Trojan horse method as surrogate indirect approach to study resonant reactions in nuclear astrophysics

Assessing the foundation of the Trojan Horse Method

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.

晕核诱导反应中的连续谱效应与特洛伊木马机制：对重同位素合成的意义

Continuum Effects and the Trojan Horse Mechanism in Halo Nuclei-Induced Reactions: Implications for Heavy Isotope Synthesis

本研究通过IAV模型与CDCC方法分析晕核诱导的NEB反应，发现连续谱效应可忽略，并验证了THM利用弱束缚晕核显著增强亚垒聚变，为合成重同位素提供新途径。

Theory of the Trojan-Horse Method

The Trojan-Horse method is an indirect approach to determine the energy dependence of S factors of astrophysically relevant two-body reactions. This is accomplished by studying closely related three-body reactions under quasi-free scattering conditions. The basic theory of the Trojan-Horse method is developed starting from a post-form distorted wave Born approximation of the T-matrix element. In the surface approximation the cross section of the three-body reaction can be related to the S-matrix elements of the two-body reaction. The essential feature of the Trojan-Horse method is the effectiv…

Two-step nuclear reactions: The Surrogate Method, the Trojan Horse Method and their common foundations

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…

Indirect techniques in nuclear astrophysics. Asymptotic Normalization Coefficient and Trojan Horse

Owing to the presence of the Coulomb barrier at astrophysically relevant kinetic energies it is very difficult, or sometimes impossible, to measure astrophysical reaction rates in the laboratory. That is why different indirect techniques are being used along with direct measurements. Here we address two important indirect techniques, the asymptotic normalization coefficient (ANC) and the Trojan Horse (TH) methods. We discuss the application of the ANC technique for calculation of the astrophysical processes in the presence of subthreshold bound states, in particular, two different mechanisms a…

Status of deep subbarrier $\mathbf{{}^{12}{\rm C}+{}^{12}{\rm C}}$ fusion and advancing the Trojan horse method

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.

Big Bang nucleosynthesis revisited via Trojan Horse Method measurements

Nuclear reaction rates are among the most important input for understanding the primordial nucleosynthesis and therefore for a quantitative description of the early Universe. An up-to-date compilation of direct cross sections of 2H(d,p)3H, 2H(d,n)3He, 7Li(p,alpha)4He and 3He(d,p)4He reactions is given. These are among the most uncertain cross sections used and input for Big Bang nucleosynthesis calculations. Their measurements through the Trojan Horse Method (THM) are also reviewed and compared with direct data. The reaction rates and the corresponding recommended errors in this work were used…

一种自洽的能谱框架用于包容非弹性破裂，Trojan Horse方法作为亚库仑共振极限

Self-consistent spectral framework for inclusive nonelastic breakup: The Trojan-horse method as its sub-Coulomb resonant limit

本文提出了一种自洽的能谱框架，用于分析包容非弹性破裂，其中Trojan Horse方法作为亚库仑共振极限。该框架引入了对吸收参与者-靶光学势的对角孤立极谱假设，并通过R矩阵表格化和模型依赖的连续解耦诊断来验证其有效性。

通过特洛伊马方法优化大爆炸核合成结果

Big Bang Nucleosynthesis results refined via the Trojan Horse Method

通过特洛伊马方法优化大爆炸核合成结果，改进了$^7$Li和氘丰度与观测数据的一致性。

Subthreshold resonances and resonances in the $R$-matrix method for binary reactions and in the Trojan Horse method

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…

12C+12C 聚变反应的平面波木马分析失效：库仑畸变的关键作用

Breakdown of the Plane-Wave Trojan Horse Analysis of the $^{12}\mathrm{C}+{}^{12}\mathrm{C}$ Fusion Reaction: Critical Role of Coulomb Distortions

本研究指出对12C+12C聚变反应的THM测量数据进行平面波分析失效，强调初末态库仑畸变的关键作用，表明平面波近似会严重扭曲聚变截面能量依赖，提取的天体物理因子不可靠。

Indirect methods in nuclear astrophysics

We discuss recent developments in indirect methods used in nuclear astrophysics to determine the capture cross sections and subsequent rates of various stellar burning processes, when it is difficult to perform the corresponding direct measurements. We discuss in brief, the basic concepts of Asymptotic Normalization Coefficients, the Trojan Horse Method, the Coulomb Dissociation Method, (d,p), and charge-exchange reactions.

High-energy direct reactions with exotic nuclei and low-energy nuclear astrophysics

Indirect methods in nuclear astrophysics are discussed. Recent work on Coulomb dissociation and an effective-range theory of low-lying electromagnetic strength of halo nuclei is presented. Coulomb dissociation of a halo nucleus bound by a zero-range potential is proposed as a homework problem (for further references see G. Baur and S. Typel, nucl-th/0504068). It is pointed out that the Trojan-Horse method (G. Baur, F. Rösel, D. Trautmann and R. Shyam, Phys. Rep. 111 (1984) 333) is a suitable tool to investigate subthreshold resonances.

Direct Reactions with Exotic Nuclei, Nuclear Structure and Astrophysics

Intermediate energy Coulomb excitation and dissociation is a useful tool for nuclear structure and astrophysics studies. Low-lying strength in nuclei far from stability was discovered by this method. The effective range theory for low-lying strength in one-neutron halo nuclei is summarized and extended to two-neutron halo nuclei. This is of special interest in view of recent rather accurate experimental results on the low-lying electric dipole strength in $^{11}$Li. Another indirect approach to nuclear astrophysics is the Trojan horse method. It is pointed out that it is a suitable tool to inv…