron capture cross section on actinide target nuclei, which has important practical application for the next generation of breeder reactors, and the Trojan Horse Method employed to extract reactions of importance to nuclear astrophysics, have a common foundation, the Inclusive Non-Elastic Breakup (INEB)Theory. Whereas the Surrogate Method relies on the premise that the extracted neutron cross section in a (d,p) reaction is predominantly a compound nucleus one, the Trojan Horse Method, assumes a predominantly direct p…
Measurement of nuclear cross sections at astrophysical energies involving unstable species is one of the most challenging tasks in experimental nuclear physics. The use of indirect methods is often unavoidable in this scenario. In this paper the Trojan Horse Method is applied for the first time to a radioactive ion beam induced reaction studying the $^{18}$F($p,α$)$^{15}$O process at low energies relevant to astrophysics via the three body reaction $^{2}$H($^{18}$F,$α^{15}$O)n. The knowledge of the $^{18}$F($p, α$)$^{15}$O reaction rate is crucial to understand the nova explosion phenomena. Th…
In this paper, I will update the current status of the carbon-carbon fusion research taking into account that after the latest analysis [Beck {\it et al.} Eur. Phys. J. A {\bf 56}, 97 (2020), Letter to the Editor] new important experimental and theoretical results had been published and will discuss how to advance new THM measurements to extract the low-energy astrophysical $S$-factors.
Indirect Measurement of the $\rm S^*(E)$ Factor for $\rm {}^{12}C({}^{12}C,\mathit{p}){}^{23}Na$ at Gamow Energies via the Trojan Horse Method with Near-0 degree Spectator Detection
Institute of Radiation Technology, Beijing Academy of Science and Technology（北京应用技术研究院辐射技术研究所）
Big Bang Nucleosynthesis results refined via the Trojan Horse Method
Laboratori Nazionali del Sud, INFN（南方国家实验室，意大利核物理研究所）；Dipartimento di Fisica e Astronomia ‘Ettore Majorana’, Universitá di Catania（卡塔尼亚大学埃托雷·马约拉纳物理与天文学系）；Centro Siciliano di Fisica Nucleare e Struttura della Materia (CSFNSM)（西西里核物理与物质结构中心）；Sezione di Napoli, INFN（意大利核物理研究所那不勒斯分部）；Dipartimento di Fisica e Astronomia ’Galileo Galilei’,Universitá degli Studi di Padova（帕多瓦大学伽利略·伽利莱物理与天文学系）；Sezione di Padova, INFN（意大利核物理研究所帕多瓦分部）
In this paper we discuss the $R$-matrix approach to treat the subthreshold resonances for the single-level and one channel, and for the single-level and two channel cases. In particular, the expression relating the ANC with the observable reduced width, when the subthreshold bound state is the only channel or coupled with an open channel, which is a resonance, is formulated. Since the ANC plays a very important role in nuclear astrophysics, these relations significantly enhance the power of the derived equations. We present the relationship between the resonance width and the ANC for the gener…
The 27Al(p,a)24Mg reaction, which drives the destruction of 27Al and the production of 24Mg in stellar hydrogen burning, has been investigated via the Trojan Horse Method (THM) by measuring the 2H(27Al,a24Mg)n three-body reaction. The experiment covered a broad energy range (-0.5 MeV < E_cm < 1.5 MeV), aiming to investigate those of interest for astrophysics.The results confirm the THM as a valuable technique for the experimental study of fusion reactions at very low energies and suggest the presence of a rich pattern of resonances in the energy region close to the Gamow window of stellar hydr…
$\rm S^*(E)$ measurement of the $\rm {}^{12}C({}^{12}C,α){}^{20}Ne$ reaction at astrophysical energies via the Trojan horse method with $\rm ^{16}O$ quasi-free breakup
Institute of Radiation Technology, Beijing Academy of Science and Technology（北京辐射技术研究所，北京 Akademija 科学技术研究院）；Department of Nuclear Physics, China Institute of Atomic Energy（原子能科学研究院核物理系）；School of Physics and Materials Science, Anhui University（安徽大学物理与材料科学学院）
Carbon and oxygen burning reactions, in particular, $^{12}$C+$^{12}$C fusion, are important for the understanding and interpretation of the late phases of stellar evolution as well as the ignition and nucleosynthesis in cataclysmic binary systems such as type Ia supernovae and x-ray superbursts. A new measurement of this reaction has been performed at the University of Notre Dame using particle-$γ$ coincidence techniques with SAND (a silicon detector array) at the high-intensity 5U Pelletron accelerator. New results for $^{12}$C+$^{12}$C fusion at low energies relevant to nuclear astrophysics …
Since the discovery of molecular resonances in $^{12}$C+$^{12}$C in the early sixties a great deal of research work has been undertaken to study $α$-clustering and resonant effects of the fusion process at sub-Coulomb barrier energies. The modified astrophysical $S^{*}$ factors of $^{12}$C+$^{12}$C fusion have been extracted from direct fusion measurements at deep sub-barrier energies near the Gamow window. They were also obtained by the indirect Trojan horse method (THM). A comparison of direct measurements and the THM, which elucidates problems in the analysis of the THM, is discussed in thi…
The $^{10}$B(p,$α$)$^{7}$Be reaction is of great interest since it has many applications in different fields of research such as nuclear astrophysics, nuclear physics, and models of new reactors for clean energy generation. This reaction has been studied at the AN2000 accelerator of the INFN National Laboratories of Legnaro (LNL). The total cross section has been measured in a wide energy range (250 $-$ 1182 keV) by using the activation method. The decays of the $^7$Be nuclei produced by the reaction were measured at the low counting facility of LNL by using two fully shielded high-purity germ…
Background: Accurate knowledge of the $^{13}$C($α$,$n$)$^{16}$O reaction cross section is important for the understanding of the s-process in AGB stars, since it is considered to be the main source of neutrons. The sub-threshold 1/2$^+$ state at excitation energy of 6.356 MeV in $^{17}$O has a strong influence on the reaction cross section at energies relevant for astrophysics. Several experiments have been performed to determine the contribution of this state to the $^{13}$C($α,n)^{16}$O reaction rate. Nevertheless, significant discrepancies between different measurements remain. Purpose: The…
Type Ia supernovae (SNe Ia) are thought to be thermonuclear explosion of white dwarfs (WDs). Their progenitors are not well understood. One popular scenario is the double-degenerate (DD) scenario, which attributes SNe Ia to WD-WD binary mergers. The fates of the WD mergers depend on the rate of $^{12}$C+$^{12}$C reaction. Recently, the $^{12}$C+$^{12}$C cross sections have been measured and the analysis of the data using the Trojan Horse Method suggested that the astrophysical reaction rate is larger than conventional rates at astrophysical temperatures due to possible resonances. The resonanc…
The $^{13}{\rm C}(α,n)^{16}{\rm O}$ reaction is considered to be the main neutron source responsible for the production of heavy nuclides (from ${\rm Sr}$ to ${\rm Bi}$) through slow $n$-capture nucleosynthesis ($s$-process) at low temperatures during the asymptotic giant branch (AGB) phase of low mass stars ($\lesssim 3-4\;{\rm M}_{\odot}$, or LMSs). In recent years, several direct and indirect measurements have been carried out to determine the cross section at the energies of astrophysical interest (around $190\pm40\;{\rm keV}$). However, they yield inconsistent results causing a highly unc…
Multi-Model Analysis of the Astrophysical $S(E)$ Factor for the $^{9}\mathrm{Be}(p,α)^{6}\mathrm{Li}$ Reaction and Its Impact on Astrophysical Reaction Rates
School of Physics, Anhui University（安徽大学物理学院）；School of Physics, Southern University of Science and Technology（南方科技大学物理学院）；College of Physics and Optoelectronic Engineering, Shenzhen University（深圳大学物理与光电工程学院）；Institute of Radiation Technology, Beijing Academy of Science and Technology（北京市科学技术研究院辐射技术研究所）；Department of Nuclear Physics, China Institute of Atomic Energy（中国原子能科学研究院核物理系）
Probing the $^{12}$C+$^{12}$C fusion reaction via zero-degree spectator measurement in the $^{12}$C($^{14}$N,$αd$)$^{20}$Ne quasi-free reaction
School of Physics, Anhui University（安徽大学物理学院）；Institute of Radiation Technology, Beijing Academy of Science and Technology（北京市科学技术研究院辐射技术研究所）；Department of Nuclear Physics, China Institute of Atomic Energy（中国原子能科学研究院核物理系）
